Flowing with Time: a New Approach to Nonlinear Cosmological Perturbations
Pietroni, Massimo
2008-01-01
Nonlinear effects are crucial in order to compute the cosmological matter power spectrum to the accuracy required by future generation surveys. Here, a new approach is presented, in which the power spectrum and the bispectrum are obtained -at any redshift and for any momentum scale- by integrating a coupled system of differential equations. The solution of the equations corresponds, in perturbation theory, to the summation of an infinite class of corrections. Compared to other resummation frameworks, the scheme discussed here is particularly suited to cosmologies other than LambdaCDM, such as those based on modifications of gravity and those containing massive neutrinos. As a first application, we compute the Baryonic Acoustic Oscillation feature of the power spectrum, and compare the results with perturbation theory, the halo model, and N-body simulations. The density-velocity and velocity-velocity power spectra are also computed, showing that they are much less contaminated by nonlinearities than the densit...
Non-Gaussianity vs. non-linearity of cosmological perturbations
Verde, L
2001-01-01
Following the discovery of the CMB, the hot big-bang model has become the standard cosmological model. In this theory, small primordial fluctuations are subsequently amplified by gravity to form the large-scale structure seen today. Different theories for unified models of particle physics, lead to different predictions for the statistical properties of the primordial fluctuations, that can be divided in two classes: gaussian and non-gaussian. Convincing evidence against or for gaussian initial conditions would rule out many scenarios and point us towards a physical theory for the origin of structures. The statistical distribution of cosmological perturbations, as we observe them, can deviate from the gaussian distribution in several different ways. Even if perturbations start off gaussian, non-linear gravitational evolution can introduce non-gaussian features. Additionally, our knowledge of the Universe comes principally from the study of luminous material such as galaxies, but these might not be faithful tr...
On the non-linear scale of cosmological perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Blas, Diego [Theory Division, CERN, 1211 Geneva (Switzerland); Garny, Mathias; Konstandin, Thomas, E-mail: diego.blas@cern.ch, E-mail: mathias.garny@desy.de, E-mail: Thomas.Konstandin@desy.de [DESY, Notkestr. 85, 22607 Hamburg (Germany)
2013-09-01
We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections at any order in perturbation theory. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.
On the non-linear scale of cosmological perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Blas, Diego [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Garny, Mathias; Konstandin, Thomas [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2013-04-15
We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.
Fully non-linear cosmological perturbations of multicomponent fluid and field systems
Hwang, Jai-chan; Noh, Hyerim; Park, Chan-Gyung
2016-09-01
We present fully non-linear and exact cosmological perturbation equations in the presence of multiple components of fluids and minimally coupled scalar fields. We ignore the tensor-type perturbation. The equations are presented without taking the temporal gauge condition in the Friedmann background with general curvature and the cosmological constant. We include the anisotropic stress. Even in the absence of anisotropic stress of individual component, the multiple component nature introduces the anisotropic stress in the collective fluid quantities. We prove the Newtonian limit of multiple fluids in the zero-shear gauge and the uniform-expansion gauge conditions, present the Newtonian hydrodynamic equations in the presence of general relativistic pressure in the zero-shear gauge, and present the fully non-linear equations and the third-order perturbation equations of the non-relativistic pressure fluids in the CDM-comoving gauge.
Cosmological perturbations of self-accelerating universe in nonlinear massive gravity
Gumrukcuoglu, A Emir; Mukohyama, Shinji
2011-01-01
We study cosmological perturbations of self-accelerating universe solutions in the recently proposed nonlinear theory of massive gravity, with general matter content. While the broken diffeomorphism invariance implies that there generically are 2 tensor, 2 vector and 2 scalar degrees of freedom in the gravity sector, we find that the scalar and vector degrees have vanishing kinetic terms and nonzero mass terms. Depending on their nonlinear behavior, this indicates either nondynamical nature of these degrees or strong couplings. Assuming the former, we integrate out the 2 vector and 2 scalar degrees of freedom. We then find that in the scalar and vector sectors, gauge-invariant variables constructed from metric and matter perturbations have exactly the same quadratic action as in general relativity. The difference from general relativity arises only in the tensor sector, where the graviton mass modifies the dispersion relation of gravitational waves, with a time-dependent effective mass. This may lead to modif...
Multi-field inflation and cosmological perturbations
Gong, Jinn-Ouk
2016-01-01
We provide a concise review on multi-field inflation and cosmological perturbations. We discuss convenient and physically meaningful bases in terms of which perturbations can be systematically studied. We give formal accounts on the gauge fixing conditions and present the perturbation action in two gauges. We also briefly review non-linear perturbations.
Cosmological Perturbations in Antigravity
Oltean, Marius
2014-01-01
We compute the evolution of cosmological perturbations in a recently proposed Weyl-symmetric theory of two scalar fields with oppositely-signed conformal couplings to Einstein gravity. It is motivated from the minimal conformal extension of the Standard Model, such that one of these scalar fields is the Higgs while the other is a new particle, the dilaton, introduced to make the Higgs mass conformally symmetric. At the background level, the theory admits novel geodesically-complete cyclic cosmological solutions characterized by a brief period of repulsive gravity, or "antigravity", during each successive transition from a Big Crunch to a Big Bang. We show that despite the necessarily wrong-signed kinetic term of the dilaton in the full action, its cosmological solutions are stable at the perturbative level.
Cosmological perturbations in antigravity
Oltean, Marius; Brandenberger, Robert
2014-10-01
We compute the evolution of cosmological perturbations in a recently proposed Weyl-symmetric theory of two scalar fields with oppositely signed conformal couplings to Einstein gravity. It is motivated from the minimal conformal extension of the standard model, such that one of these scalar fields is the Higgs while the other is a new particle, the dilaton, introduced to make the Higgs mass conformally symmetric. At the background level, the theory admits novel geodesically complete cyclic cosmological solutions characterized by a brief period of repulsive gravity, or "antigravity," during each successive transition from a big crunch to a big bang. For simplicity, we consider scalar perturbations in the absence of anisotropies, with potential set to zero and without any radiation. We show that despite the necessarily wrong-signed kinetic term of the dilaton in the full action, these perturbations are neither ghostlike nor tachyonic in the limit of strongly repulsive gravity. On this basis, we argue—pending a future analysis of vector and tensor perturbations—that, with respect to perturbative stability, the cosmological solutions of this theory are viable.
Frame independent cosmological perturbations
Energy Technology Data Exchange (ETDEWEB)
Prokopec, Tomislav; Weenink, Jan, E-mail: t.prokopec@uu.nl, E-mail: j.g.weenink@uu.nl [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, Leuvenlaan 4, 3585 CE Utrecht (Netherlands)
2013-09-01
We compute the third order gauge invariant action for scalar-graviton interactions in the Jordan frame. We demonstrate that the gauge invariant action for scalar and tensor perturbations on one physical hypersurface only differs from that on another physical hypersurface via terms proportional to the equation of motion and boundary terms, such that the evolution of non-Gaussianity may be called unique. Moreover, we demonstrate that the gauge invariant curvature perturbation and graviton on uniform field hypersurfaces in the Jordan frame are equal to their counterparts in the Einstein frame. These frame independent perturbations are therefore particularly useful in relating results in different frames at the perturbative level. On the other hand, the field perturbation and graviton on uniform curvature hypersurfaces in the Jordan and Einstein frame are non-linearly related, as are their corresponding actions and n-point functions.
Renormalized Cosmological Perturbation Theory
Crocce, M
2006-01-01
We develop a new formalism to study nonlinear evolution in the growth of large-scale structure, by following the dynamics of gravitational clustering as it builds up in time. This approach is conveniently represented by Feynman diagrams constructed in terms of three objects: the initial conditions (e.g. perturbation spectrum), the vertex (describing non-linearities) and the propagator (describing linear evolution). We show that loop corrections to the linear power spectrum organize themselves into two classes of diagrams: one corresponding to mode-coupling effects, the other to a renormalization of the propagator. Resummation of the latter gives rise to a quantity that measures the memory of perturbations to initial conditions as a function of scale. As a result of this, we show that a well-defined (renormalized) perturbation theory follows, in the sense that each term in the remaining mode-coupling series dominates at some characteristic scale and is subdominant otherwise. This is unlike standard perturbatio...
Cosmological perturbations in massive bigravity
Energy Technology Data Exchange (ETDEWEB)
Lagos, Macarena; Ferreira, Pedro G., E-mail: m.lagos13@imperial.ac.uk, E-mail: p.ferreira1@physics.ox.ac.uk [Astrophysics, University of Oxford, DWB, Keble road, Oxford OX1 3RH (United Kingdom)
2014-12-01
We present a comprehensive analysis of classical scalar, vector and tensor cosmological perturbations in ghost-free massive bigravity. In particular, we find the full evolution equations and analytical solutions in a wide range of regimes. We show that there are viable cosmological backgrounds but, as has been found in the literature, these models generally have exponential instabilities in linear perturbation theory. However, it is possible to find stable scalar cosmological perturbations for a very particular choice of parameters. For this stable subclass of models we find that vector and tensor perturbations have growing solutions. We argue that special initial conditions are needed for tensor modes in order to have a viable model.
Applications of Cosmological Perturbation Theory
Christopherson, Adam J
2011-01-01
Cosmological perturbation theory is crucial for our understanding of the universe. The linear theory has been well understood for some time, however developing and applying the theory beyond linear order is currently at the forefront of research in theoretical cosmology. This thesis studies the applications of perturbation theory to cosmology and, specifically, to the early universe. Starting with some background material introducing the well-tested 'standard model' of cosmology, we move on to develop the formalism for perturbation theory up to second order giving evolution equations for all types of scalar, vector and tensor perturbations, both in gauge dependent and gauge invariant form. We then move on to the main result of the thesis, showing that, at second order in perturbation theory, vorticity is sourced by a coupling term quadratic in energy density and entropy perturbations. This source term implies a qualitative difference to linear order. Thus, while at linear order vorticity decays with the expan...
Nonlinear field space cosmology
Mielczarek, Jakub; Trześniewski, Tomasz
2017-08-01
We consider the FRW cosmological model in which the matter content of the Universe (playing the role of an inflaton or quintessence) is given by a novel generalization of the massive scalar field. The latter is a scalar version of the recently introduced nonlinear field space theory, where the physical phase space of a given field is assumed to be compactified at large energies. For our analysis, we choose the simple case of a field with the spherical phase space and endow it with the generalized Hamiltonian analogous to the XXZ Heisenberg model, normally describing a system of spins in condensed matter physics. Subsequently, we study both the homogenous cosmological sector and linear perturbations of such a test field. In the homogenous sector, we find that nonlinearity of the field phase space is becoming relevant for large volumes of the Universe and can lead to a recollapse, and possibly also at very high energies, leading to the phase of a bounce. Quantization of the field is performed in the limit where the nontrivial nature of its phase space can be neglected, while there is a nonvanishing contribution from the Lorentz symmetry breaking term of the Hamiltonian. As a result, in the leading order of the XXZ anisotropy parameter, we find that the inflationary spectral index remains unmodified with respect to the standard case but the total amplitude of perturbations is subject to a correction. The Bunch-Davies vacuum state also becomes appropriately corrected. The proposed new approach is bringing cosmology and condensed matter physics closer together, which may turn out to be beneficial for both disciplines.
Cosmological density perturbations from perturbed couplings
Tsujikawa, S
2003-01-01
The density perturbations generated when the inflaton decay rate is perturbed by a light scalar field $\\chi$ are studied. By explicitly solving the perturbation equations for the system of two scalar fields and radiation, we show that even in low energy-scale inflation nearly scale-invariant spectra of scalar perturbations with an amplitude set by observations are obtained through the conversion of $\\chi$ fluctuations into adiabatic density perturbations. We demonstrate that the spectra depend on the average decay rate of the inflaton & on the inflaton fluctuations. We then apply this new mechanism to string cosmologies & generalized Einstein theories and discuss the conditions under which scale-invariant spectra are possible.
Cosmological perturbations in teleparallel Loop Quantum Cosmology
Haro, Jaime
2013-01-01
Cosmological perturbations in Loop Quantum Cosmology (LQC) could be studied from two totally different ways. The first one, called holonomy corrected LQC, is performed in the Hamiltonian framework, where the Asthekar connection is replaced by a suitable sinus function (holonomy correction), in order to have a well-defined quantum analogue. The alternative approach is based in the fact that isotropic LQC could be also obtained as a particular case of teleparallel $F(T)$ gravity (teleparallel LQC). Then, working in the Lagrangian framework and using the well-know perturbation equations in $F(T)$ gravity, we have obtained, in teleparallel LQC, the equations for scalar and tensor perturbations, and the corresponding Mukhanov-Sasaki equations. For scalar perturbations, our equation only differs from the one obtained by holonomy corrections in the velocity of sound, leading both formulations, essentially to the same scale invariant power spectrum when a matter-dominated universe is considered. However for tensor pe...
Gauge Invariant Cosmological Perturbation Theory
Durrer, R
1993-01-01
After an introduction to the problem of cosmological structure formation, we develop gauge invariant cosmological perturbation theory. We derive the first order perturbation equations of Einstein's equations and energy momentum ``conservation''. Furthermore, the perturbations of Liouville's equation for collisionless particles and Boltzmann's equation for Compton scattering are worked out. We fully discuss the propagation of photons in a perturbed Friedmann universe, calculating the Sachs--Wolfe effect and light deflection. The perturbation equations are extended to accommodate also perturbations induced by seeds. With these general results we discuss some of the main aspects of the texture model for the formation of large scale structure in the Universe (galaxies, clusters, sheets, voids). In this model, perturbations in the dark matter are induced by texture seeds. The gravitational effects of a spherically symmetric collapsing texture on dark matter, baryonic matter and photons are calculated in first orde...
Back Reaction of Cosmological Perturbations
Brandenberger, R H
2000-01-01
The presence of cosmological perturbations affects the background metric and matter configuration in which the perturbations propagate. This effect, studied a long time ago for gravitational waves, also is operational for scalar gravitational fluctuations, inhomogeneities which are believed to be more important in inflationary cosmology. The back-reaction of fluctuations can be described by an effective energy-momentum tensor. The issue of coordinate invariance makes the analysis more complicated for scalar fluctuations than for gravitational waves. We show that the back-reaction of fluctuations can be described in a diffeomorphism-invariant way. In an inflationary cosmology, the back-reaction is dominated by infrared modes. We show that these modes give a contribution to the effective energy-momentum tensor of the form of a negative cosmological constant whose absolute value grows in time. We speculate that this may lead to a self-regulating dynamical relaxation mechanism for the cosmological constant. This ...
Brane World Cosmological Perturbations
Casali, A G; Wang, B; Casali, Adenauer G.; Abdalla, Elcio; Wang, Bin
2004-01-01
We consider a brane world and its gravitational linear perturbations. We present a general solution of the perturbations in the bulk and find the complete perturbed junction conditions for generic brane dynamics. We also prove that (spin 2) gravitational waves in the great majority of cases can only arise in connection with a non-vanishing anisotropic stress. This has far reaching consequences for inflation in the brane world. Moreover, contrary to the case of the radion, perturbations are stable.
Disformal transformation of cosmological perturbations
Directory of Open Access Journals (Sweden)
Masato Minamitsuji
2014-10-01
Full Text Available We investigate the gauge-invariant cosmological perturbations in the gravity and matter frames in the general scalar–tensor theory where two frames are related by the disformal transformation. The gravity and matter frames are the extensions of the Einstein and Jordan frames in the scalar–tensor theory where two frames are related by the conformal transformation, respectively. First, it is shown that the curvature perturbation in the comoving gauge to the scalar field is disformally invariant as well as conformally invariant, which gives the predictions from the cosmological model where the scalar field is responsible both for inflation and cosmological perturbations. Second, in case that the disformally coupled matter sector also contributes to curvature perturbations, we derive the evolution equations of the curvature perturbation in the uniform matter energy density gauge from the energy (nonconservation in the matter sector, which are independent of the choice of the gravity sector. While in the matter frame the curvature perturbation in the uniform matter energy density gauge is conserved on superhorizon scales for the vanishing nonadiabatic pressure, in the gravity frame it is not conserved even if the nonadiabatic pressure vanishes. The formula relating two frames gives the amplitude of the curvature perturbation in the matter frame, once it is evaluated in the gravity frame.
Causal compensated perturbations in cosmology
Energy Technology Data Exchange (ETDEWEB)
Veeraraghavan, S.; Stebbins, A. (Harvard-Smithsonian Center for Astrophysics, Cambridge, MA (USA) California Univ., Berkeley (USA) Canadian Institute for Theoretical Astrophysics, Toronto (Canada))
1990-12-01
A theoretical framework is developed to calculate linear perturbations in the gravitational and matter fields which arise causally in response to the presence of stiff matter sources in a FRW cosmology. It is shown that, in order to satisfy energy and momentum conservation, the gravitational fields of the source must be compensated by perturbations in the matter and gravitational fields, and the role of such compensation in containing the initial inhomogeneities in their subsequent evolution is discussed. A complete formal solution is derived in terms of Green functions for the perturbations produced by an arbitrary source in a flat universe containing cold dark matter. Approximate Green function solutions are derived for the late-time density perturbations and late-time gravitational waves in a universe containing a radiation fluid. A cosmological energy-momentum pseudotensor is defined to clarify the nature of energy and momentum conservation in the expanding universe. 55 refs.
Cosmological Perturbations in Extended Massive Gravity
Gumrukcuoglu, A Emir; Lin, Chunshan; Mukohyama, Shinji; Trodden, Mark
2013-01-01
We study cosmological perturbations around self-accelerating solutions to two extensions of nonlinear massive gravity: the quasi-dilaton theory and the mass-varying theory. We examine stability of the cosmological solutions, and the extent to which the vanishing of the kinetic terms for scalar and vector perturbations of self-accelerating solutions in massive gravity is generic when the theory is extended. We find that these kinetic terms are in general non-vanishing in both extensions, though there are constraints on the parameters and background evolution from demanding that they have the correct sign. In particular, the self-accelerating solutions of the quasi-dilaton theory are always unstable to scalar perturbations with wavelength shorter than the Hubble length.
Cosmological perturbations beyond linear order
CERN. Geneva
2013-01-01
Cosmological perturbation theory is the standard tool to understand the formation of the large scale structure in the Universe. However, its degree of applicability is limited by the growth of the amplitude of the matter perturbations with time. This problem can be tackled with by using N-body simulations or analytical techniques that go beyond the linear calculation. In my talk, I'll summarise some recent efforts in the latter that ameliorate the bad convergence of the standard perturbative expansion. The new techniques allow better analytical control on observables (as the matter power spectrum) over scales very relevant to understand the expansion history and formation of structure in the Universe.
Junction conditions of cosmological perturbations
Tomita, K
2004-01-01
The behavior of perturbations is studied in cosmological models which consist of two different homogeneous regions connected in a spherical shell boundary. The junction conditions for the metric perturbations and the displacements of the shell boundary are analyzed and the surface densities of the perturbed energy and momentum in the shell are derived, using Mukohyama's gauge-invariant formalism and the Israel discontinuity condition. In both homogeneous regions the perturbations of scalar, vector and tensor types are expanded using the 3-dimensional harmonic functions, but the model coupling among them is caused in the shell by the inhomogeneity. By treating the perturbations with odd and even parities separately, it is found, however, that we can have consistent displacements and surface densities for given metric parturbations
Perturbations in Massive Gravity Cosmology
Crisostomi, Marco; Pilo, Luigi
2012-01-01
We study cosmological perturbations for a ghost free massive gravity theory formulated with a dynamical extra metric that is needed to massive deform GR. In this formulation FRW background solutions fall in two branches. In the dynamics of perturbations around the first branch solutions, no extra degree of freedom with respect to GR ispresent at linearized level, likewise what is found in the Stuckelberg formulation of massive gravity where the extra metric isflat and non dynamical. In the first branch, perturbations are probably strongly coupled. On the contrary, for perturbations around the second branch solutions all expected degrees of freedom propagate. While tensor and vector perturbations of the physical metric that couples with matter follow closely the ones of GR, scalars develop an exponential Jeans-like instability on sub-horizon scales. On the other hand, around a de Sitter background there is no instability. We argue that one could get rid of the instabilities by introducing a mirror dark matter ...
Cosmological perturbations without inflation
Melia, Fulvio
2017-01-01
A particularly attractive feature of inflation is that quantum fluctuations in the inflaton field may have seeded inhomogeneities in the cosmic microwave background (CMB) and the formation of large-scale structure. In this paper, we demonstrate that a scalar field with zero active mass, i.e. with an equation of state ρ +3p=0 , where ρ and p are its energy density and pressure, respectively, could also have produced an essentially scale-free fluctuation spectrum, though without inflation. This alternative mechanism is based on the Hollands–Wald concept of a minimum wavelength for the emergence of quantum fluctuations into the semi-classical universe. A cosmology with zero active mass does not have a horizon problem, so it does not need inflation to solve this particular (non) issue. In this picture, the {{1}\\circ}{ {--}}{{10}\\circ} fluctuations in the CMB correspond almost exactly to the Planck length at the Planck time, firmly supporting the view that CMB observations may already be probing trans-Planckian physics.
Cosmological Perturbations without Inflation
Melia, Fulvio
2016-01-01
A particularly attractive feature of inflation is that quantum fluctuations in the inflaton field may have seeded inhomogeneities in the cosmic microwave background (CMB) and the formation of large-scale structure. In this paper, we demonstrate that a scalar field with zero active mass, i.e., with an equation of state rho+3p=0, where rho and p are its energy density and pressure, respectively, could also have produced an essentially scale-free fluctuation spectrum, though without inflation. This alternative mechanism is based on the Hollands-Wald concept of a minimum wavelength for the emergence of quantum fluctuations into the semi-classical universe. A cosmology with zero active mass does not have a horizon problem, so it does not need inflation to solve this particular (non) issue. In this picture, the 1-10 degree fluctuations in the CMB correspond almost exactly to the Planck length at the time these modes were produced, firmly supporting the view that CMB observations may already be probing trans-Plancki...
Noncommutative Fluid and Cosmological Perturbations
Das, Praloy
2016-01-01
In the present paper we have developed a Non-Commutative (NC) generalization of perfect fluid model from first principles, in a Hamiltonian framework. The noncommutativity is introduced at the Lagrangian (particle) coordinate space brackets and the induced NC fluid bracket algebra for the Eulerian (fluid) field variables is derived. Together with a Hamiltonian this NC algebra generates the generalized fluid dynamics that satisfies exact local conservation laws for mass and energy thereby maintaining mass and energy conservation. However, nontrivial NC correction terms appear in charge and energy fluxes. Other non-relativistic spacetime symmetries of the NC fluid are also discussed in detail. This constitutes the NC fluid dynamics and kinematics. In the second part we construct an extension of Friedmann-Robertson-Walker (FRW) cosmological model based on the NC fluid dynamics presented here. We outline the way in which NC effects generate cosmological perturbations bringing in anisotropy and inhomogeneity in th...
FRW Cosmological Perturbations in Massive Bigravity
Comelli, D; Pilo, L
2014-01-01
Cosmological perturbations of FRW solutions in ghost free massive bigravity, including also a second matter sector, are studied in detail. At early time, we find that sub horizon exponential instabilities are unavoidable and they lead to a premature departure from the perturbative regime of cosmological perturbations.
Cosmological perturbation theory and quantum gravity
Brunetti, Romeo; Hack, Thomas-Paul; Pinamonti, Nicola; Rejzner, Katarzyna
2016-01-01
It is shown how cosmological perturbation theory arises from a fully quantized perturbative theory of quantum gravity. Central for the derivation is a non-perturbative concept of gauge-invariant local observables by means of which perturbative invariant expressions of arbitrary order are generated. In particular, in the linearised theory, first order gauge-invariant observables familiar from cosmological perturbation theory are recovered. Explicit expressions of second order quantities are presented as well.
Cosmological perturbation theory and quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Brunetti, Romeo [Dipartimento di Matematica, Università di Trento,Via Sommarive 14, 38123 Povo TN (Italy); Fredenhagen, Klaus [II Institute für Theoretische Physik, Universität Hamburg,Luruper Chaussee 149, 22761 Hamburg (Germany); Hack, Thomas-Paul [Institute für Theoretische Physik, Universität Leipzig,Brüderstr. 16, 04103 Leipzig (Germany); Pinamonti, Nicola [Dipartimento di Matematica, Università di Genova,Via Dodecaneso 35, 16146 Genova (Italy); INFN, Sezione di Genova,Via Dodecaneso 33, 16146 Genova (Italy); Rejzner, Katarzyna [Department of Mathematics, University of York,Heslington, York YO10 5DD (United Kingdom)
2016-08-04
It is shown how cosmological perturbation theory arises from a fully quantized perturbative theory of quantum gravity. Central for the derivation is a non-perturbative concept of gauge-invariant local observables by means of which perturbative invariant expressions of arbitrary order are generated. In particular, in the linearised theory, first order gauge-invariant observables familiar from cosmological perturbation theory are recovered. Explicit expressions of second order quantities are presented as well.
BRST quantization of cosmological perturbations
Energy Technology Data Exchange (ETDEWEB)
Armendariz-Picon, Cristian [Physics Department, St. Lawrence University,Canton, NY 13617 (United States); Şengör, Gizem [Department of Physics, Syracuse University,Syracuse, NY 13244 (United States)
2016-11-08
BRST quantization is an elegant and powerful method to quantize theories with local symmetries. In this article we study the Hamiltonian BRST quantization of cosmological perturbations in a universe dominated by a scalar field, along with the closely related quantization method of Dirac. We describe how both formalisms apply to perturbations in a time-dependent background, and how expectation values of gauge-invariant operators can be calculated in the in-in formalism. Our analysis focuses mostly on the free theory. By appropriate canonical transformations we simplify and diagonalize the free Hamiltonian. BRST quantization in derivative gauges allows us to dramatically simplify the structure of the propagators, whereas Dirac quantization, which amounts to quantization in synchronous gauge, dispenses with the need to introduce ghosts and preserves the locality of the gauge-fixed action.
BRST Quantization of Cosmological Perturbations
Armendariz-Picon, Cristian
2016-01-01
BRST quantization is an elegant and powerful method to quantize theories with local symmetries. In this article we study the Hamiltonian BRST quantization of cosmological perturbations in a universe dominated by a scalar field, along with the closely related quantization method of Dirac. We describe how both formalisms apply to the perturbations in a time-dependent background, and how expectation values of gauge-invariant operators can be calculated in the in-in formalism. Our analysis focuses mostly on the free theory. By appropriate canonical transformations we simplify and diagonalize the free Hamiltonian. BRST quantization in derivative gauges allows us to dramatically simplify the structure of the propagators, whereas quantization in synchronous gauge, which amounts to Dirac quantization, dispenses with the need to introduce ghosts and preserves the locality of the gauge-fixed action.
Asymptotic analysis of perturbed dust cosmologies to second order
Uggla, Claes; Wainwright, John
2013-08-01
Nonlinear perturbations of Friedmann-Lemaitre cosmologies with dust and a cosmological constant Λ >0 have recently attracted considerable attention. In this paper our first goal is to compare the evolution of the first and second order perturbations by determining their asymptotic behaviour at late times in ever-expanding models. We show that in the presence of spatial curvature K or a cosmological constant, the density perturbation approaches a finite limit both to first and second order, but the rate of approach depends on the model, being power law in the scale factor if Λ >0 but logarithmic if Λ =0 and K0 the decaying mode does not die away, i.e. it contributes on an equal footing as the growing mode to the asymptotic expression for the density perturbation. On the other hand, the future asymptotic regime of the Einstein-de Sitter universe (K=Λ =0) is completely different, as exemplified by the density perturbation which diverges; moreover, the second order perturbation diverges faster than the first order perturbation, which suggests that the Einstein-de Sitter universe is unstable to perturbations, and that the perturbation series do not converge towards the future. We conclude that the presence of spatial curvature or a cosmological constant stabilizes the perturbations. Our second goal is to derive an explicit expression for the second order density perturbation that can be used to study the effects of including a cosmological constant and spatial curvature.
Effective Field Theory of Cosmological Perturbations
Piazza, Federico
2013-01-01
The effective field theory of cosmological perturbations stems from considering a cosmological background solution as a state displaying spontaneous breaking of time translations and (adiabatic) perturbations as the related Nambu-Goldstone modes. With this insight, one can systematically develop a theory for the cosmological perturbations during inflation and, with minor modifications, also describe in full generality the gravitational interactions of dark energy, which are relevant for late-time cosmology. The formalism displays a unique set of Lagrangian operators containing an increasing number of cosmological perturbations and derivatives. We give an introductory description of the unitary gauge formalism for theories with broken gauge symmetry---that allows to write down the most general Lagrangian---and of the Stueckelberg "trick"---that allows to recover gauge invariance and to make the scalar field explicit. We show how to apply this formalism to gravity and cosmology and we reproduce the detailed ana...
Inflationary Perturbations and Precision Cosmology
Habib, S; Heitmann, K; Jungman, G; Habib, Salman; Heinen, Andreas; Heitmann, Katrin; Jungman, Gerard
2005-01-01
Inflationary cosmology provides a natural mechanism for the generation of primordial perturbations which seed the formation of observed cosmic structure and lead to specific signals of anisotropy in the cosmic microwave background radiation. In order to test the broad inflationary paradigm as well as particular models against precision observations, it is crucial to be able to make accurate predictions for the power spectrum of both scalar and tensor fluctuations. We present detailed calculations of these quantities utilizing direct numerical approaches as well as error-controlled uniform approximations, comparing with the (uncontrolled) traditional slow-roll approach. A simple extension of the leading-order uniform approximation yields results for the power spectra amplitudes, the spectral indices, and the running of spectral indices, with accuracy of the order of 0.1% - approximately the same level at which the transfer functions are known. Several representative examples are used to demonstrate these resul...
Initial conditions for cosmological perturbations
Ashtekar, Abhay
2016-01-01
Penrose proposed that the big bang singularity should be constrained by requiring that the Weyl curvature vanishes there. The idea behind this past hypothesis is attractive because it constrains the initial conditions for the universe in geometric terms and is not confined to a specific early universe paradigm. However, the precise statement of Penrose's hypothesis is tied to classical space-times and furthermore restricts only the gravitational degrees of freedom. These are encapsulated only in the tensor modes of the commonly used cosmological perturbation theory. Drawing inspiration from the underlying idea, we propose a quantum generalization of Penrose's hypothesis using the Planck regime in place of the big bang, and simultaneously incorporating tensor as well as scalar modes. Initial conditions selected by this generalization constrain the universe to be as homogeneous and isotropic in the Planck regime \\emph{as permitted by the Heisenberg uncertainty relations}.
Cosmological Perturbations: Vorticity, Isocurvature and Magnetic Fields
Christopherson, Adam J
2014-01-01
In this paper I review some recent, interlinked, work undertaken using cosmological perturbation theory -- a powerful technique for modelling inhomogeneities in the Universe. The common theme which underpins these pieces of work is the presence of non-adiabatic pressure, or entropy, perturbations. After a brief introduction covering the standard techniques of describing inhomogeneities in both Newtonian and relativistic cosmology, I discuss the generation of vorticity. As in classical fluid mechanics, vorticity is not present in linearized perturbation theory (unless included as an initial condition). Allowing for entropy perturbations, and working to second order in perturbation theory, I show that vorticity is generated, even in the absence of vector perturbations, by purely scalar perturbations, the source term being quadratic in the gradients of first order energy density and isocurvature, or non-adiabatic pressure perturbations. This generalizes Crocco's theorem to a cosmological setting. I then introduc...
Density Perturbation Growth in Teleparallel Cosmology
Geng, Chao-Qiang
2012-01-01
We study the cosmological perturbations in teleparallel dark energy models in which there is a dynamical scalar field with a non-minimal coupling to gravity. We find that the propagating degrees of freedom are the same as in quintessence cosmology despite that variables of the perturbed vierbein field are greater than those in metric theories. The resulting growth evolution shows that gravitational interactions are enhanced during the unique tracker evolution of teleparallel dark energy models.
Cosmological effects of nonlinear electrodynamics
Energy Technology Data Exchange (ETDEWEB)
Novello, M [Instituto de Cosmologia Relatividade Astrofisica (ICRA-Brasil/CBPF), Rua Dr Xavier Sigaud, 150, CEP 22290-180, Rio de Janeiro (Brazil); Goulart, E [Instituto de Cosmologia Relatividade Astrofisica (ICRA-Brasil/CBPF), Rua Dr Xavier Sigaud, 150, CEP 22290-180, Rio de Janeiro (Brazil); Salim, J M [Instituto de Cosmologia Relatividade Astrofisica (ICRA-Brasil/CBPF), Rua Dr Xavier Sigaud, 150, CEP 22290-180, Rio de Janeiro (Brazil); Bergliaffa, S E Perez [Departamento de Fisica Teorica, Universidade do Estado do Rio de Janeiro, R. Sao Francisco Xavier, 524, Maracana, CEP 20559-900, Rio de Janeiro (Brazil)
2007-06-07
It will be shown that a given realization of nonlinear electrodynamics, used as a source of Einstein's equations, generates a cosmological model with interesting features, namely a phase of current cosmic acceleration, and the absence of an initial singularity, thus pointing to a way of solving two important problems in cosmology.
Asymptotic analysis of perturbed dust cosmologies to second order
Uggla, Claes
2013-01-01
Nonlinear perturbations of Friedmann-Lemaitre cosmologies with dust and a positive cosmological constant have recently attracted considerable attention. In this paper our first goal is to compare the evolution of the first and second order perturbations by determining their asymptotic behaviour at late times in ever-expanding models. We show that in the presence of spatial curvature K or a positive cosmological constant, the density perturbation approaches a finite limit both to first and second order, but the rate of approach depends on the model, being power law in the scale factor if the cosmological constant is positive but logarithmic if it is zero and and K<0. Scalar perturbations in general contain a growing and a decaying mode. We find, somewhat surprisingly, that if the cosmological constant is positive the decaying mode does not die away, i.e. it contributes on an equal footing as the growing mode to the asymptotic expression for the density perturbation. On the other hand, the future asymptotic ...
Density perturbation growth in teleparallel cosmology
Energy Technology Data Exchange (ETDEWEB)
Geng, Chao-Qiang [College of Mathematics and Physics, Chongqing University of Posts and Telecommunications, Chongqing, 400065 (China); Wu, Yi-Peng, E-mail: geng@phys.nthu.edu.tw, E-mail: s9822508@m98.nthu.edu.tw [Department of Physics, National Tsing Hua University, Hsinchu, 300 Taiwan (China)
2013-04-01
We study the cosmological perturbations in teleparallel dark energy models in which there is a dynamical scalar field with a non-minimal coupling to gravity. We find that the propagating degrees of freedom are the same as in quintessence cosmology despite that variables of the perturbed vierbein field are greater than those in metric theories. We numerically show some evident discrepancy from general relativity in the evolutions of the perturbations on all scales of the universe. We also demonstrate that the gravitational interactions are enhanced during the unique tracker evolutions in these models.
Newtonian Limits of the Relativistic Cosmological Perturbations
Hwang, J
1997-01-01
Relativistic cosmological perturbation analyses can be made based on several different fundamental gauge conditions. In the pressureless limit the variables in certain gauge conditions show the correct Newtonian behaviors. We consider the general curvature and the cosmological constant in the background medium. The perturbed density in the comoving gauge, and the perturbed velocity and the perturbed potential in the zero-shear gauge show the same behavior as the Newtonian ones in a general scale. Far inside horizon, except for the uniform-density gauge, density perturbations in all the fundamental gauge conditions show the correct Newtonian behavior. In this paper we elaborate these Newtonian correspondences. We also present the relativistic results considering general pressures in the background and perturbation.
Cosmological perturbations in a noncommutative braneworld inflation
Institute of Scientific and Technical Information of China (English)
Kourosh Nozari; Siamak Akhshabi
2012-01-01
We use the smeared,coherent state picture of noncommutativity to study evolution of perturbations in a noncommutative braneworld scenario.Within the standard procedure of studying braneworld cosmological perturbations,we study the evolution of the Bardeen metric potential and curvature perturbations in this model.We show that in this setup,the early stage of the universe's evolution has a transient phantom evolution with imaginary effective sound speed.
Metric perturbations in Einstein-Cartan Cosmology
Garcia de Andrade, L C
2002-01-01
Metric perturbations the stability of solution of Einstein-Cartan cosmology (ECC) are given. The first addresses the stability of solutions of Einstein-Cartan (EC) cosmological model against Einstein static universe background. In this solution we show that the metric is stable against first-order perturbations and correspond to acoustic oscillations. The second example deals with the stability of de Sitter metric also against first-order perturbations. Torsion and shear are also computed in these cases. The resultant perturbed anisotropic spacetime with torsion is only de Sitter along one direction or is unperturbed along one direction and perturbed against the other two. Cartan torsion contributes to the frequency of oscillations in the model. Therefore gravitational waves could be triggered by the spin-torsion scalar density .
Note on the semiclassicality of cosmological perturbations
Donà, Pietro; Marcianò, Antonino
2016-12-01
Moving from the consideration that matter fields must be treated in terms of their fundamental quantum counterparts, we show straightforward arguments, within the framework of ordinary quantum mechanics and quantum field theory, in order to convince readers that cosmological perturbations must be addressed in term of the semiclassical limit of the expectation value of quantum fields. We first take into account cosmological perturbations originated by a quantum scalar field, and then extend our treatment in order to account for the expectation values of bilinears of Dirac fermion fields. The latter can indeed transform as scalar quantities under diffeomorphisms, as well as all the other bilinear of the Dirac fields that belong to the Clifford algebra. This is the first of a series of works that is intended to prove that cosmological quantum perturbations can actually be accounted for in terms of Dirac fermion fields, which must be treated as fundamental quantum objects, and their dynamics.
Cosmological perturbations from an inhomogeneous phase transition
Energy Technology Data Exchange (ETDEWEB)
Matsuda, Tomohiro, E-mail: matsuda@sit.ac.j [Laboratory of Physics, Saitama Institute of Technology, Fusaiji, Okabe-machi, Saitama 369-0293 (Japan)
2009-07-21
A mechanism for generating metric perturbations in inflationary models is considered. Long-wavelength inhomogeneities of light scalar fields in a decoupled sector may give rise to superhorizon fluctuations of couplings and masses in the low-energy effective action. Cosmological phase transitions may then occur that are not simultaneous in space, but occur with time lags in different Hubble patches that arise from the long-wavelength inhomogeneities. Here an interesting model in which cosmological perturbations may be created at the electroweak phase transition is considered. The results show that phase transitions may be a generic source of non-Gaussianity.
On counterterms in cosmological perturbation theory
Goswami, Gaurav
2014-01-01
Cosmological perturbation theory is the theory of fluctuations (scalar as well as tensor) around the inflationary cosmological background solution. It is important to understand the details of the process of renormalization in this theory. In more familiar applications of quantum field theory, the dependence on the external momenta of the dimensionally regulated expression of the one-loop contribution to a correlator determines the number of counter terms (and their forms) required to renormalize it. In this work, it is pointed out that in cosmological perturbation theory, though this still happens, it happens in a completely different way such that in the late time limit, the information about the number and forms of counter terms required gets erased. This is to be compared with what happens in spontaneous symmetry breaking where the use of fluctuation fields around a chosen vacuum seems to suggest that more counter terms shall be needed to renormalize the theory than are actually required. We also comment ...
Cosmological perturbations in mimetic matter model
Matsumoto, Jiro; Sushkov, Sergey V
2015-01-01
We investigate the cosmological evolution of mimetic matter model with arbitrary scalar potential. The cosmological reconstruction is explicitly done for different choices of potential. The cases that mimetic matter model shows the evolution as Cold Dark Matter(CDM), wCDM model, dark matter and dark energy with dynamical $Om(z)$ or phantom dark energy with phantom-non-phantom crossing are presented in detail. The cosmological perturbations for such evolution are studied in mimetic matter model. For instance, the evolution behavior of the matter density contrast which is different from usual one, i.e. $\\ddot \\delta + 2 H \\dot \\delta - \\kappa ^2 \\rho \\delta /2 = 0$ is investigated. The possibility of peculiar evolution of $\\delta$ in the model under consideration is shown. Special attention is paid to the behavior of matter density contrast near to future singularity where decay of perturbations may occur much earlier the singularity.
Dynamics of Cosmological Perturbations in Position Space
Bashinsky, S V; Bashinsky, Sergei; Bertschinger, Edmund
2002-01-01
We show that the linear dynamics of cosmological perturbations can be described by coupled wave equations, allowing their efficient numerical and, in certain limits, analytical integration directly in position space. The linear evolution of any perturbation can then be analyzed with the Green's function method. Prior to hydrogen recombination, assuming tight coupling between photons and baryons, neglecting neutrino perturbations, and taking isentropic (adiabatic) initial conditions, the obtained Green's functions for all metric, density, and velocity perturbations vanish beyond the acoustic horizon. At the acoustic wavefronts, a positive gravitational potential perturbation produces narrow photon-baryon density spikes, which provide one of the major contributions to the observed cosmic microwave background radiation anisotropy on all scales. The gravitational interaction between cold dark matter and baryons causes a dip in the observed temperature of the radiation at the center of the initial perturbation. We...
Enea Romano, Antonio; Sanes Negrete, Sergio; Sasaki, Misao; Starobinsky, Alexei A.
2014-06-01
We study effects on the luminosity distance of a local inhomogeneity seeded by primordial curvature perturbations of the type predicted by the inflationary scenario and constrained by the cosmic microwave background radiation. We find that a local underdensity originated from a one, two or three standard deviations peaks of the primordial curvature perturbations field can induce corrections to the value of a cosmological constant of the order of 0.6{%},1{%},1.5{%} , respectively. These effects cannot be neglected in the precision cosmology era in which we are entering. Our results can be considered an upper bound for the effect of the monopole component of the local non-linear structure which can arise from primordial curvature perturbations and requires a fully non-perturbative relativistic treatment.
Cosmological perturbations through a simple bounce
Allen, L E
2004-01-01
We present a detailed study of a simple scalar field model that yields non-singular cosmological solutions. We study both the qualitative dynamics of the homogeneous and isotropic background and the evolution of inhomogeneous linear perturbations. We calculate the spectrum of perturbations generated on super-Hubble scales during the collapse phase from initial vacuum fluctuations on small scales and then evolve these numerically through the bounce. We show there is a gauge that remains well-defined throughout the bounce, even though other commonly used gauges break down. We show that the comoving curvature perturbation calculated during the collapse phase provides a good estimate of the resulting large scale adiabatic perturbation in the expanding phase while the Bardeen metric potential is dominated by what becomes a decaying mode after the bounce. We show that a power-law collapse phase with scale factor proportional $(-t)^{2/3}$ can yield a scale-invariant spectrum of adiabatic scalar perturbations in the ...
Nonspherical Szekeres models in the language of cosmological perturbations
Sussman, Roberto A.; Hidalgo, Juan Carlos; Delgado Gaspar, Ismael; Germán, Gabriel
2017-03-01
We study the differences and equivalences between the nonperturbative description of the evolution of cosmic structure furnished by the Szekeres dust models (a nonspherical exact solution of Einstein's equations) and the dynamics of cosmological perturbation theory (C P T ) for dust sources in a Λ CDM background. We show how the dynamics of Szekeres models can be described by evolution equations given in terms of "exact fluctuations" that identically reduce (at all orders) to evolution equations of C P T in the comoving isochronous gauge. We explicitly show how Szekeres linearized exact fluctuations are specific (deterministic) realizations of standard linear perturbations of C P T given as random fields, but, as opposed to the latter perturbations, they can be evolved exactly into the full nonlinear regime. We prove two important results: (i) the conservation of the curvature perturbation (at all scales) also holds for the appropriate linear approximation of the exact Szekeres fluctuations in a Λ CDM background, and (ii) the different collapse morphologies of Szekeres models yields, at nonlinear order, different functional forms for the growth factor that follows from the study of redshift space distortions. The metric-based potentials used in linear C P T are computed in terms of the parameters of the linearized Szekeres models, thus allowing us to relate our results to linear C P T results in other gauges. We believe that these results provide a solid starting stage to examine the role of non-perturbative general relativity in current cosmological research.
Adiabatic perturbations in coupled scalar field cosmologies
Beyer, Joschka
2014-01-01
We present a comprehensive and gauge invariant treatment of perturbations around cosmological scaling solutions for two canonical scalar fields coupled through a common potential in the early universe, in the presence of neutrinos, photons and baryons, but excluding cold dark matter. This setup is relevant for analyzing cosmic perturbations in scalar field models of dark matter with a coupling to a quintessence field. We put strong restrictions on the shape of the common potential and adopt a matrix-eigensystem approach to determine the dominant perturbations modes in such models. Similar to recent results in scenarios where standard cold dark matter couples to quintessence, we show that the stability of the adiabatic perturbation mode can be an issue for this class of scalar field dark matter models, but only for specific choices of the common potential. For an exponential coupling potential, a rather common shape arising naturally in many instances, this problem can be avoided. We explicitly calculate the d...
Perturbation Theory of the Cosmological Log-Density Field
Wang, Xin; Szapudi, István; Szalay, Alex; Chen, Xuelei; Lesgourgues, Julien; Riotto, Antonio; Sloth, Martin; 10.1088/0004-637X/735/1/32
2011-01-01
The matter density field exhibits a nearly lognormal probability density distribution (PDF) after entering into the nonlinear regime. Recently, it has been shown that the shape of the power spectrum of a logarithmically transformed density field is very close to the linear density power spectrum, motivating an analytic study of it. In this paper, we develop cosmological perturbation theory for the power spectrum of this field. Our formalism is developed in the context of renormalized perturbation theory, which helps to regulate the convergence behavior of the perturbation series, and of the Taylor- series expansion we use of the logarithmic mapping. This approach allows us to handle the critical issue of density smoothing in a straightforward way. We also compare our perturbative results with simulation measurements.
Cosmological Perturbations with Multiple Fluids and Fields
Hwang, J
2002-01-01
We consider the evolution of perturbed cosmological spacetime with multiple fluid and field system in Einstein gravity. Equations are presented in gauge-ready forms, and are presented using the adiabatic and isocurvature perturbation variables. We present equations in the general background with $K$ and $\\Lambda$. We also clarify the conditions for conserved adiabatic and isocurvature perturbations in the large-scale limit. One interesting conclusion is that, for ideal fluid system, although the isocurvature modes can seed the adiabatic mode in the large-scale limit, the isocurvature modes decouple from the adiabatic one which is not the case for the field system. Useful sets of equations readily applicable to the quintessence models and the warm inflation scenario can be found in this work. An application to the scaling regime with an exponential field potential is made in the Appendix.
Nonlinear stability of cosmological solutions in massive gravity
De Felice, Antonio; Lin, Chunshan; Mukohyama, Shinji
2013-01-01
We investigate nonlinear stability of two classes of cosmological solutions in massive gravity: isotropic Friedmann-Lemaitre-Robertson-Walker (FLRW) solutions and anisotropic FLRW solutions. For this purpose we construct the linear cosmological perturbation theory around axisymmetric Bianchi type--I backgrounds. We then expand the background around the two classes of solutions, which are fixed points of the background evolution equation, and analyze linear perturbations on top of it. This provides a consistent truncation of nonlinear perturbations around these fixed point solutions and allows us to analyze nonlinear stability in a simple way. In particular, it is shown that isotropic FLRW solutions exhibit nonlinear ghost instability. On the other hand, anisotropic FLRW solutions are shown to be ghost-free for a range of parameters and initial conditions.
Scalar cosmological perturbations from inflationary black holes
Energy Technology Data Exchange (ETDEWEB)
Prokopec, Tomislav; Reska, Paul, E-mail: t.prokopec@uu.nl, E-mail: p.m.reska@uu.nl [Spinoza Institute and Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, 3584 CE Utrecht (Netherlands)
2011-03-01
We study the correction to the scale invariant power spectrum of a scalar field on de Sitter space from small black holes that formed during a pre-inflationary matter dominated era. The formation probability of such black holes is estimated from primordial Gaussian density fluctuations. We determine the correction to the spectrum of scalar cosmological perturbations from the Keldysh propagator of a massless scalar field on Schwarzschild-de Sitter space. Our results suggest that the effect is strong enough to be tested — and possibly even ruled out — by observations.
Cosmological perturbations on the phantom brane
Bag, Satadru; Viznyuk, Alexander; Shtanov, Yuri; Sahni, Varun
2016-07-01
We obtain a closed system of equations for scalar perturbations in a multi-component braneworld. Our braneworld possesses a phantom-like equation of state at late times, weff Consequently, the quasi-static approximation of Koyama and Maartens provides a good fit to the exact results during the matter-dominated epoch. We find that the late-time growth of density perturbations on the brane proceeds at a faster rate than in ΛCDM. Additionally, the gravitational potentials Φ and Ψ evolve differently on the brane than in ΛCDM, for which Φ = Ψ. On the brane, by contrast, the ratio Φ/Ψ exceeds unity during the late matter-dominated epoch (z lesssim 50). These features emerge as smoking gun tests of phantom brane cosmology and allow predictions of this scenario to be tested against observations of galaxy clustering and large-scale structure.
Quantum Cosmological Perturbations of Multiple Fluids
Peter, Patrick; Vitenti, Sandro Dias Pinto
2015-01-01
The formalism to treat quantization and evolution of cosmological perturbations of multiple fluids is described. We first construct the Lagrangian for both the gravitational and matter parts, providing the necessary relevant variables and momenta leading to the quadratic Hamiltonian describing linear perturbations. The final Hamiltonian is obtained without assuming any equations of motions for the background variables. This general formalism is applied to the special case of two fluids, having in mind the usual radiation and matter mix which made most of our current Universe history. Quantization is achieved using an adiabatic expansion of the basis functions. This allows for an unambiguous definition of a vacuum state up to the given adiabatic order. Using this basis, we show that particle creation is well defined for a suitable choice of vacuum and canonical variables, so that the time evolution of the corresponding quantum fields is unitary. This provides constraints for setting initial conditions for an a...
Efficient Cosmological Perturbation Theory with FAST-PT
Fang, Xiao; Blazek, Jonathan; McEwen, Joseph; Hirata, Christopher M.
2017-01-01
Cosmological perturbation theory is a powerful tool to model observations of large-scale structure in the weakly non-linear regime. However, even at next-to-leading order, it results in computationally expensive mode-coupling integrals. In this talk, I will focus on the physics behind our extremely efficient algorithm, FAST-PT. I will show how the algorithm can be applied to calculate 1-loop power spectra for several cosmological observables, including the matter density, galaxy bias, galaxy intrinsic alignments, the Ostriker-Vishniac effect, the secondary CMB polarization due to baryon flows, and redshift-space distortions. Our public code is written in Python and is easy to use and adapt to additional applications.
Cosmological perturbations from the Standard Model Higgs
Energy Technology Data Exchange (ETDEWEB)
Simone, Andrea De [SISSA, Via Bonomea 265, I-34136 Trieste (Italy); Riotto, Antonio, E-mail: andrea.desimone@sissa.it, E-mail: antonio.riotto@unige.ch [Department of Theoretical Physics and Center for Astroparticle Physics (CAP), 24 quai E. Ansermet, CH-1211 Geneva 4 (Switzerland)
2013-02-01
We propose that the Standard Model (SM) Higgs is responsible for generating the cosmological perturbations of the universe by acting as an isocurvature mode during a de Sitter inflationary stage. In view of the recent ATLAS and CMS results for the Higgs mass, this can happen if the Hubble rate during inflation is in the range (10{sup 10}−10{sup 14}) GeV (depending on the SM parameters). Implications for the detection of primordial tensor perturbations through the B-mode of CMB polarization via the PLANCK satellite are discussed. For example, if the Higgs mass value is confirmed to be m{sub h} = 125.5 GeV and m{sub t},α{sub s} are at their central values, our mechanism predicts tensor perturbations too small to be detected in the near future. On the other hand, if tensor perturbations will be detected by PLANCK through the B-mode of CMB, then there is a definite relation between the Higgs and top masses, making the mechanism predictive and falsifiable.
Uniqueness of the gauge invariant action for cosmological perturbations
Energy Technology Data Exchange (ETDEWEB)
Prokopec, Tomislav; Weenink, Jan, E-mail: t.prokopec@uu.nl, E-mail: j.g.weenink@uu.nl [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, Leuvenlaan 4, 3585 CE Utrecht (Netherlands)
2012-12-01
In second order perturbation theory different definitions are known of gauge invariant perturbations in single field inflationary models. Consequently the corresponding gauge invariant cubic actions do not have the same form. Here we show that the cubic action for one choice of gauge invariant variables is unique in the following sense: the action for any other, non-linearly related variable can be brought to the same bulk action, plus additional boundary terms. These boundary terms correspond to the choice of hypersurface and generate extra, disconnected contributions to the bispectrum. We also discuss uniqueness of the action with respect to conformal frames. When expressed in terms of the gauge invariant curvature perturbation on uniform field hypersurfaces the action for cosmological perturbations has a unique form, independent of the original Einstein or Jordan frame. Crucial is that the gauge invariant comoving curvature perturbation is frame independent, which makes it extremely helpful in showing the quantum equivalence of the two frames, and therefore in calculating quantum effects in nonminimally coupled theories such as Higgs inflation.
de Sitter limit of inflation and nonlinear perturbation theory
Jarnhus, Philip R
2007-01-01
We study the fourth order action of comoving curvature perturbations in an inflationary universe in order to understand more systematically the de Sitter limit in nonlinear cosmological perturbation theory. We derive the action of the curvature perturbations to fourth order in the comoving gauge, and show that it vanishes sufficiently fast in the de Sitter limit. By studying the de Sitter limit, we then extrapolate to the n'th order action of comoving curvature perturbations and discuss the slow-roll order of the n-point correlation function.
Running vacuum cosmological models: linear scalar perturbations
Perico, E. L. D.; Tamayo, D. A.
2017-08-01
In cosmology, phenomenologically motivated expressions for running vacuum are commonly parameterized as linear functions typically denoted by Λ(H2) or Λ(R). Such models assume an equation of state for the vacuum given by bar PΛ = - bar rhoΛ, relating its background pressure bar PΛ with its mean energy density bar rhoΛ ≡ Λ/8πG. This equation of state suggests that the vacuum dynamics is due to an interaction with the matter content of the universe. Most of the approaches studying the observational impact of these models only consider the interaction between the vacuum and the transient dominant matter component of the universe. We extend such models by assuming that the running vacuum is the sum of independent contributions, namely bar rhoΛ = Σibar rhoΛi. Each Λ i vacuum component is associated and interacting with one of the i matter components in both the background and perturbation levels. We derive the evolution equations for the linear scalar vacuum and matter perturbations in those two scenarios, and identify the running vacuum imprints on the cosmic microwave background anisotropies as well as on the matter power spectrum. In the Λ(H2) scenario the vacuum is coupled with every matter component, whereas the Λ(R) description only leads to a coupling between vacuum and non-relativistic matter, producing different effects on the matter power spectrum.
Quantum cosmological perturbations of multiple fluids
Peter, Patrick; Pinto-Neto, N.; Vitenti, Sandro D. P.
2016-01-01
The formalism to treat quantization and evolution of cosmological perturbations of multiple fluids is described. We first construct the Lagrangian for both the gravitational and matter parts, providing the necessary relevant variables and momenta leading to the quadratic Hamiltonian describing linear perturbations. The final Hamiltonian is obtained without assuming any equations of motions for the background variables. This general formalism is applied to the special case of two fluids, having in mind the usual radiation and matter mix which made most of our current Universe history. Quantization is achieved using an adiabatic expansion of the basis functions. This allows for an unambiguous definition of a vacuum state up to the given adiabatic order. Using this basis, we show that particle creation is well defined for a suitable choice of vacuum and canonical variables, so that the time evolution of the corresponding quantum fields is unitary. This provides constraints for setting initial conditions for an arbitrary number of fluids and background time evolution. We also show that the common choice of variables for quantization can lead to an ill-defined vacuum definition. Our formalism is not restricted to the case where the coupling between fields is small, but is only required to vary adiabatically with respect to the ultraviolet modes, thus paving the way to consistent descriptions of general models not restricted to single-field (or fluid).
Manifestly Covariant Gauge-invariant Cosmological Perturbation Theory
Miedema, P G
2010-01-01
It is shown that a first-order cosmological perturbation theory for the open, flat and closed Friedmann-Lemaitre-Robertson-Walker universes admits one, and only one, gauge-invariant variable which describes the perturbation to the energy density and which becomes equal to the usual Newtonian energy density in the non-relativistic limit. The same holds true for the perturbation to the particle number density. Using these two new variables, a new manifestly gauge-invariant cosmological perturbation theory has been developed. Density perturbations evolve diabatically. Perturbations in the total energy density are gravitationally coupled to perturbations in the particle number density, irrespective of the nature of the particles. There is, in first-order, no back-reaction of perturbations to the global expansion of the universe. Small-scale perturbations in the radiation-dominated era oscillate with an increasing amplitude, whereas in older, less precise treatments, oscillating perturbations are found with a decr...
Kurtosis, skewness, and non-Gaussian cosmological density perturbations
Luo, Xiaochun; Schramm, David N.
1993-01-01
Cosmological topological defects as well as some nonstandard inflation models can give rise to non-Gaussian density perturbations. Skewness and kurtosis are the third and fourth moments that measure the deviation of a distribution from a Gaussian. Measurement of these moments for the cosmological density field and for the microwave background temperature anisotropy can provide a test of the Gaussian nature of the primordial fluctuation spectrum. In the case of the density field, the importance of measuring the kurtosis is stressed since it will be preserved through the weakly nonlinear gravitational evolution epoch. Current constraints on skewness and kurtosis of primeval perturbations are obtained from the observed density contrast on small scales and from recent COBE observations of temperature anisotropies on large scales. It is also shown how, in principle, future microwave anisotropy experiments might be able to reveal the initial skewness and kurtosis. It is shown that present data argue that if the initial spectrum is adiabatic, then it is probably Gaussian, but non-Gaussian isocurvature fluctuations are still allowed, and these are what topological defects provide.
Perturbation Theory of the Cosmological Log-Density Field
DEFF Research Database (Denmark)
Wang, Xin; Neyrinck, Mark; Szapudi, István
2011-01-01
, motivating an analytic study of it. In this paper, we develop cosmological perturbation theory for the power spectrum of this field. Our formalism is developed in the context of renormalized perturbation theory, which helps to regulate the convergence behavior of the perturbation series, and of the Taylor...
Cosmological history in York time: inflation and perturbations
Roser, Philipp
2016-01-01
The constant mean extrinsic curvature on a spacelike slice may constitute a physically preferred time coordinate, `York time'. One line of enquiry to probe this idea is to understand processes in our cosmological history in terms of York time. Following a review of the theoretical motivations, we focus on slow-roll inflation and the freezing and Hubble re-entry of cosmological perturbations. We show how the mathematical account of these processes is distinct from the conventional account in terms of standard cosmological or conformal time. We also consider the cosmological York-timeline more broadly and contrast it with the conventional cosmological timeline.
Cosmological history in York time: inflation and perturbations
Roser, Philipp; Valentini, Antony
2017-02-01
The constant mean extrinsic curvature on a spacelike slice may constitute a physically preferred time coordinate, `York time'. One line of enquiry to probe this idea is to understand processes in our cosmological history in terms of York time. Following a review of the theoretical motivations, we focus on slow-roll inflation and the freezing and Hubble re-entry of cosmological perturbations. While the physics is, of course, observationally equivalent, we show how the mathematical account of these processes is distinct from the conventional account in terms of standard cosmological or conformal time. We also consider the cosmological York-timeline more broadly and contrast it with the conventional cosmological timeline.
Cosmology on all scales: a two-parameter perturbation expansion
Goldberg, Sophia R; Malik, Karim A
2016-01-01
We propose and construct a two-parameter perturbative expansion around a Friedmann-Lema\\^{i}tre-Robertson-Walker geometry that can be used to model high-order gravitational effects in the presence of non-linear structure. This framework reduces to the weak-field and slow-motion post-Newtonian treatment of gravity in the appropriate limits, but also includes the low-amplitude large-scale fluctuations that are important for cosmological modelling. We derive a set of field equations that can be applied to the late Universe, where non-linear structure exists on supercluster scales, and perform a detailed investigation of the associated gauge problem. This allows us to identify a consistent set of perturbed quantities in both the gravitational and matter sectors, and to construct a set of gauge-invariant quantities that correspond to each of them. The field equations, written in terms of these quantities, take on a relatively simple form, and allow the effects of small-scale structure on the large-scale properties...
On Perturbative Instability of Cosmology from Quantum Potential
Tawfik, Abdel Nasser; Dahab, Eiman Abou El; Harko, Tiberiu
2016-01-01
Apart from its debatable correctness, we examine the pertubative stability of the recently proposed cosmology from quantum potential. We find that the proposed quantum corrections invoke additional parameters which apparently introduce perturbative instability to the Universe.
Cosmological perturbations in massive gravity with doubly coupled matter
Gümrükçüoğlu, A Emir; Mukohyama, Shinji
2014-01-01
We investigate the cosmological perturbations around FLRW solutions to non- linear massive gravity with a new effective coupling to matter proposed recently. Unlike the case with minimal matter coupling, all five degrees of freedom in the gravity sector propagate on generic self-accelerating FLRW backgrounds. We study the stability of the cosmological solutions and put constraints on the parameters of the theory by demanding the correct sign for the kinetic terms for scalar, vector and tensor perturbations.
Cosmological perturbations in massive gravity with doubly coupled matter
Gümrükçüoğlu, A. Emir; Heisenberg, Lavinia; Mukohyama, Shinji
2015-02-01
We investigate the cosmological perturbations around FLRW solutions to non- linear massive gravity with a new effective coupling to matter proposed recently. Unlike the case with minimal matter coupling, all five degrees of freedom in the gravity sector propagate on generic self-accelerating FLRW backgrounds. We study the stability of the cosmological solutions and put constraints on the parameters of the theory by demanding the correct sign for the kinetic terms for scalar, vector and tensor perturbations.
A general theory of linear cosmological perturbations: bimetric theories
Lagos, Macarena
2016-01-01
We implement the method developed in [1] to construct the most general parametrised action for linear cosmological perturbations of bimetric theories of gravity. Specifically, we consider perturbations around a homogeneous and isotropic background, and identify the complete form of the action invariant under diffeomorphism transformations, as well as the number of free parameters characterising this cosmological class of theories. We discuss, in detail, the case without derivative interactions, and compare our results with those found in massive bigravity.
Dynamical Systems Approach to Magnetised Cosmological Perturbations
Hobbs, S; Hobbs, Stacey; Dunsby, Peter K. S.
2000-01-01
Assuming a large-scale homogeneous magnetic field, we follow the covariant and gauge-invariant approach used by Tsagas and Barrow to describe the evolution of density and magnetic field inhomogeneities and curvature perturbations in a matter-radiation universe. We use a two parameter approximation scheme to linearize their exact non-linear general-relativistic equations for magneto-hydrodynamic evolution. Using a two-fluid approach we set up the governing equations as a fourth order autonomous dynamical system. Analysis of the equilibrium points for the radiation dominated era lead to solutions similar to the super-horizon modes found analytically by Tsagas and Maartens. We find that a study of the dynamical system in the dust-dominated era leads naturally to a magnetic critical length scale closely related to the Jeans Length. Depending on the size of wavelengths relative to this scale, these solutions show three distinct behaviours: large-scale stable growing modes, intermediate decaying modes, and small-sc...
The Energy-Momentum Tensor for Cosmological Perturbations
Abramo, L R W; Mukhanov, V M
1997-01-01
We study the effective energy-momentum tensor (EMT) for cosmological perturbations and formulate the gravitational back-reaction problem in a gauge invariant manner. We analyze the explicit expressions for the EMT in the cases of scalar metric fluctuations and of gravitational waves and derive the resulting equations of state. The formalism is applied to investigate the back-reaction effects in chaotic inflation. We find that for long wavelength scalar and tensor perturbations, the effective energy density is negative and thus counteracts any pre-existing cosmological constant. For scalar perturbations during an epoch of inflation, the equation of state is de Sitter-like.
Approach to exact solutions of cosmological perturbations: Tachyon field inflation
Herrera, Ramón; Pérez, Roberto G.
2016-03-01
An inflationary universe scenario in the context of a tachyon field is studied. This study is carried out using an ansatz for the effective potential of cosmological perturbations U (η ). We describe in great detail the analytical solutions of the scalar and tensor perturbations for two different Ansätze for the effective potential of cosmological perturbations: Easther's model and an effective potential similar to power-law inflation. Also, we find from the background equations that the effective tachyonic potentials V (φ ) in both models satisfy the properties of a tachyonic potential. We consider the recent data from the Planck to constrain the parameters in our effective potential generating the cosmological perturbations.
The cosmological origins of nonlinear Electrodynamics
Novello, M
2016-01-01
We present a mechanism that allows to describe any nonlinear theory of Electrodynamics as a consequence of the coupling of the electromagnetic field to gravity in the presence of a vacuum represented by the cosmological constant. We emphasize gravity\\rq s exclusive role of catalysis.
Cosmological N -body simulations including radiation perturbations
DEFF Research Database (Denmark)
Brandbyge, Jacob; Rampf, Cornelius; Tram, Thomas
2017-01-01
Cosmological $N$-body simulations are the standard tool to study the emergence of the observed large-scale structure of the Universe. Such simulations usually solve for the gravitational dynamics of matter within the Newtonian approximation, thus discarding general relativistic effects such as th......Cosmological $N$-body simulations are the standard tool to study the emergence of the observed large-scale structure of the Universe. Such simulations usually solve for the gravitational dynamics of matter within the Newtonian approximation, thus discarding general relativistic effects...
xPand: An algorithm for perturbing homogeneous cosmologies
Pitrou, Cyril; Umeh, Obinna
2013-01-01
In the present paper, we develop in detail a fully geometrical method for deriving perturbation equations about a spatially homogeneous background. This method relies on the 3+1 splitting of the background space-time and does not use any particular set of coordinates: it is implemented in terms of geometrical quantities only, using the tensor algebra package xTensor in the xAct distribution along with the extension for perturbations xPert. Our algorithm allows one to obtain the perturbation equations for all types of homogeneous cosmologies, up to any order and in all possible gauges. As applications, we recover the well-known perturbed Einstein equations for Friedmann--Lema\\^itre--Robertson--Walker cosmologies up to second order and for Bianchi I cosmologies at first order. This work opens the door to the study of these models at higher order and to that of any other perturbed Bianchi cosmologies, by circumventing the usually too cumbersome derivation of the perturbed equations.
Hamilton-Jacobi formalism of tachyon inflation and cosmological perturbations
Directory of Open Access Journals (Sweden)
LIU Daojun
2014-08-01
Full Text Available We study the cosmological inflation models driven by the rolling tachyon field which has a Born-Infeld-type action.We drive the Hamilton-Jacobi equation for the cosmological dynamics of tachyon inflation and the mode equations for the scalar and tensor perturbations of tachyon field and spacetime, then a solution under the slow-roll condition is given. In the end,a realistic model from string theory is discussed.
Exactly solvable model for cosmological perturbations in dilatonic brane worlds
Koyama, K; Koyama, Kazuya; Takahashi, Keitaro
2003-01-01
We construct a model where cosmological perturbations are analytically solved based on dilatonic brane worlds. A bulk scalar field has an exponential potential in the bulk and an exponential coupling to the brane tension. The bulk scalar field yields a power-law inflation on the brane. The exact background metric can be found including the back-reaction of the scalar field. Then exact solutions for cosmological perturbations which properly satisfy the junction conditions on the brane are derived. These solutions provide us an interesting model to understand the connection between the behavior of cosmological perturbations on the brane and the geometry of the bulk. Using these solutions, the behavior of an anisotropic stress induced on the inflationary brane by bulk gravitational fields is investigated.
Remarks on the Theory of Cosmological Perturbation
Institute of Scientific and Technical Information of China (English)
林文斌
2001-01-01
It is shown that the power spectrum defined in the synchronous gauge cannot be directly used to calculate the predictions of cosmological models on the large-scale structure of the Universe, which should be calculated directly by a suitable gauge-invariant power spectrum or the power spectrum defined in the Newtonian gauge.
Scale invariant density perturbations from cyclic cosmology
Frampton, Paul Howard
2016-04-01
It is shown how quantum fluctuations of the radiation during the contraction era of a comes back empty (CBE) cyclic cosmology can provide density fluctuations which re-enter the horizon during the subsequent expansion era and at lowest order are scale invariant, in a Harrison-Zel’dovich-Peebles sense. It is necessary to be consistent with observations of large scale structure.
Non-linear (loop) quantum cosmology
Bojowald, Martin; Dantas, Christine C; Jaffe, Matthew; Simpson, David
2012-01-01
Inhomogeneous quantum cosmology is modeled as a dynamical system of discrete patches, whose interacting many-body equations can be mapped to a non-linear minisuperspace equation by methods analogous to Bose-Einstein condensation. Complicated gravitational dynamics can therefore be described by more-manageable equations for finitely many degrees of freedom, for which powerful solution procedures are available, including effective equations. The specific form of non-linear and non-local equations suggests new questions for mathematical and computational investigations, and general properties of non-linear wave equations lead to several new options for physical effects and tests of the consistency of loop quantum gravity. In particular, our quantum cosmological methods show how sizeable quantum corrections in a low-curvature universe can arise from tiny local contributions adding up coherently in large regions.
Fully nonlinear and exact perturbations of the Friedmann world model
Hwang, Jai-chan
2012-01-01
In 1988 Bardeen has suggested a pragmatic formulation of cosmological perturbation theory which is powerful in practice to employ various fundamental gauge conditions easily depending on the character of the problem. The perturbation equations are presented without fixing the temporal gauge condition and are arranged so that one can easily impose fundamental gauge conditions by simply setting one of the perturbation variables in the equations equal to zero. In this way one can use the gauge degrees of freedom as an advantage in handling problems. Except for the synchronous gauge condition, all the other fundamental gauge conditions completely fix the gauge mode, and consequently, each variable in such a gauge has a unique gauge invariant counterpart, so that we can identify the variable as the gauge-invariant one. Here, we extend Bardeen's linear formulation to fully nonlinear order in perturbations, with the gauge advantage kept intact. Derived equations are exact, and from these we can easily expand to high...
Producing a scale-invariant spectrum of perturbations in a Hagedorn phase of string cosmology.
Nayeri, Ali; Brandenberger, Robert H; Vafa, Cumrun
2006-07-14
We study the generation of cosmological perturbations during the Hagedorn phase of string gas cosmology. Using tools of string thermodynamics we provide indications that it may be possible to obtain a nearly scale-invariant spectrum of cosmological fluctuations on scales which are of cosmological interest today. In our cosmological scenario, the early Hagedorn phase of string gas cosmology goes over smoothly into the radiation-dominated phase of standard cosmology, without having a period of cosmological inflation.
Cosmological perturbations in mimetic Horndeski gravity
Arroja, Frederico; Karmakar, Purnendu; Matarrese, Sabino
2016-01-01
We study linear scalar perturbations around a flat FLRW background in mimetic Horndeski gravity. In the absence of matter, we show that the Newtonian potential satisfies a second-order differential equation with no spatial derivatives. This implies that the sound speed for scalar perturbations is exactly zero on this background. We also show that in mimetic $G^3$ theories the sound speed is equally zero. We obtain the equation of motion for the comoving curvature perturbation (first order differential equation) and solve it to find that the comoving curvature perturbation is constant on all scales in mimetic Horndeski gravity. We find solutions for the Newtonian potential evolution equation in two simple models. Finally we show that the sound speed is zero on all backgrounds and therefore the system does not have any wave-like scalar degrees of freedom.
Cosmological scalar field perturbations can grow
Alcubierre, Miguel; Diez-Tejedor, Alberto; Torres, José M
2015-01-01
It has been argued that the small perturbations in the energy density to the homogeneous and isotropic configurations of a canonical scalar field in an expanding universe do not grow. We show that this is not true in general, and clarify the root of the misunderstanding. We revisit a simple model in which the linear perturbations grow like those in the standard cold dark matter scenario, but with the Jeans length at the scale of the Compton wavelength of the scalar particle.
A decoupled system of hyperbolic equations for linearized cosmological perturbations
Ramírez, J
2002-01-01
A decoupled system of hyperbolic partial differential equations for linear perturbations around spatially flat FRW universes is obtained for the first time. The two key ingredients in obtaining this system are i) the explicit decomposition of the perturbing energy momentum tensor into two pieces: intrinsic and free, which have definite and distinct mathematical properties and physical interpretation, and ii) the introduction of a new gauge which plays a similar role as harmonic gauge does for perturbations around Minkowski space-time. The proposed formalism could be highly relevant for physical cosmology, since our universe is most likely flat. We deal with classical perturbations, but our treatment, being covariant, is also very appropriate for the description of linearized quantum gravity around cosmological backgrounds.
Perturbations of Kantowski-Sachs models with a cosmological constant
Keresztes, Zoltán; Bradley, Michael; Dunsby, Peter K S; Gergely, László Á
2013-01-01
We investigate perturbations of Kantowski-Sachs models with a positive cosmological constant, using the gauge invariant 1+3 and 1+1+2 covariant splits of spacetime together with a harmonic decomposition. The perturbations are assumed to be vorticity-free and of perfect fluid type, but otherwise include general scalar, vector and tensor modes. In this case the set of equations can be reduced to six evolution equations for six harmonic coefficients.
Cosmological perturbation effects on gravitational-wave luminosity distance estimates
Bertacca, Daniele; Raccanelli, Alvise; Bartolo, Nicola; Matarrese, Sabino
2017-01-01
Waveforms of gravitational waves provide information about a variety of parameters for the binary system merging. However, standard calculations have been performed assuming a FLRW universe with no perturbations. In reality this assumption should be dropped: we show that the inclusion of cosmological perturbations translates into corrections to the estimate of astrophysical parameters derived for the merging binary systems. We compute corrections to the estimate of the luminosity distance due...
Cosmological perturbations on the Phantom brane
Bag, Satadru; Shtanov, Yuri; Sahni, Varun
2016-01-01
We obtain a closed system of equations for scalar perturbations in a multi-component braneworld. Our braneworld possesses a phantom-like equation of state at late times, $w_{\\rm eff} < -1$, but no big-rip future singularity. In addition to matter and radiation, the braneworld possesses a new effective degree of freedom - the 'Weyl fluid' or 'dark radiation'. Setting initial conditions on super-Hubble spatial scales at the epoch of radiation domination, we evolve perturbations of radiation, pressureless matter and the Weyl fluid until the present epoch. We observe a gradual decrease in the amplitude of the Weyl-fluid perturbations after Hubble-radius crossing, which results in a negligible effect of the Weyl fluid on the evolution of matter perturbations on spatial scales relevant for structure formation. Consequently, the quasi-static approximation of Koyama and Maartens provides a good fit to the exact results during the matter-dominated epoch. We find that the late-time growth of density perturbations on...
A parametrisation of modified gravity on nonlinear cosmological scales
Lombriser, Lucas
2016-11-01
Viable modifications of gravity on cosmological scales predominantly rely on screening mechanisms to recover Einstein's Theory of General Relativity in the Solar System, where it has been well tested. A parametrisation of the effects of such modifications in the spherical collapse model is presented here for the use of modelling the modified nonlinear cosmological structure. The formalism allows an embedding of the different screening mechanisms operating in scalar-tensor theories through large values of the gravitational potential or its first or second derivatives as well as of linear suppression effects or more general transitions between modified and Einstein gravity limits. Each screening or suppression mechanism is parametrised by a time, mass, and environment dependent screening scale, an effective modified gravitational coupling in the fully unscreened limit that can be matched to linear theory, the exponent of a power-law radial profile of the screened coupling, determined by derivatives, symmetries, and potentials in the scalar field equation, and an interpolation rate between the screened and unscreened limits. Along with generalised perturbative methods, the parametrisation may be used to formulate a nonlinear extension to the linear parametrised post-Friedmannian framework to enable generalised tests of gravity with the wealth of observations from the nonlinear cosmological regime.
Fractality in a Perturbed Einstein-de Sitter Cosmology
Abdalla, Elcio; Ribeiro, M B; Abdalla, Elcio; Mohayaee, Roya; Ribeiro, Marcelo B.
1999-01-01
This work presents the first step of an attempt to check the validity of a hypothesis known as the ``apparent fractal conjecture'' (Ribeiro 1999), according to which the observed fractal structure of large-scale distribution of galaxies arises when observational quantities are calculated along the past light cone. Inasmuch as general relativity states that astronomical observations are carried out in this spacetime hypersurface, observational quantities relevant for direct comparison with astronomical data must be calculated along it. Implementing this condition profoundly changes the behaviour of many observables in the standard cosmological models. In particular, the observed average density, becomes inhomogeneous, even in the spatially homogeneous spacetime of standard cosmology. Such a change in the observational quantities has already been fully analysed in previous works by Ribeiro (1992b, 1993, 1994, 1995) for a non-perturbed cosmological model. Here we derive observational relations in a perturbed Ein...
Gauge invariant cosmological perturbations for the nonminimally coupled inflaton field
Weenink, J.; Prokopec, T.
2010-01-01
We construct the gauge invariant free action for cosmological perturbations for the nonminimally coupled inflaton field in the Jordan frame. For this the phase space formalism is used, which keeps track of all the dynamical and constraint fields. We perform explicit conformal transformations to demo
Cosmological perturbations in transient phantom inflation scenarios
Energy Technology Data Exchange (ETDEWEB)
Richarte, Martin G. [Universidade Federal do Parana, Departamento de Fisica, Caixa Postal 19044, Curitiba (Brazil); Universidad de Buenos Aires, Ciudad Universitaria 1428, Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Buenos Aires (Argentina); Kremer, Gilberto M. [Universidade Federal do Parana, Departamento de Fisica, Caixa Postal 19044, Curitiba (Brazil)
2017-01-15
We present a model of inflation where the inflaton is accommodated as a phantom field which exhibits an initial transient pole behavior and then decays into a quintessence field which is responsible for a radiation era. We must stress that the present unified model only deals with a single field and that the transition between the two eras is achieved in a smooth way, so the model does not suffer from the eternal inflation issue. We explore the conditions for the crossing of the phantom divide line within the inflationary era along with the structural stability of several critical points. We study the behavior of the phantom field within the slow-climb approximation along with the necessary conditions to have sufficient inflation. We also examine the model at the level of classical perturbations within the Newtonian gauge and determine the behavior of the gravitational potential, contrast density and perturbed field near the inflation stage and the subsequent radiation era. (orig.)
Cosmological scalar field perturbations can grow
Alcubierre, Miguel; de la Macorra, Axel; Diez-Tejedor, Alberto; Torres, José M.
2015-09-01
It has been argued that the small perturbations to the homogeneous and isotropic configurations of a canonical scalar field in an expanding universe do not grow. We show that this is not true in general, and clarify the root of the misunderstanding. We revisit a simple model in which the zero mode of a free scalar field oscillates with high frequency around the minimum of the potential. Under this assumption the linear perturbations grow like those in the standard cold dark matter scenario, but with a Jeans length at the scale of the Compton wavelength of the scalar particle. Contrary to previous analyses in the literature our results do not rely on time averages and/or fluid identifications, and instead we solve both analytically (in terms of a well-defined series expansion) and numerically the linearized Einstein-Klein-Gordon system. Also, we use gauge-invariant fields, which makes the physical analysis more transparent and simplifies the comparison with previous works carried out in different gauges. As a byproduct of this study we identify a time-dependent modulation of the different physical quantities associated to the background as well as the perturbations with potential observational consequences in dark matter models.
Amplification of curvature perturbations in cyclic cosmology
Zhang, Jun; Liu, Zhi-Guo; Piao, Yun-Song
2010-12-01
We analytically and numerically show that through the cycles with nonsingular bounce, the amplitude of curvature perturbation on a large scale will be amplified and the power spectrum will redden. In some sense, this amplification will eventually destroy the homogeneity of the background, which will lead to the ultimate end of cycles of the global universe. We argue that for the model with increasing cycles, it might be possible that a fissiparous multiverse will emerge after one or several cycles, in which the cycles will continue only at corresponding local regions.
Inflationary cosmology with nonlinear dispersion relations
Zhu, Tao; Cleaver, Gerald; Kirsten, Klaus; Sheng, Qin
2013-01-01
We present a technique, {\\em the uniform asymptotic approximation}, to construct accurate analytical solutions of the linear perturbations of inflation after quantum effects of the early universe are taken into account, for which the dispersion relations generically become nonlinear. We construct explicitly the error bounds associated with the approximations and then study them in detail. With the understanding of the errors and the proper choice of the Liouville transformations of the differential equations of the perturbations, we show that the analytical solutions describe the exact evolution of the linear perturbations extremely well even only to the first-order approximations. As a simple application of the approximate analytical solutions, we calculate the power spectra and indices of scalar and tensor perturbations in the de Sitter background, and find that the amplitudes of the power spectra get modified due to the quantum effects, while the power spectrum indices remain the same as in the linear case...
Cosmological Perturbations in Restricted f(R)-Gravity
Chaichian, M; Kluson, J
2016-01-01
We investigate the metric perturbations of the restricted f(R) theory of gravity in the cosmological context and explore the phenomenological implications of this model. We show that it is possible to construct a restricted model of gravity, in which the background equations are the same as the equations of motion which are derived from the Einstein-Hilbert action with the cosmological constant term. We argue that the deviation from the Einstein-Hilbert model emerges in the perturbed equations, for which we have a non-vanishing anisotropic stress. Further, with the help of the results of Planck data for the modified gravity we obtain constraints on the parameters of the model.
One-particle-irreducible consistency relations for cosmological perturbations
Goldberger, Walter D; Nicolis, Alberto
2013-01-01
We derive consistency relations for correlators of scalar cosmological perturbations which hold in the "squeezed limit" in which one or more of the external momenta become soft. Our results are formulated as relations between suitably defined one-particle irreducible N-point and (N-1)-point functions that follow from residual spatial conformal diffeomorphisms of the unitary gauge Lagrangian. As such, some of these relations are exact to all orders in perturbation theory, and do not rely on approximate deSitter invariance or other dynamical assumptions (e.g., properties of the operator product expansion or the behavior of modes at horizon crossing). The consistency relations apply model-independently to cosmological scenarios where the time evolution is driven by a single scalar field. Besides reproducing the known results for single-field inflation in the slow roll limit, we verify that our consistency relations hold more generally, for instance in ghost condensate models in flat space. We comment on possible...
Hamiltonian cosmological perturbation theory with loop quantum gravity corrections
Bojowald, M; Kagan, M; Singh, P; Skirzewski, A; Bojowald, Martin; Hern\\'andez, Hector H.; Kagan, Mikhail; Singh, Parampreet; Skirzewski, Aureliano
2006-01-01
Cosmological perturbation equations are derived systematically in a canonical scheme based on Ashtekar variables. A comparison with the covariant derivation and various subtleties in the calculation and choice of gauges are pointed out. Nevertheless, the treatment is more systematic when correction terms of canonical quantum gravity are to be included. This is done throughout the paper for one characteristic modification expected from loop quantum gravity.
Non-linear interactions in a cosmological background in the DGP braneworld
Koyama, K; Koyama, Kazuya; Silva, Fabio P
2007-01-01
We study quasi-static perturbations in a cosmological background in the Dvali-Gabadadze-Porrati (DGP) braneworld model. We identify the Vainshtein radius at which the non-linear interactions of the brane bending mode become important in a cosmological background. The Vainshtein radius in the early universe is much smaller than the one in the Minkowski background, but in a self-accelerating universe it is the same as the Minkowski background. Our result shows that the perturbative approach is applicable beyond the Vainshtein radius for weak gravity by taking into account the second order effects of the brane bending mode. The linearised cosmological perturbations are shown to be smoothly matched to the solutions inside the Vainshtein radius. We emphasize the importance of imposing a regularity condition in the bulk by solving the 5D perturbations and we highlight the problem of ad hoc assumptions on the bulk gravity that lead to different conclusions.
Primordial power spectra for scalar perturbations in loop quantum cosmology
de Blas, Daniel Martín
2016-01-01
We provide the power spectrum of small scalar perturbations propagating in an inflationary scenario within loop quantum cosmology. We consider the hybrid quantization approach applied to a Friedmann--Robertson--Walker spacetime with flat spatial sections coupled to a massive scalar field. We study the quantum dynamics of scalar perturbations on an effective background within this hybrid approach. We consider in our study adiabatic states of different orders. For them, we find that the hybrid quantization is in good agreement with the predictions of the dressed metric approach. We also propose an initial vacuum state for the perturbations, and compute the primordial and the anisotropy power spectrum in order to qualitatively compare with the current observations of Planck mission. We find that our vacuum state is in good agreement with them, showing a suppression of the power spectrum for large scale anisotropies. We compare with other choices already studied in the literature.
Early time perturbations behaviour in scalar field cosmologies
Perrotta, F; Perrotta, Francesca; Baccigalupi, Carlo
1999-01-01
We consider the problem of the initial conditions and behaviour of the perturbations in scalar field cosmology with general potential. We use the general definition of adiabatic and isocurvature conditions to set the appropriate initial values for the perturbation in the scalar field and in the ordinary matter and radiation components. In both the cases of initial adiabaticity and isocurvature, we solve the Einstein and fluid equation at early times and on superhorizon scales to find the initial behaviour of the relevant quantities. In particular, in the isocurvature case, we consider models in which the initial perturbation arises from the matter as well as from the scalar field itself, provided that the initial value of the gauge invariant curvature is zero. We extend the standard code to include all these cases, and we show some results concerning the power spectrum of the cosmic microwave background temperature anisotropies. In particular, it turns out that the acoustic peaks follow opposite behaviours in...
Perturbations of normally solvable nonlinear operators, I
Directory of Open Access Journals (Sweden)
William O. Ray
1985-01-01
Full Text Available Let X and Y be Banach spaces and let ℱ and be Gateaux differentiable mappings from X to Y In this note we study when the operator ℱ+ is surjective for sufficiently small perturbations of a surjective operator ℱ The methods extend previous results in the area of normal solvability for nonlinear operators.
Coupled Oscillator Model for Nonlinear Gravitational Perturbations
Yang, Huan; Green, Stephen R; Lehner, Luis
2015-01-01
Motivated by the gravity/fluid correspondence, we introduce a new method for characterizing nonlinear gravitational interactions. Namely we map the nonlinear perturbative form of the Einstein equation to the equations of motion of a collection of nonlinearly-coupled harmonic oscillators. These oscillators correspond to the quasinormal or normal modes of the background spacetime. We demonstrate the mechanics and the utility of this formalism within the context of perturbed asymptotically anti-de Sitter black brane spacetimes. We confirm in this case that the boundary fluid dynamics are equivalent to those of the hydrodynamic quasinormal modes of the bulk spacetime. We expect this formalism to remain valid in more general spacetimes, including those without a fluid dual. In other words, although borne out of the gravity/fluid correspondence, the formalism is fully independent and it has a much wider range of applicability. In particular, as this formalism inspires an especially transparent physical intuition, w...
SOLVABILITY FOR NONLINEAR ELLIPTIC EQUATION WITH BOUNDARY PERTURBATION
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The solvability of nonlinear elliptic equation with boundary perturbation is considered. The perturbed solution of original problem is obtained and the uniformly valid expansion of solution is proved.
FAST-PT: a novel algorithm to calculate convolution integrals in cosmological perturbation theory
McEwen, Joseph E.; Fang, Xiao; Hirata, Christopher M.; Blazek, Jonathan A.
2016-09-01
We present a novel algorithm, FAST-PT, for performing convolution or mode-coupling integrals that appear in nonlinear cosmological perturbation theory. The algorithm uses several properties of gravitational structure formation—the locality of the dark matter equations and the scale invariance of the problem—as well as Fast Fourier Transforms to describe the input power spectrum as a superposition of power laws. This yields extremely fast performance, enabling mode-coupling integral computations fast enough to embed in Monte Carlo Markov Chain parameter estimation. We describe the algorithm and demonstrate its application to calculating nonlinear corrections to the matter power spectrum, including one-loop standard perturbation theory and the renormalization group approach. We also describe our public code (in Python) to implement this algorithm. The code, along with a user manual and example implementations, is available at https://github.com/JoeMcEwen/FAST-PT.
FAST-PT: a novel algorithm to calculate convolution integrals in cosmological perturbation theory
McEwen, Joseph E; Hirata, Christopher M; Blazek, Jonathan A
2016-01-01
We present a novel algorithm, FAST-PT, for performing convolution or mode-coupling integrals that appear in nonlinear cosmological perturbation theory. The algorithm uses several properties of gravitational structure formation -- the locality of the dark matter equations and the scale invariance of the problem -- as well as Fast Fourier Transforms to describe the input power spectrum as a superposition of power laws. This yields extremely fast performance, enabling mode-coupling integral computations fast enough to embed in Monte Carlo Markov Chain parameter estimation. We describe the algorithm and demonstrate its application to calculating nonlinear corrections to the matter power spectrum, including one-loop standard perturbation theory and the renormalization group approach. We also describe our public code (in Python) to implement this algorithm, including the applications described here.
Effective gravitational couplings for cosmological perturbations in generalized Proca theories
De Felice, Antonio; Heisenberg, Lavinia; Kase, Ryotaro; Mukohyama, Shinji; Tsujikawa, Shinji; Zhang, Ying-li
2016-08-01
We consider the finite interactions of the generalized Proca theory including the sixth-order Lagrangian and derive the full linear perturbation equations of motion on the flat Friedmann-Lemaître-Robertson-Walker background in the presence of a matter perfect fluid. By construction, the propagating degrees of freedom (besides the matter perfect fluid) are two transverse vector perturbations, one longitudinal scalar, and two tensor polarizations. The Lagrangians associated with intrinsic vector modes neither affect the background equations of motion nor the second-order action of tensor perturbations, but they do give rise to nontrivial modifications to the no-ghost condition of vector perturbations and to the propagation speeds of vector and scalar perturbations. We derive the effective gravitational coupling Geff with matter density perturbations under a quasistatic approximation on scales deep inside the sound horizon. We find that the existence of intrinsic vector modes allows a possibility for reducing Geff. In fact, within the parameter space, Geff can be even smaller than the Newton gravitational constant G at the late cosmological epoch, with a peculiar phantom dark energy equation of state (without ghosts). The modifications to the slip parameter η and the evolution of the growth rate f σ8 are discussed as well. Thus, dark energy models in the framework of generalized Proca theories can be observationally distinguished from the Λ CDM model according to both cosmic growth and expansion history. Furthermore, we study the evolution of vector perturbations and show that outside the vector sound horizon the perturbations are nearly frozen and start to decay with oscillations after the horizon entry.
Garcia-Salcedo, Ricardo; Quiros, Israel
2013-01-01
Here we investigate the cosmic dynamics of Friedmann-Robertson-Walker universes -- flat spatial sections -- which are driven by nonlinear electrodynamics (NLED) Lagrangians. We pay special attention to the check of the sign of the square sound speed since, whenever the latter quantity is negative, the corresponding cosmological model is classically unstable against small perturbations of the background energy density. Besides, based on causality arguments, one has to require that the mentioned small perturbations of the background should propagate at most at the local speed of light. We also look for the occurrence of curvature singularities. Our results indicate that several cosmological models which are based in known NLED Lagrangians, either are plagued by curvature singularities of the sudden and/or big rip type, or are violently unstable against small perturbations of the cosmological background -- due to negative sign of the square sound speed -- or both. In addition, causality issues associated with su...
Fully nonlinear and exact perturbations of the Friedmann world model: non-flat background
Energy Technology Data Exchange (ETDEWEB)
Noh, Hyerim, E-mail: hr@kasi.ac.kr [Korea Astronomy and Space Science Institute, Daejeon, 305-348 (Korea, Republic of)
2014-07-01
We extend the fully non-linear and exact cosmological perturbation equations in a Friedmann background universe to include the background curvature. The perturbation equations are presented in a gauge ready form, so any temporal gauge condition can be adopted freely depending on the problem to be solved. We consider the scalar, and vector perturbations without anisotropic stress. As an application, we analyze the equations in the special case of irrotational zero-pressure fluid in the comoving gauge condition. We also present the fully nonlinear formulation for a minimally coupled scalar field.
Fully nonlinear and exact perturbations of the Friedmann world model: Non-flat background
Noh, Hyerim
2014-01-01
We extend the fully non-linear and exact cosmological perturbation equations in a Friedmann background universe to include the background curvature. The perturbation equations are presented in a gauge ready form, so any temporal gauge condition can be adopted freely depending on the problem to be solved. %The background curvature term explicitly appears only in the energy and momentum constraint equations. We consider the scalar, and vector perturbations without anisotropic stress. As an application, we analyze the equations in the special case of irrotational zero-pressure fluid in the comoving gauge condition. We also present the fully nonlinear formulation for a minimally coupled scalar field.
Nonlinear Effects in the Amplitude of Cosmological Density Fluctuations
Juszkiewicz, Roman; Fry, J N; Jaffe, Andrew H
2009-01-01
The amplitude of cosmological density fluctuations, $\\sigma_8$, has been studied and estimated by analysing many cosmological observations. The values of the estimates vary considerably between the various probes. However, different estimators probe the value of $\\sigma_8$ in different cosmological scales and do not take into account the nonlinear evolution of the parameter at late times. We show that estimates of the amplitude of cosmological density fluctuations derived from cosmic flows are systematically higher than those inferred at early epochs because of nonlinear evolution at later times. Here we derive corrections to the value of $\\sigma_8$ and compare amplitudes after accounting for this effect.
Adiabaticity and gravity theory independent conservation laws for cosmological perturbations
Romano, Antonio Enea; Sasaki, Misao
2015-01-01
We carefully study the implications of adiabaticity for the behavior of cosmological perturbations. There are essentially three similar but different definitions of non-adiabaticity: one is appropriate for a thermodynamic fluid $\\delta P_{nad}$, another is for a general matter field $\\delta P_{c,nad}$, and the last one is valid only on superhorizon scales. The first two definitions coincide if $c_s^2=c_w^2$ where $c_s$ is the propagation speed of the perturbation, while $c_w^2=\\dot P/\\dot\\rho$. Assuming the adiabaticity in the general sense, $\\delta P_{c,nad}=0$, we derive a relation between the lapse function in the comoving slicing $A_c$ and $\\delta P_{nad}$ valid for arbitrary matter field in any theory of gravity, by using only momentum conservation. The relation implies that as long as $c_s\
Cosmological perturbation theory in the synchronous and conformal newtonian gauges
Ma Chung Pei; Ma, Chung Pei; Bertschinger, Edmund
1995-01-01
This paper presents a systematic treatment of the linear theory of scalar gravitational perturbations in the synchronous gauge and the conformal Newtonian (or longitudinal) gauge. It differs from others in the literature in that we give, in both gauges, a complete discussion of all particle species that are relevant to any flat cold dark matter (CDM), hot dark matter (HDM), or CDM+HDM models (including a possible cosmological constant). The particles considered include CDM, baryons, photons, massless neutrinos, and massive neutrinos (an HDM candidate), where the CDM and baryons are treated as fluids while a detailed phase-space description is given to the photons and neutrinos. Particular care is applied to the massive neutrino component, which has been either ignored or approximated crudely in previous works. Isentropic initial conditions on super-horizon scales are derived. The coupled, linearized Boltzmann, Einstein and fluid equations that govern the evolution of the metric and density perturbations are t...
Can superhorizon cosmological perturbations explain the acceleration of the universe?
Hirata, C M; Hirata, Christopher M.; Seljak, Uros
2005-01-01
We investigate the recent suggestions by Barausse et al. (astro-ph/0501152) and Kolb et al. (hep-th/0503117) that the acceleration of the universe could be explained by large superhorizon fluctuations generated by inflation. We show that no acceleration can be produced by this mechanism. We begin by showing how the application of Raychaudhuri equation to inhomogeneous cosmologies results in several ``no go'' theorems for accelerated expansion. Next we derive an exact solution for a specific case of initial perturbations, for which application of the Kolb et al. expressions leads to an acceleration, while the exact solution reveals that no acceleration is present. We show that the discrepancy can be traced to higher order terms that were dropped in the Kolb et al. analysis. We proceed with the analysis of initial value formulation of general relativity to argue that causality severely limits what observable effects can be derived from superhorizon perturbations. By constructing a Riemann normal coordinate syst...
Shortcomings in the Understanding of Why Cosmological Perturbations Look Classical
Sudarsky, Daniel
2009-01-01
There is a persistent state of confusion regarding the account of the quantum origin of the seeds of cosmological structure during inflation. In fact, a recent article (C. Kiefer & D. Polarski, ArXiv: 0810.0087 [astro-ph]) addresses the question "Why do the Cosmological Perturbations look Classical?" and offers an answer based on unitary quantum mechanics (i.e., without reference to the projection postulate) relying on the decoherence type of analysis. The argument is, thus, implicitly assuming that decoherence offers a satisfactory solution to the measurement problem in quantum mechanics. We will review here, why do we, together with various other researchers in the field, consider that this is not the case, in general, and particularly not at all in the situation at hand. In fact, as has been previously discussed (A. Perez, H. Sahlmann, and D. Sudarsky, CQG 23, 2317, (2006);[arXiv: gr-qc/0508100]), we will argue that the cosmological situation is one where the measurement problem of quantum mechanics ap...
Strongly Nonlinear Transverse Perturbations in Phononic Crystals
Directory of Open Access Journals (Sweden)
S. Nikitenkova
2014-01-01
Full Text Available The dynamics of the surface heterogeneities formation in low-dimensional phononic crystals is studied. It is shown that phononic transverse perturbations in this medium are highly nonlinear. They can be described with the help of the Riemann wave and may form stable wave structures of the finite amplitude. The Riemann wave deformation is described analytically. The Riemann wave time existence up to the beginning of the gradient catastrophe is calculated.
The de Sitter limit of inflation and non-linear perturbation theory
DEFF Research Database (Denmark)
Jarnhus, Philip; Sloth, Martin Snoager
2008-01-01
We study the fourth order action of the comoving curvature perturbation in an inflationary universe in order to understand more systematically the de Sitter limit in nonlinear cosmological perturbation theory. We derive the action of the curvature perturbation to fourth order in the comoving gaug......, and show that it vanishes sufficiently fast in the de Sitter limit. By studying the de Sitter limit, we then extrapolate to the n'th order action of the comoving curvature perturbation and discuss the slow-roll order of the n-point correlation function....
The de Sitter limit of inflation and non-linear perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Jarnhus, Philip R; Sloth, Martin S, E-mail: pjarn@phys.au.dk, E-mail: sloth@phys.au.dk [Department of Physics and Astronomy, University of Aarhus, DK-8000 Aarhus C (Denmark)
2008-02-15
We study the fourth-order action of the comoving curvature perturbation in an inflationary universe in order to understand more systematically the de Sitter limit in non-linear cosmological perturbation theory. We derive the action of the curvature perturbation to fourth order in the comoving gauge, and show that it vanishes sufficiently fast in the de Sitter limit. By studying the de Sitter limit, we then extrapolate to the nth-order action of the comoving curvature perturbation and discuss the slow-roll order of the n-point correlation function.
One-particle-irreducible consistency relations for cosmological perturbations
Goldberger, Walter D.; Hui, Lam; Nicolis, Alberto
2013-05-01
We derive consistency relations for correlators of scalar cosmological perturbations that hold in the “squeezed limit” in which one or more of the external momenta become soft. Our results are formulated as relations between suitably defined one-particle-irreducible N-point and (N-1)-point functions that follow from residual spatial conformal diffeomorphisms of the unitary gauge Lagrangian. As such, some of these relations are exact to all orders in perturbation theory and do not rely on approximate de Sitter invariance or other dynamical assumptions (e.g., properties of the operator product expansion or the behavior of modes at the horizon crossing). The consistency relations apply model-independently to cosmological scenarios in which the time evolution is driven by a single scalar field. Besides reproducing the known results for single-field inflation in the slow-roll limit, we verify that our consistency relations hold more generally, for instance, in ghost condensate models in flat space. We comment on possible extensions of our results to multifield models.
Cosmological perturbations in coherent oscillating scalar field models
Energy Technology Data Exchange (ETDEWEB)
Cembranos, J.A.R.; Maroto, A.L.; Jareño, S.J. Núñez [Departamento de Física Teórica I, Universidad Complutense de Madrid,Avenida Complutense s/n, Madrid (Spain)
2016-03-03
The fact that fast oscillating homogeneous scalar fields behave as perfect fluids in average and their intrinsic isotropy have made these models very fruitful in cosmology. In this work we will analyse the perturbations dynamics in these theories assuming general power law potentials V(ϕ)=λ|ϕ|{sup n}/n. At leading order in the wavenumber expansion, a simple expression for the effective sound speed of perturbations is obtained c{sub eff}{sup 2}=ω=(n−2)/(n+2) with ω the effective equation of state. We also obtain the first order correction in k{sup 2}/ω{sub eff}{sup 2}, when the wavenumber k of the perturbations is much smaller than the background oscillation frequency, ω{sub eff}. For the standard massive case we have also analysed general anharmonic contributions to the effective sound speed. These results are reached through a perturbed version of the generalized virial theorem and also studying the exact system both in the super-Hubble limit, deriving the natural ansatz for δϕ; and for sub-Hubble modes, exploiting Floquet’s theorem.
Cosmological perturbations in coherent oscillating scalar field models
Cembranos, J A R; Jareño, S J Núñez
2015-01-01
The fact that fast oscillating homogeneous scalar fields behave as perfect fluids in average and their intrinsic isotropy have made these models very fruitful in cosmology. In this work we will analyse the perturbations dynamics in these theories assuming general power law potentials $V(\\phi)=\\lambda \\vert\\phi\\vert^{n}/n$. At leading order in the wavenumber expansion, a simple expression for the effective sound speed of perturbations is obtained $c_{\\text{eff}}^2 = \\omega=(n-2)/(n+2)$ with $\\omega$ the effective equation of state. We also obtain the first order correction in $k^2/\\omega_{\\text{eff}}^2$, when the wavenumber $k$ of the perturbations is much smaller than the background oscillation frequency, $\\omega_{\\text{eff}}$. For the standard massive case we have also analysed general anharmonic contributions to the effective sound speed. These results are reached through a perturbed version of the generalized virial theorem and also studying the exact system both in the super-Hubble limit, deriving the nat...
Inflaton perturbations in brane-world cosmology with induced gravity
Koyama, K; Koyama, Kazuya; Mizuno, Shuntaro
2006-01-01
We study cosmological perturbations in the brane models with an induced Einstein-Hilbert term on a brane. We consider an inflaton confined to a de Sitter brane in a five-dimensional Minkowski spacetime. Inflaton fluctuations excite Kaluza-Klein modes of bulk metric perturbations with mass $m^2 = -2(2\\ell-1) (\\ell +1) H^2$ and $m^2 = -2\\ell(2\\ell+3) H^2$ where $\\ell$ is an integer. There are two branches ($\\pm$ branches) of solutions for the background spacetime. In the $+$ branch, which includes the self-accelerating universe, a resonance appears for a mode with $m^2 = 2 H^2$ due to a spin-0 perturbation with $m^2 = 2H^2$. The self-accelerating universe has a distinct feature because there is also a helicity-0 mode of spin-2 perturbations with $m^2 = 2H^2$. In the $-$ branch, which can be thought as the Randall-Sundrum type brane-world with the high energy quantum corrections, there is no resonance. At high energies, we analytically confirm that four-dimensional Einstein gravity is recovered, which is related...
Cosmological perturbations in coherent oscillating scalar field models
Cembranos, J. A. R.; Maroto, A. L.; Jareño, S. J. Núñez
2016-03-01
The fact that fast oscillating homogeneous scalar fields behave as perfect fluids in average and their intrinsic isotropy have made these models very fruitful in cosmology. In this work we will analyse the perturbations dynamics in these theories assuming general power law potentials V( ϕ) = λ| ϕ| n /n. At leading order in the wavenumber expansion, a simple expression for the effective sound speed of perturbations is obtained c eff 2 = ω = ( n - 2)/( n + 2) with ω the effective equation of state. We also obtain the first order correction in k 2/ ω eff 2 , when the wavenumber k of the perturbations is much smaller than the background oscillation frequency, ω eff. For the standard massive case we have also analysed general anharmonic contributions to the effective sound speed. These results are reached through a perturbed version of the generalized virial theorem and also studying the exact system both in the super-Hubble limit, deriving the natural ansatz for δϕ; and for sub-Hubble modes, exploiting Floquet's theorem.
Nonlinear Acoustics -- Perturbation Theory and Webster's Equation
Jorge, Rogério
2013-01-01
Webster's horn equation (1919) offers a one-dimensional approximation for low-frequency sound waves along a rigid tube with a variable cross-sectional area. It can be thought as a wave equation with a source term that takes into account the nonlinear geometry of the tube. In this document we derive this equation using a simplified fluid model of an ideal gas. By a simple change of variables, we convert it to a Schr\\"odinger equation and use the well-known variational and perturbative methods to seek perturbative solutions. As an example, we apply these methods to the Gabriel's Horn geometry, deriving the first order corrections to the linear frequency. An algorithm to the harmonic modes in any order for a general horn geometry is derived.
Cosmological Electromagnetic Fields due to Gravitational Wave Perturbations
Marklund, M; Brodin, G; Marklund, Mattias; Dunsby, Peter K. S.; Brodin, Gert
2000-01-01
We consider the dynamics of electromagnetic fields in an almost-Friedmann-Robertson-Walker universe using the covariant and gauge-invariant approach of Ellis and Bruni. Focusing on the situation where deviations from the background model are generated by tensor perturbations only, we demonstrate that the coupling between gravitational waves and a weak magnetic test field can generate electromagnetic waves. We show that this coupling leads to an initial pulse of electromagnetic waves whose width and amplitude is determined by the wavelengths of the magnetic field and gravitational waves. A number of implications for cosmology are discussed, in particular we calculate an upper bound of the magnitude of this effect using limits on the quadrapole anisotropy of the Cosmic Microwave Background.
Adiabatic density perturbations in a cosmological model with massive neutrinos
Jaroszynski, M.
Lifshitz (1946) has investigated the gravitational instability of a Friedmann Universe model. He treated the matter content of the universe as a single perfect fluid. In other studies, a two fluid approach was used to represent neutrinos and other kinds of matter separately. A distribution function was used by Peebles and Yu (1970), and also by Silk and Wilson (1980) to describe photons of the black-body background during and after the recombination of the primeval plasma. The approach used in the present investigation is similar, except for two differences. No collisional term is used in the kinetic equation, and massive particles are considered. A detailed description is provided of the method used to investigate the gravitational instability of a cosmological model with massive neutrinos. It is pointed out that the obtained results are preliminary. The final spectrum of perturbations is similar to those of Peebles and Yu (1970), and Wilson and Silk (1981).
Perturbation analysis of nonlinear matrix population models
Directory of Open Access Journals (Sweden)
Hal Caswell
2008-03-01
Full Text Available Perturbation analysis examines the response of a model to changes in its parameters. It is commonly applied to population growth rates calculated from linear models, but there has been no general approach to the analysis of nonlinear models. Nonlinearities in demographic models may arise due to density-dependence, frequency-dependence (in 2-sex models, feedback through the environment or the economy, and recruitment subsidy due to immigration, or from the scaling inherent in calculations of proportional population structure. This paper uses matrix calculus to derive the sensitivity and elasticity of equilibria, cycles, ratios (e.g. dependency ratios, age averages and variances, temporal averages and variances, life expectancies, and population growth rates, for both age-classified and stage-classified models. Examples are presented, applying the results to both human and non-human populations.
Nonlinear cosmological consistency relations and effective matter stresses
Energy Technology Data Exchange (ETDEWEB)
Ballesteros, Guillermo [Museo Storico della Fisica e Centro Studi e Ricerche ' ' Enrico Fermi' ' , Piazza del Viminale 1, I-00184 Rome (Italy); Hollenstein, Lukas; Jain, Rajeev Kumar; Kunz, Martin, E-mail: guillermo.ballesteros@pd.infn.it, E-mail: lukas.hollenstein@unige.ch, E-mail: rajeev.jain@unige.ch, E-mail: martin.kunz@unige.ch [Département de Physique Théorique and Center for Astroparticle Physics, Université de Genève, Quai E. Ansermet 24, CH-1211 Genève 4 (Switzerland)
2012-05-01
We propose a fully nonlinear framework to construct consistency relations for testing generic cosmological scenarios using the evolution of large scale structure. It is based on the covariant approach in combination with a frame that is purely given by the metric, the normal frame. As an example, we apply this framework to the ΛCDM model, by extending the usual first order conditions on the metric potentials to second order, where the two potentials start to differ from each other. We argue that working in the normal frame is not only a practical choice but also helps with the physical interpretation of nonlinear dynamics. In this frame, effective pressures and anisotropic stresses appear at second order in perturbation theory, even for ''pressureless'' dust. We quantify their effect and compare them, for illustration, to the pressure of a generic clustering dark energy fluid and the anisotropic stress in the DGP model. Besides, we also discuss the effect of a mismatch of the potentials on the determination of galaxy bias.
Cosmological $N$-body simulations including radiation perturbations
Brandbyge, Jacob; Tram, Thomas; Leclercq, Florent; Fidler, Christian; Hannestad, Steen
2016-01-01
Cosmological $N$-body simulations are the standard tool to study the emergence of the observed large-scale structure of the Universe. Such simulations usually solve for the gravitational dynamics of matter within the Newtonian approximation, thus discarding general relativistic effects such as the coupling between matter and radiation ($\\equiv$ photons and neutrinos). In this paper we investigate novel hybrid simulations which incorporate interactions between radiation and matter to the leading order in General Relativity, whilst evolving the matter dynamics in full non-linearity according to Newtonian theory. Our hybrid simulations come with a relativistic space-time and make it possible to investigate structure formation in a unified framework. In the present work we focus on simulations initialized at $z=99$, and show that the extracted matter power spectrum receives up to $3\\%$ corrections on very large scales through radiation. Our numerical findings compare favourably with linear analytical results from...
Nonlinearly perturbed semi-Markov processes
Silvestrov, Dmitrii
2017-01-01
The book presents new methods of asymptotic analysis for nonlinearly perturbed semi-Markov processes with a finite phase space. These methods are based on special time-space screening procedures for sequential phase space reduction of semi-Markov processes combined with the systematical use of operational calculus for Laurent asymptotic expansions. Effective recurrent algorithms are composed for getting asymptotic expansions, without and with explicit upper bounds for remainders, for power moments of hitting times, stationary and conditional quasi-stationary distributions for nonlinearly perturbed semi-Markov processes. These results are illustrated by asymptotic expansions for birth-death-type semi-Markov processes, which play an important role in various applications. The book will be a useful contribution to the continuing intensive studies in the area. It is an essential reference for theoretical and applied researchers in the field of stochastic processes and their applications that will cont...
Cosmological Perturbation Theory and the Evolution of Small-Scale Inhomogeneities
Miedema, P G
2011-01-01
It is shown that a first-order cosmological perturbation theory for the open, flat and closed Friedmann-Lemaitre-Robertson-Walker universes admits one, and only one, gauge-invariant variable which describes the perturbation to the energy density and which becomes equal to the usual Newtonian energy density in the non-relativistic limit. The same holds true for the perturbation to the particle number density. Using these two new variables, a new manifestly gauge-invariant cosmological perturbation theory based on the Lifshitz-Khalatnikov theory has been developed. Perturbations in the total energy density are gravitationally coupled to perturbations in the particle number density, irrespective of the nature of the particles. There is, in first-order, no back-reaction of perturbations to the global expansion of the universe. Small-scale perturbations in the radiation-dominated era oscillate with an increasing amplitude. Density perturbations do not evolve adiabatically, as is usually assumed, but diabatically, ...
Calculating Luminosity Distance versus Redshift in FRW Cosmology via Homotopy Perturbation Method
Shchigolev, V K
2015-01-01
We propose an efficient analytical method for estimating the luminosity distance in a homogenous Friedmann-Robertson-Walker (FRW) model of the Universe. This method is based on the homotopy perturbation method (HPM), which has high accuracy in many nonlinear problems, and can be easily implemented. For analytical calculation of the luminosity distance, we offer to proceed not from the computation of the integral, which determines it, but from the solution of a certain differential equation with corresponding initial conditions. Solving this equation by means of HPM, we obtain the approximate analytical expressions for the luminosity distance as a function of redshift for two different types of homotopy. Possible extension of this method to other cosmological models is also discussed.
Shapiro, P R; Raga, A C; Shapiro, Paul R.; Iliev, Ilian; Raga, Alejandro C.
1998-01-01
The postcollapse structure of objects which form by gravitational condensation out of the expanding cosmological background universe is a key element in the theory of galaxy formation. Towards this end, we have reconsidered the outcome of the nonlinear growth of a uniform, spherical density perturbation in an unperturbed background universe - the cosmological ``top-hat'' problem. We adopt the usual assumption that the collapse to infinite density at a finite time predicted by the top-hat solution is interrupted by a rapid virialization caused by the growth of small-scale inhomogeneities in the initial perturbation. We replace the standard description of the postcollapse object as a uniform sphere in virial equilibrium by a more self-consistent one as a truncated, nonsingular, isothermal sphere in virial and hydrostatic equilibrium, including for the first time a proper treatment of the finite-pressure boundary condition on the sphere. The results differ significantly from both the uniform sphere and the singu...
Rubakov, V A
2014-01-01
In these lectures we first concentrate on the cosmological problems which, hopefully, have to do with the new physics to be probed at the LHC: the nature and origin of dark matter and generation of matter-antimatter asymmetry. We give several examples showing the LHC cosmological potential. These are WIMPs as cold dark matter, gravitinos as warm dark matter, and electroweak baryogenesis as a mechanism for generating matter-antimatter asymmetry. In the remaining part of the lectures we discuss the cosmological perturbations as a tool for studying the epoch preceeding the conventional hot stage of the cosmological evolution.
A Unified Approach for Solving Nonlinear Regular Perturbation Problems
Khuri, S. A.
2008-01-01
This article describes a simple alternative unified method of solving nonlinear regular perturbation problems. The procedure is based upon the manipulation of Taylor's approximation for the expansion of the nonlinear term in the perturbed equation. An essential feature of this technique is the relative simplicity used and the associated unified…
Grishchuk, L P
1994-01-01
A theory of quantum-mechanical generation of cosmological perturbations is considered. The conclusion of this study is that if the large-angular-scale anisotropy in the cosmic microwave background radiation is caused by the long-wavelength cosmological perturbations of quantum mechanical origin, they are, most likely, gravitational waves, rather than density perturbations or rotational perturbations. Some disagreements with previous publications are clarified. This contribution to the Proceedings is based on Reference~[34]. NOTE: To generate an output, please extract and save the file crckapb.sty which appear at the beginning of the main file.
Cosmological perturbations in SFT inspired non-local scalar field models
Energy Technology Data Exchange (ETDEWEB)
Koshelev, Alexey S. [Vrije Universiteit Brussel and The International Solvay Institutes, Theoretische Natuurkunde, Brussels (Belgium); Vernov, Sergey Yu. [Instituto de Ciencias del Espacio (ICE/CSIC) and Institut d' Estudis Espacials de Catalunya (IEEC), Bellaterra, Barcelona (Spain); Lomonosov Moscow State University, Theoretical High Energy Physics Division, Skobeltsyn Institute of Nuclear Physics, Moscow (Russian Federation)
2012-10-15
We study cosmological perturbations in models with a single non-local scalar field originating from the string field theory description of the rolling tachyon dynamics. We construct the equation for the energy density perturbations of the non-local scalar field and explicitly prove that for the free field it is identical to a system of local cosmological perturbation equations in a particular model with multiple (maybe infinitely many) local free scalar fields. We also show that vector and tensor perturbations are absent in this set-up. (orig.)
Direct Perturbation Method for Derivative Nonlinear Schrodinger Equation
Institute of Scientific and Technical Information of China (English)
CHENG Xue-Ping; LIN Ji; HAN Ping
2008-01-01
We extend Lou's direct perturbation method for solving the nonlinear SchrSdinger equation to the case of the derivative nonlinear Schrodinger equation (DNLSE). By applying this method, different types of perturbation solutions axe obtained. Based on these approximate solutions, the analytical forms of soliton parameters, such as the velocity, the width and the initial position, are carried out and the effects of perturbation on solitons are analyzed at the same time. A numerical simulation of perturbed DNLSE finally verifies the results of the perturbation method.
Cosmological nonlinear structure formation in full general relativity
Torres, Jose M; Diez-Tejedor, Alberto; Nunez, Dario
2014-01-01
We perform numerical evolutions of cosmological scenarios using a standard general relativistic code in spherical symmetry. We concentrate on two different situations: initial matter distributions that are homogeneous and isotropic, and perturbations to those that respect the spherical symmetry. As matter models we consider the case of a pressureless perfect fluid, i.e. dust, and the case of a real massive scalar field oscillating around the minimum of the potential. Both types of matter have been considered as possible dark matter candidates in the cosmology literature, dust being closely related to the standard cold dark matter paradigm. We confirm that in the linear regime the perturbations associated with these types of matter grow in essentially the same way, the main difference being that in the case of a scalar field the dynamics introduce a cut-off in the power spectrum of the density perturbations at scales comparable with the Compton wavelength of the field. We also follow the evolutions well beyond...
On the conservation of second-order cosmological perturbations in a scalar field dominated universe
Vernizzi, F
2005-01-01
We discuss second-order cosmological perturbations on super-Hubble scales, in a scalar field dominated universe, such as during single field inflation. In this contest we show that the gauge-invariant curvature perturbations defined on the uniform density and comoving hypersurfaces coincide and that perturbations are adiabatic in the large scale limit. Since it has been recently shown that the uniform curvature perturbation is conserved on large scales if perturbations are adiabatic, we conclude that both the uniform and comoving curvature perturbations at second-order in a scalar field dominated universe are conserved.
Parameter information from nonlinear cosmological fields
Watts, A T P
2000-01-01
We develop a general formalism for analysing parameter information from non-Gaussian cosmic fields. The method can be adapted to include the nonlinear effects in galaxy redshift surveys, weak lensing surveys and cosmic velocity field surveys as part of parameter estimation. It can also be used as a test of non-Gaussianity of the Cosmic Microwave Background. Generalising Maximum Likelihood analysis to second-order, we calculate the nonlinear Fisher Information matrix and likelihood surfaces in parameter space. To this order we find that the information content is always increased by including nonlinearity. Our methods are applied to a realistic model of a galaxy redshift survey, including nonlinear evolution, galaxy bias, shot-noise and redshift-space distortions to second-order. We find that including nonlinearities allows all of the degeneracies between parameters to be lifted. Marginalised parameter uncertainties of a few percent will then be obtainable using forthcoming galaxy redshift surveys.
Nonlinear evolution of density and flow perturbations on a Bjorken background
Brouzakis, Nikolaos; Tetradis, Nikolaos; Wiedemann, Urs Achim
2015-01-01
Density perturbations and their dynamic evolution from early to late times can be used for an improved understanding of interesting physical phenomena both in cosmology and in the context of heavy-ion collisions. We discuss the spectrum and bispectrum of these perturbations around a longitudinally expanding fireball after a heavy-ion collision. The time-evolution equations couple the spectrum and bispectrum to each other, as well as to higher-order correlation functions through nonlinear terms. A non-trivial bispectrum is thus always generated, even if absent initially. For initial conditions corresponding to a model of independent sources, we discuss the linear and nonlinear evolution is detail. We show that, if the initial conditions are sufficiently smooth for fluid dynamics to be applicable, the nonlinear effects are relatively small.
Nonlinear evolution of density and flow perturbations on a Bjorken background
Brouzakis, Nikolaos; Floerchinger, Stefan; Tetradis, Nikolaos; Wiedemann, Urs Achim
2015-03-01
Density perturbations and their dynamic evolution from early to late times can be used for an improved understanding of interesting physical phenomena both in cosmology and in the context of heavy-ion collisions. We discuss the spectrum and bispectrum of these perturbations around a longitudinally expanding fireball after a heavy-ion collision. The time-evolution equations couple the spectrum and bispectrum to each other, as well as to higher-order correlation functions through nonlinear terms. A nontrivial bispectrum is thus always generated, even if absent initially. For initial conditions corresponding to a model of independent sources, we discuss the linear and nonlinear evolution in detail. We show that, if the initial conditions are sufficiently smooth for fluid dynamics to be applicable, the nonlinear effects are relatively small.
Cosmological Structure Formation with Augmented Lagrangian Perturbation Theory
Kitaura, Francisco-Shu
2012-01-01
We present a new fast and efficient approach to model structure formation with aug- mented Lagrangian perturbation theory (ALPT). Our method is based on splitting the dis- placement field into a long and a short range component. The long range component is computed by second order LPT (2LPT). This approximation contains a tidal nonlocal and nonlinear term. Unfortunately, 2LPT fails on small scales due to severe shell crossing and a crude quadratic behaviour in the low density regime. The spherical collapse (SC) approximation has been recently reported to correct for both effects by adding an ideal collapse truncation. However, this approach fails to reproduce the structures on large scales where it is significantly less correlated with the N-body result than 2LPT or linear LPT (the Zeldovich approximation). We propose to combine both approximations using for the short range displacement field the SC solution. A Gaussian filter with a smoothing radius r_S is used to separate between both regimes. We use the re...
Late time behavior of cosmological perturbations in a single brane model
Koyama, K
2004-01-01
We present solutions for the late time evolution of cosmological tensor and scalar perturbations in a single Randall-Sundrum brane world model. Assuming that the bulk is Anti-de Sitter spacetime, the solutions for cosmological perturbations are derived by summing up mode functions in Poincar\\'e coordinate. The junction conditions imposed at the moving brane are solved numerically. The recovery of 4-dimensional Einstein gravity at late times is shown by solving the 5-dimensional perturbations throughout the infinite bulk. We also comment on several possibilities to have deviations from 4-dimensional Einstein gravity.
The perturbed universe in the deformed algebra approach of Loop Quantum Cosmology
Grain, J
2016-01-01
Loop quantum cosmology is a tentative approach to model the universe down to the Planck era where quantum gravity settings are needed. The quantization of the universe as a dynamical space-time is inspired by Loop Quantum Gravity ideas. In addition, loop quantum cosmology could bridge contact with astronomical observations, and thus potentially investigate quantum cosmology modellings in the light of observations. To do so however, modelling both the background evolution and its perturbations is needed. The latter describe cosmic inhomogeneities that are the main cosmological observables. In this context, we present the so-called deformed algebra approach implementing the quantum corrections to the perturbed universe at an effective level by taking great care of gauge issues. We particularly highlight that in this framework, the algebra of hypersurface deformation receives quantum corrections, and we discuss their meaning. The primordial power spectra of scalar and tensor inhomogeneities are then presented, a...
Effective gravitational couplings for cosmological perturbations in generalized Proca theories
De Felice, Antonio; Kase, Ryotaro; Mukohyama, Shinji; Tsujikawa, Shinji; Zhang, Ying-li
2016-01-01
We consider the finite interactions of the generalized Proca theory including the sixth-order Lagrangian and derive the full linear perturbation equations of motion on the flat Friedmann-Lema\\^{i}tre-Robertson-Walker background in the presence of a matter perfect fluid. By construction, the propagating degrees of freedom (besides the matter perfect fluid) are two transverse vector perturbations, one longitudinal scalar, and two tensor polarizations. The Lagrangians associated with intrinsic vector modes neither affect the background equations of motion nor the second-order action of tensor perturbations, but they do give rise to non-trivial modifications to the no-ghost condition of vector perturbations and to the propagation speeds of vector and scalar perturbations. We derive the effective gravitational coupling $G_{\\rm eff}$ with matter density perturbations under a quasi-static approximation on scales deep inside the sound horizon. We find that the existence of intrinsic vector modes allows a possibility ...
Cosmology in nonlinear multidimensional gravity and the Casimir effect
Bolokhov, S. V.; Bronnikov, K. A.
2017-01-01
We study the possible cosmological models in Kaluza-Klein-type multidimensional gravity with a curvature-nonlinear Lagrangian and a spherical extra space, taking into account the Casimir energy. First, we find a minimum of the effective potential of extra dimensions, leading to a physically reasonable value of the effective cosmological constant in our 4D space-time. In this model, the huge Casimir energy density is compensated by a fine-tuned contribution of the curvature-nonlinear terms in the original action. Second, we present a viable model with slowly evolving extra dimensions and power-law inflation in our space-time. In both models, the results formulated in Einstein and Jordan frames are compared.
Robust Monotone Iterates for Nonlinear Singularly Perturbed Boundary Value Problems
Directory of Open Access Journals (Sweden)
Boglaev Igor
2009-01-01
Full Text Available This paper is concerned with solving nonlinear singularly perturbed boundary value problems. Robust monotone iterates for solving nonlinear difference scheme are constructed. Uniform convergence of the monotone methods is investigated, and convergence rates are estimated. Numerical experiments complement the theoretical results.
Scalar perturbations in two-temperature cosmological plasmas
Moortgat, J.B.; Marklund, M.
2006-01-01
We study the properties of density perturbations of a two-component plasma with a temperature difference on a homogeneous and isotropic background. For this purpose, we extend the general relativistic gauge-invariant and covariant (GIC) perturbation theory to include a multifluid with a particular e
Effects of primordial curvature perturbations on the value of the cosmological constant
Romano, Antonio Enea; Sasaki, Misao
2013-01-01
In this paper we study the effects on the luminosity distance of a local inhomogeneity seeded by primordial curvature perturbations as predicted by the inflationary scenario and constrained by the cosmic microwave background radiation. We find that a local overdensity originated from a one, two or three standard deviations peaks of the primordial curvature perturbations field can induce corrections to the value of the cosmological constant respectively of order of $0.6%,1%,1.5%$. These effects cannot be neglected in the precision cosmology era in which we are entering.
On the non-linear stability of scalar field cosmologies
Energy Technology Data Exchange (ETDEWEB)
Alho, Artur; Mena, Filipe C [Centro de Matematica, Universidade do Minho, 4710-057 Braga (Portugal); Kroon, Juan A Valiente, E-mail: aalho@math.uminho.pt, E-mail: fmena@math.uminho.pt, E-mail: jav@maths.qmul.ac.uk [School of Mathematical Sciences, Queen Mary, University of London, London E1 4NS (United Kingdom)
2011-09-22
We review recent work on the stability of flat spatially homogeneous and isotropic backgrounds with a self-interacting scalar field. We derive a first order quasi-linear symmetric hyperbolic system for the Einstein-nonlinear-scalar field system. Then, using the linearized system, we show how to obtain necessary and sufficient conditions which ensure the exponential decay to zero of small non-linear perturbations.
Cosmological perturbations from a Spectator field during inflation
Wang, Lingfei
2013-01-01
In this paper we will discuss analytically the perturbations created from a slowly rolling subdominant spectator field which decays much before the end of inflation. The quantum fluctuations of such a spectator field can seed perturbations on very large scales and explain the temperature anisotropy in the cosmic microwave background radiation with moderate non-Gaussianity, provided the relevant modes leave the Hubble patch while the spectator is slowly rolling. Furthermore, the perturbations are purely {\\it adiabatic} since the inflaton decay dominates and creates all the Standard Model degrees of freedom. We will provide two examples for the spectator field potential, one with a step function profile, and the other with an inflection point. In both the cases we will compute higher order curvature perturbations, i.e.\\ local bispectrum and trispectrum, which can be constrained by the forthcoming Planck data.
The probability equation for the cosmological comoving curvature perturbation
Energy Technology Data Exchange (ETDEWEB)
Riotto, Antonio; Sloth, Martin S., E-mail: antonio.riotto@pd.infn.it, E-mail: sloth@cern.ch [CERN, PH-TH Division, CH-1211, Genève 23 (Switzerland)
2011-10-01
Fluctuations of the comoving curvature perturbation with wavelengths larger than the horizon length are governed by a Langevin equation whose stochastic noise arise from the quantum fluctuations that are assumed to become classical at horizon crossing. The infrared part of the curvature perturbation performs a random walk under the action of the stochastic noise and, at the same time, it suffers a classical force caused by its self-interaction. By a path-interal approach and, alternatively, by the standard procedure in random walk analysis of adiabatic elimination of fast variables, we derive the corresponding Kramers-Moyal equation which describes how the probability distribution of the comoving curvature perturbation at a given spatial point evolves in time and is a generalization of the Fokker-Planck equation. This approach offers an alternative way to study the late time behaviour of the correlators of the curvature perturbation from infrared effects.
Cosmological perturbations of axion with a dynamical decay constant
Kobayashi, Takeshi; Takahashi, Fuminobu
2016-08-01
A QCD axion with a time-dependent decay constant has been known to be able to accommodate high-scale inflation without producing topological defects or too large isocurvature perturbations on CMB scales. We point out that a dynamical decay constant also has the effect of enhancing the small-scale axion isocurvature perturbations. The enhanced axion perturbations can even exceed the periodicity of the axion potential, and thus lead to the formation of axionic domain walls. Unlike the well-studied axionic walls, the walls produced from the enhanced perturbations are not bounded by cosmic strings, and thus would overclose the universe independently of the number of degenerate vacua along the axion potential.
Adiabatic CMB perturbations in pre-big bang string cosmology
Enqvist, Kari; Enqvist, Kari; Sloth, Martin S.
2002-01-01
We consider the pre-big bang scenario with a massive axion field which starts to dominate energy density when oscillating in an instanton-induced potential and subsequently reheats the universe as it decays into photons, thus creating adiabatic CMB perturbations. We find that the fluctuations in the axion field can give rise to a nearly flat spectrum of adiabatic perturbations with a spectral tilt $\\Delta n$ in the range $-0.1 \\lesssim \\Delta n \\lesssim 0.3$.
A look to nonlinear interacting Ghost dark energy cosmology
Khurshudyan, Martiros
2016-07-01
In this paper, we organize a look to nonlinear interacting Ghost dark energy cosmology involving a discussion on the thermodynamics of the Ghost dark energy, when the universe is bounded via the Hubble horizon. One of the ways to study a dark energy model, is to reconstruct thermodynamics of it. Ghost dark energy is one of the models of the dark energy which has an explicitly given energy density as a function of the Hubble parameter. There is an active discussion towards various cosmological scenarios, where the Ghost dark energy interacts with the pressureless cold dark matter (CDM). Recently, various models of the varying Ghost dark energy has been suggested, too. To have a comprehensive understanding of suggested models, we will discuss behavior of the cosmological parameters on parameter-redshift z plane. Some discussion on Om and statefinder hierarchy analysis of these models is presented. Moreover, up to our knowledge, suggested forms of interaction between the Ghost dark energy and cold dark matter (CDM) are new, therefore, within obtained results, we provide new contribution to previously discussed models available in the literature. Our study demonstrates that the forms of the interactions considered in the Ghost dark energy cosmology are not exotic and the justification of this is due to the recent observational data.
Cosmological Perturbations of Quantum-Mechanical Origin and Anisotropy of the Microwave Background
Grishchuk, L P
1993-01-01
Cosmological perturbations generated quantum-mechanically (as a particular case, during inflation) possess statistical properties of squeezed quantum states. The power spectra of the perturbations are modulated and the angular distribution of the produced temperature fluctuations of the CMBR is quite specific. An exact formula is derived for the angular correlation function of the temperature fluctuations caused by squeezed gravitational waves. The predicted angular pattern can, in principle, be revealed by the COBE-type observations.
Cosmological perturbations of quantum-mechanical origin and anisotropy of the microwave background
Grishchuk, L. P.
1993-01-01
Cosmological perturbations generated quantum mechanically (as a particular case, during inflation) possess statistical properties of squeezed quantum states. The power spectra of the perturbations are modulated and the angular distribution of the produced temperature fluctuations of the cosmic microwave background radiation is quite specific. An exact formula is derived for the angular correlation function of the temperature fluctuations caused by squeezed gravitational waves. The predicted angular pattern can, in principle, be revealed by observations like those by the Cosmic Background Explorer.
Wilson, Michael J
2016-01-01
I investigate the consistency of the VIMOS Public Extragalactic Redshift Survey v7 galaxy sample with the expansion history and linear growth rate predicted by General Relativity (GR) and a Planck (2015) cosmology. To do so, I measure the redshift-space power spectrum, which is anisotropic due to both redshift-space distortions (RSD) and the Alcock-Paczynski (AP) effect. In Chapter 6, I place constraints of $f \\sigma_8(0.76) = 0.44 \\pm 0.04$ and $f \\sigma_8(1.05) = 0.28 \\pm 0.08$, which remain consistent with GR at 95% confidence. Marginalising over the anisotropic AP effect degrades the constraints by a factor of three but allows $F_{AP} \\equiv (1+z) D_A H/c$ to be simultaneously constrained. The VIPERS v7 joint-posterior on $(f \\sigma_8, F_{AP})$ shows no compelling deviation from GR. Chapter 7 investigates the inclusion of a simple density transform: `clipping' prior to the RSD analysis. This tackles the root-cause of non-linearity and may extend the validity of perturbation theory. Moreover, this marked s...
A parametrisation of modified gravity on nonlinear cosmological scales
Lombriser, Lucas
2016-01-01
Viable modifications of gravity on cosmological scales predominantly rely on screening mechanisms to recover Einstein's Theory of General Relativity in the Solar System, where it has been well tested. A parametrisation of the effects of such modifications in the spherical collapse model is presented here for the use of modelling the modified nonlinear cosmological structure. The formalism allows an embedding of the different screening mechanisms operating in scalar-tensor theories through large values of the gravitational potential or its first or second derivatives as well as of linear suppression effects or more general transitions between modified and Einstein gravity limits. Each screening or suppression mechanism is parametrised by a time, mass, and environment dependent screening scale, an effective modified gravitational coupling in the fully unscreened limit that can be matched to linear theory, the exponent of a power-law radial profile of the screened coupling, determined by derivatives, symmetries,...
Physical consequences of black holes in non-perturbative quantum gravity and inflationary cosmology
Reska, P.M.
2011-01-01
In this thesis the consequences of the presence of a Schwarzschild black hole in de Sitter space are studied in the setting of non-perturbative quantum gravity and in inflationary cosmology. We first review the formalism of Causal Dynamical Triangulations (CDT) which implements a lattice regularizat
Cosmological perturbation theory at three-loop order
Energy Technology Data Exchange (ETDEWEB)
Blas, Diego [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Garny, Mathias; Konstandin, Thomas [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2013-09-15
We analyze the dark matter power spectrum at three-loop order in standard perturbation theory of large scale structure. We observe that at late times the loop expansion does not converge even for large scales (small momenta) well within the linear regime, but exhibits properties compatible with an asymptotic series. We propose a technique to restore the convergence in the limit of small momentum, and use it to obtain a perturbative expansion with improved convergence for momenta in the range where baryonic acoustic oscillations are present. Our results are compared with data from N-body simulations at different redshifts, and we find good agreement within this range.
Effects of Dark Energy Perturbations on Cosmological Tests of General Relativity
Dossett, Jason
2013-01-01
Cosmological tests to distinguish between dark energy (DE) and modifications to gravity are a promising route to obtain clues on the origin of cosmic acceleration. We study here the robustness of these tests to the presence of DE density, velocity, and anisotropic stress perturbations. We find that the dispersion in the growth index parameter remains small enough to distinguish between extreme cases of DE models and some commonly used modified gravity models. The sign of the slope parameter for a redshift dependent growth index was found to be inconsistent as an additional test in extreme cases of DE models with perturbations. Next, we studied the effect of DE perturbations on the modified growth (MG) parameters that enter the perturbed Einstein equations. We find that while the dark energy perturbations affect the MG parameters, the deviations remain smaller than those due to modified gravity models. Additionally, the deviations due to DE perturbations with a non-zero effective sound speed occur at scale ran...
Evolution of cosmological perturbations in a stage dominated by an oscillatory scalar field
Kodama, H; Kodama, Hideo; Hamazaki, Takashi
1996-01-01
In the investigation of the evolution of cosmological perturbations in inflationary universe models the behavior of perturbations during the reheating stage is the most unclear point. In particular in the early reheating phase in which a rapidly oscillating scalar field dominates the energy density, the behavior of perturbations is not known well because their evolution equation expressed in terms of the curvature perturbation becomes singular. In this paper it is shown that in spite of this singular behavior of the evolution equation the Bardeen parameter stays constant in a good accuracy during this stage for superhorizon-scale perturbations except for a sequence of negligibly short intervals around the zero points of the time derivative of the scalar field. This justifies the conventional formula relating the amplitudes of quantum fluctuations during inflation and those of adiabatic perturbations at horizon crossing in the Friedmann stage, except for possible corrections produced by the energy transfer fro...
Adiabatic CMB perturbations in pre-big bang string cosmology
DEFF Research Database (Denmark)
Enqvist, Kari; Sloth, Martin Snoager
2001-01-01
We consider the pre-big bang scenario with a massive axion field which starts to dominate energy density when oscillating in an instanton-induced potential and subsequently reheats the universe as it decays into photons, thus creating adiabatic CMB perturbations. We find that the fluctuations...
THIRD-ORDER NONLINEAR SINGULARLY PERTURBED BOUNDARY VALUE PROBLEM
Institute of Scientific and Technical Information of China (English)
王国灿; 金丽
2002-01-01
Third order singulary perturbed boundary value problem by means of differential inequality theories is studied. Based on the given results of second order nonlinear boundary value problem, the upper and lower solutions method of third order nonlinear boundary value problems by making use of Volterra type integral operator was established.Specific upper and lower solutions were constructed, and existence and asymptotic estimates of solutions under suitable conditions were obtained.The result shows that it seems to be new to apply these techniques to solving these kinds of third order singularly perturbed boundary value problem. An example is given to demonstrate the applications.
A new approach to cosmological perturbations in f(R) models
Energy Technology Data Exchange (ETDEWEB)
Bertacca, Daniele; Bartolo, Nicola; Matarrese, Sabino, E-mail: daniele.bertacca@pd.infn.it, E-mail: nicola.bartolo@pd.infn.it, E-mail: sabino.matarrese@pd.infn.it [Dipartimento di Fisica Galileo Galilei, Università di Padova, via F. Marzolo, 8 I-35131 Padova (Italy)
2012-08-01
We propose an analytic procedure that allows to determine quantitatively the deviation in the behavior of cosmological perturbations between a given f(R) modified gravity model and a ΛCDM reference model. Our method allows to study structure formation in these models from the largest scales, of the order of the Hubble horizon, down to scales deeply inside the Hubble radius, without employing the so-called 'quasi-static' approximation. Although we restrict our analysis here to linear perturbations, our technique is completely general and can be extended to any perturbative order.
The quantum-to-classical transition of primordial cosmological perturbations
Pinto-Neto, Nelson; Struyve, Ward
2011-01-01
There is a widespread belief that the classical small inhomogeneities which gave rise to all structures in the Universe through gravitational instability originated from primordial quantum cosmological fluctuations. However, this transition from quantum to classical fluctuations is plagued with important conceptual issues, most of them related to the application of standard quantum theory to the Universe as a whole. In this paper, we show how these issues can easily be overcome in the framework of the de Broglie-Bohm quantum theory. This theory is an alternative to standard quantum theory that provides an objective description of physical reality, where rather ambiguous notions of measurement or observer play no fundamental role, and which can hence be applied to the Universe as a whole. In addition, it allows for a simple and unambiguous characterization of the classical limit.
Kostouki, Anna
2009-01-01
Applying a novel non-perturbative functional method framework to a two-dimensional bosonic sigma model with tachyon, dilaton and graviton backgrounds we construct exact (non perturbative in the Regge slope) inflationary solutions, consistent with world-sheet Weyl Invariance. The mechanism for inflation entails a (partial) "alignment" between tachyon and dilaton backgrounds in the solution space. Some cosmological solutions which contain inflationary eras for a short period and interpolate between flat universes in the far past and far future are also discussed. These solutions are characterized by the absence of cosmological horizons, and therefore have well-defined scattering amplitudes. This makes them compatible with a perturbative string framework, and therefore it is these solutions that we consider as self-consistent in our approach. Within the context of the interpolating solutions, string production at the end of inflation (preheating) may also be studied. The advantage of our method is that the solut...
Cosmological perturbations of unimodular gravity and general relativity are identical
Basak, Abhishek; Fabre, Ophélia; Shankaranarayanan, S.
2016-10-01
Unimodular gravity (UG) is a restricted version of general relativity (GR) in which the variation of the metric determinant is set to zero and the field equations are given by the trace-free part of the full Einstein equations. The background equations in UG and GR are identical. It was recently claimed that the first order contribution in the temperature fluctuations of the Cosmic Microwave Background (CMB) in UG is different from GR. In this work, we calculate the first order perturbation equations in UG and show that the Sachs-Wolfe effect in UG, in terms of gauge invariant variables, is identical to GR. We also show that the second order perturbation equation of Mukhanov-Sasaki variable in UG, is identical to GR. The only difference comes from the gauge choices due the constraint on the metric determinant. Hence, UG and GR are identical and indistinguishable in CMB data on large scales.
Linear Perturbations in a coupled cosmon-bolon cosmology
Beyer, Joschka
2014-01-01
We investigate linear perturbations in the recently proposed cosmon-bolon model of coupled scalar field dark matter and quintessence. We provide an analytical mechanism to average over the quick oscillations appearing both in the background and at the perturbative level and evolve the effective equations numerically. The resulting matter power spectra are used to predict total halo number counts as well as substructure abundances in a typical galaxy by employing the extended Press-Schechter excursion set approach. We discuss in some detail the ambiguities arising in this formalism, starting from issues with generalizing spherical collapse to our model to filter choices and different barriers. The results are used to put a lower bound on the current bolon mass of roughly $9 \\times 10^{-22}$ eV.
Correlated mixtures of adiabatic and isocurvature cosmological perturbations
Langlois, D; Langlois, David; Riazuelo, Alain
2000-01-01
We examine the consequences of the existence of correlated mixtures of adiabatic and isocurvature perturbations on the CMB and large scale structure. In particular, we consider the four types of ``elementary'' totally correlated hybrid initial conditions, where only one of the four matter species (photons, baryons, neutrinos, CDM) deviates from adiabaticity. We then study the height and position of the acoustic peaks with respect to the large angular scale plateau as a function of the isocurvature to adiabatic ratio.
Perturbative instability of inflationary cosmology from quantum potentials
Tawfik, Abdel Nasser; Dahab, Eiman Abou El
2016-01-01
It was argued that the Raychaudhuri equation with a quantum correction term avoids the Big Bang singularity and proposes an everlasting Universe [PLB741,276(2015)]. Critical comments on both conclusions and on the correctness of the key expressions of this work are discussed in literature [1505.03070]. In the present work, we have analyses the stability conditions by means of a small perturbation and concluded that the quantum corrections and their additional parameters lead to an unstable Universe. We focused on perturbative instability in the inflationary era of the early Universe and found that both unstable and stable modes are incompatible with the corresponding ones obtained in the standard FLRW Universe. We have shown that in the evolutionary era, only unstable modes exist for a small (an)isotropic perturbation and with different equations of state. Inequalities for both unstable and stable solutions with the standard FLRW space are derived. They reveal that in the FLRW flat Universe both instability a...
Random perturbations of nonlinear parabolic systems
Beck, Lisa
2011-01-01
Several aspects of regularity theory for parabolic systems are investigated under the effect of random perturbations. The deterministic theory, when strict parabolicity is assumed, presents both classes of systems where all weak solutions are in fact more regular, and examples of systems with weak solutions which develop singularities in finite time. Our main result is the extension of a regularity result due to Kalita to the stochastic case. Concerning the examples with singular solutions (outside the setting of Kalita's regularity result), we do not know whether stochastic noise may prevent the emergence of singularities, as it happens for easier PDEs. We can only prove that, for a linear stochastic parabolic system with coefficients outside the previous regularity theory, the expected value of the solution is not singular.
Perturbations of cosmological and black hole solutions in massive gravity and bi-gravity
Kobayashi, Tsutomu; Siino, Masaru; Yamaguchi, Masahide; Yoshida, Daisuke
2016-10-01
We investigate perturbations of a class of spherically symmetric solutions in massive gravity and bi-gravity. The background equations of motion for the particular class of solutions we are interested in reduce to a set of the Einstein equations with a cosmological constant. Thus, the solutions in this class include all the spherically symmetric solutions in general relativity, such as the Friedmann-Lemaître-Robertson-Walker solution and the Schwarzschild (-de Sitter) solution, though the one-parameter family of two parameters of the theory admits such a class of solutions. We find that the equations of motion for the perturbations of this class of solutions also reduce to the perturbed Einstein equations at first and second order. Therefore, the perturbative stability of the solutions coincides with that of the corresponding solutions in general relativity at least up to the second-order perturbations.
Kulczycki, Wojciech
2016-01-01
We analyze propagation equations for the polar modes of gravitational waves in cosmological space-times. We prove that polar gravitational waves must perturb --- unlike axial modes --- the material content of the Friedman-Lemaitre-Robertson-Walker spacetimes. The whole gravitational dynamics reduces to the single "master equation" that has the same form as for axial modes. That allows us to conclude that the status of the Huygens principle is the same for axial and gravitational waves. In particular, this principle is valid exactly in radiation spacetimes with the vanishing cosmological constant, and it is broken otherwise.
Comparison of alternative improved perturbative methods for nonlinear oscillations
Energy Technology Data Exchange (ETDEWEB)
Amore, Paolo [Facultad de Ciencias, Universidad de Colima, Bernal Diaz del Castillo 340, Colima (Mexico)]. E-mail: paolo@ucol.mx; Raya, Alfredo [Facultad de Ciencias, Universidad de Colima, Bernal Diaz del Castillo 340, Colima (Mexico); Fernandez, Francisco M. [INIFTA (Conicet, UNLP), Diag. 113 y 64 S/N, Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina)
2005-06-06
We discuss and compare two alternative perturbation approaches for the calculation of the period of nonlinear systems based on the Lindstedt-Poincare technique. As illustrative examples we choose one-dimensional anharmonic oscillators and the Van der Pol equation. Our results show that each approach is better for just one type of model considered here.
Warm-tachyon Gauss-Bonnet inflation and cosmological perturbations
Motaharfar, Maysam
2016-01-01
We study a warm-tachyon inflationary model non-minimally coupled to a Gauss-Bonnet term. The general conditions required for reliability of the model are obtained by considerations of a combined hierarchy of Hubble and Gauss-Bonnet flow functions. The perturbed equations are derived in the longitudinal gauge in the presence of slow-roll and quasi-stable conditions. General expressions for observable quantities of interest such as the tensor-to-scalar ratio, scalar spectral index and its running are found in the high dissipation regime. Finally, the model is solved using exponential and inverse power-law potentials with parameters of the model being constrained within the framework of the Planck 2015 data. We show that the Gauss-Bonnet coupling constant controls termination of inflation in such a way as to be in good agreement with Planck 2015 data.
Iliev, I. T.; Shapiro, P. R.; Raga, A. C.
1998-12-01
The postcollapse structure of objects which form by gravitational condensation out of the expanding cosmological background universe is a key element in the theory of galaxy formation. Towards this end, we have reconsidered the outcome of the nonlinear growth of a uniform, spherical density perturbation in an unperturbed background universe - the cosmological ``top-hat'' problem. We adopt the usual assumption that the collapse to infinite density at a finite time predicted by the top-hat solution is interrupted by a rapid virialization caused by the growth of small-scale inhomogeneities in the initial perturbation. We replace the standard description of the postcollapse object as a uniform sphere in virial equilibrium by a more self-consistent one as a truncated, nonsingular, isothermal sphere in virial and hydrostatic equilibrium, including for the first time a proper treatment of the finite-pressure boundary condition on the sphere. The results differ significantly from both the uniform sphere and the singular isothermal sphere approximations for the postcollapse objects. These results will have a significant effect on a wide range of applications of the Press-Schechter and other semi-analytical models to cosmology. The truncated isothermal sphere solution presented here predicts the virial temperature and integrated mass distribution of the X-ray clusters formed in the CDM model as found by detailed, 3D, numerical gas and N-body dynamical simulations remarkably well. This solution allows us to derive analytically the numerically-calibrated mass-temperature and radius-temperature scaling laws for X-ray clusters which were derived empirically by Evrard, Metzler and Navarro from simulation results for the CDM model.
Grishchuk, L P
1996-01-01
It is likely that the observed large-angular-scale anisotropies in the microwave background radiation are induced by the cosmological perturbations of quantum-mechanical origin. Such perturbations are now placed in squeezed vacuum quantum states and, hence, are characterized by large variances of their amplitude. The statistical properties of the anisotropies should reflect the underlying statistics of the squeezed vacuum quantum states. The theoretical variances for the temperature angular correlation function are derived and described quantitatively. It is shown that they are indeed large. Unfortunately, these large theoretical statistical uncertainties will make the extraction of cosmological information from the measured anisotropies a much more difficult problem than we wanted it to be.
Scalar and tensor perturbations in loop quantum cosmology: High-order corrections
Zhu, Tao; Cleaver, Gerald; Kirsten, Klaus; Sheng, Qin; Wu, Qiang
2015-01-01
Loop quantum cosmology (LQC) provides promising resolutions to the trans-Planckian issue and initial singularity arising in the inflationary models of general relativity. In general, due to different quantization approaches, LQC involves two types of quantum corrections, the holonomy and inverse-volume, to both of the cosmological background evolution and perturbations. In this paper, using {\\em the third-order uniform asymptotic approximations}, we derive explicitly the observational quantities of the slow-roll inflation in the framework of LQC with these quantum corrections. We calculate the power spectra, spectral indices, and running of the spectral indices for both scalar and tensor perturbations, whereby the tensor-to-scalar ratio is obtained. We expand all the observables at the time when the inflationary mode crosses the Hubble horizon. As the upper error bounds for the uniform asymptotic approximation at the third-order are $\\lesssim 0.15\\%$, these results represent the most accurate results obtained...
Holographic curvature perturbations in a cosmology with a space-like singularity
Energy Technology Data Exchange (ETDEWEB)
Ferreira, Elisa G.M. [Department of Physics, McGill University,3600 University St., Montréal, QC, H3A 2T8 (Canada); Brandenberger, Robert [Department of Physics, McGill University,3600 University St., Montréal, QC, H3A 2T8 (Canada); Institute for Theoretical Studies, ETH Zürich,Clausiusstr. 47, Zürich, CH-8092 (Switzerland)
2016-07-19
We study the evolution of cosmological perturbations in an anti-de-Sitter (AdS) bulk through a cosmological singularity by mapping the dynamics onto the boundary conformal fields theory by means of the AdS/CFT correspondence. We consider a deformed AdS space-time obtained by considering a time-dependent dilaton which induces a curvature singularity in the bulk at a time which we call t=0, and which asymptotically approaches AdS both for large positive and negative times. The boundary field theory becomes free when the bulk curvature goes to infinity. Hence, the evolution of the fluctuations is under better controle on the boundary than in the bulk. To avoid unbounded particle production across the bounce it is necessary to smooth out the curvature singularity at very high curvatures. We show how the bulk cosmological perturbations can be mapped onto boundary gauge field fluctuations. We evolve the latter and compare the spectrum of fluctuations on the infrared scales relevant for cosmological observations before and after the bounce point. We find that the index of the power spectrum of fluctuations is the same before and after the bounce.
Primordial magnetic fields from second-order cosmological perturbations:Tight coupling approximation
Maeda, Satoshi; Kobayashi, Tsutomu; Shiromizu, Tetsuya
2008-01-01
We explore the possibility of generating large-scale magnetic fields from second-order cosmological perturbations during the pre-recombination era. The key process for this is Thomson scattering between the photons and the charged particles within the cosmic plasma. To tame the multi-component interacting fluid system, we employ the tight coupling approximation. It is shown that the source term for the magnetic field is given by the product of the first order perturbations and so the intrinsically second-order quantities do not contribute to magnetogenesis. The magnetic fields generated by this process are estimated to be \\sim 10^{-26},Gauss on the horizon scale.
Cosmological perturbations in theories with non-minimal coupling between curvature and matter
Bertolami, Orfeu; Páramos, Jorge
2013-01-01
In this work, one examines how the presence of a non-minimal coupling between the spacetime curvature and matter affects the evolution of cosmological perturbations around a homogeneous and isotropic Universe and hence the formation of large-scale structure. This framework places constraints on the terms which arise due to the coupling with matter and, in particular, on the modification in the growth of matter density perturbations. One obtains approximate analytical solutions for the evolution of matter overdensities during the matter dominated era and shows that these favor the presence of a coupling function that is compatible with the late-time cosmic acceleration.
Fang, Xiao; Blazek, Jonathan A.; McEwen, Joseph E.; Hirata, Christopher M.
2017-02-01
Cosmological perturbation theory is a powerful tool to predict the statistics of large-scale structure in the weakly non-linear regime, but even at 1-loop order it results in computationally expensive mode-coupling integrals. Here we present a fast algorithm for computing 1-loop power spectra of quantities that depend on the observer's orientation, thereby generalizing the FAST-PT framework (McEwen et al., 2016) that was originally developed for scalars such as the matter density. This algorithm works for an arbitrary input power spectrum and substantially reduces the time required for numerical evaluation. We apply the algorithm to four examples: intrinsic alignments of galaxies in the tidal torque model; the Ostriker-Vishniac effect; the secondary CMB polarization due to baryon flows; and the 1-loop matter power spectrum in redshift space. Code implementing this algorithm and these applications is publicly available at https://github.com/JoeMcEwen/FAST-PT.
Fang, Xiao; McEwen, Joseph E; Hirata, Christopher M
2016-01-01
Cosmological perturbation theory is a powerful tool to predict the statistics of large-scale structure in the weakly non-linear regime, but even at 1-loop order it results in computationally expensive mode-coupling integrals. Here we present a fast algorithm for computing 1-loop power spectra of quantities that depend on the observer's orientation, thereby generalizing the FAST-PT framework (McEwen et al., 2016) that was originally developed for scalars such as the matter density. This algorithm works for an arbitrary input power spectrum and substantially reduces the time required for numerical evaluation. We apply the algorithm to four examples: intrinsic alignments of galaxies in the tidal torque model; the Ostriker-Vishniac effect; the secondary CMB polarization due to baryon flows; and the 1-loop matter power spectrum in redshift space. Code implementing this algorithm and these applications is publicly available at https://github.com/JoeMcEwen/FAST-PT.
Linear and non-linear perturbations in dark energy models
Escamilla-Rivera, Celia; Fabris, Julio C; Alcaniz, Jailson S
2016-01-01
In this work we discuss observational aspects of three time-dependent parameterisations of the dark energy equation of state $w(z)$. In order to determine the dynamics associated with these models, we calculate their background evolution and perturbations in a scalar field representation. After performing a complete treatment of linear perturbations, we also show that the non-linear contribution of the selected $w(z)$ parameterisations to the matter power spectra is almost the same for all scales, with no significant difference from the predictions of the standard $\\Lambda$CDM model.
Application of the homotopy perturbation method to the nonlinear pendulum
Energy Technology Data Exchange (ETDEWEB)
Belendez, A; Hernandez, A; Belendez, T; Neipp, C; Marquez, A [Departamento de Fisica, IngenierIa de Sistemas y TeorIa de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2007-01-15
The homotopy perturbation method is used to solve the nonlinear differential equation that governs the nonlinear oscillations of a simple pendulum, and an approximate expression for its period is obtained. Only one iteration leads to high accuracy of the solutions and the relative error for the approximate period is less than 2% for amplitudes as high as 130{sup 0}. Another important point is that this method provides an analytical expression for the angular displacement as a function of time as the sum of an infinite number of harmonics; although for practical purposes it is sufficient to consider only a finite number of harmonics. We believe that the present study may be a suitable and fruitful exercise for teaching and better understanding perturbation techniques in advanced undergraduate courses on classical mechanics.
Institute of Scientific and Technical Information of China (English)
Jingsun Yao; Jiaqi Mo
2005-01-01
The nonlinear nonlocal singularly perturbed initial boundary value problems for reaction diffusion equations with a boundary perturbation is considered. Under suitable conditions, the outer solution of the original problem is obtained. Using the stretched variable, the composing expansion method and the expanding theory of power series the initial layer is constructed. And then using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems is studied. Finally the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation are discussed.
Comment on the "Influence of Cosmological Transitions on the Evolution of Density Perturbations"
Grishchuk, L P
1998-01-01
The "standard inflationary result" has been confirmed once again. This time, by Martin and Schwarz [1]. The fallacy - "the closer the inflationary epoch is to the de Sitter space-time, the less important are large-scale gravitational waves in the CMBR today" - has been repeated and has been claimed to be finally proved. The paper [1] is somewhat better than many other incorrect inflationary papers on the subject of cosmological perurbations. This paper at least operates with correct equations (taken from the criticized work of Grishchuk [2, 3]). Martin and Schwarz say that Grishchuk's conclusion about approximate equality of metric amplitudes for gravitational waves and density perturbations "is wrong because the time evolution of the scalar metric perturbation through the (smooth) reheating transition was not calculated correctly". They reiterate an old inflationary fantasy about "big amplification" of scalar perturbations (in contrast to gravitational waves) during "reheating". They say that after appropria...
Noether Identities and Gauge-Fixing the Action for Cosmological Perturbations
Lagos, Macarena; Ferreira, Pedro G; García-Sáenz, Sebastián
2014-01-01
We propose and develop a general algorithm for finding the action for cosmological perturbations which rivals the conventional, gauge-invariant approach and can be applied to theories with more than one metric. We then apply it to a particular case of bigravity, focusing on the Eddington- inspired Born-Infeld theory, and show that we can obtain a nearly scale-invariant power spectrum for both scalar and tensor primordial quantum perturbations. Unfortunately, in the case of the minimal Eddington-inspired Born-Infeld theory, we find that the tensor-to-scalar ratio of perturbations is unacceptably large. We discuss the applicability of our general method and the possibility of resurrecting the specific theory we have looked at.
Cosmological Perturbation Theory as a Tool for Estimating Box-Scale Effects in N-body Simulations
Orban, Chris
2013-01-01
In performing cosmological N-body simulations, it is widely appreciated that the growth of structure on the largest scales within a simulation box will be inhibited by the finite size of the simulation volume. Following ideas set forth in Seto 1999, this paper shows that standard (a.k.a. 1-loop) cosmological perturbation theory (SPT) can be used to predict at an order-of-magnitude level the deleterious effect of the box scale on the power spectrum of density fluctuations in simulation volumes. Alternatively, this approach can be used to quickly estimate post facto the effect of the box scale on power spectrum results from existing simulations. In this way SPT can help determine whether larger box sizes or other more-sophisticated methods are needed to achieve a particular level of precision for a given application (e.g. simulations to measure the non-linear evolution of baryon acoustic oscillations). I focus on SPT in this note and show that its predictions are order-of-magnitude accurate compared to N-body s...
Silent initial conditions for cosmological perturbations with a change of space-time signature
Mielczarek, Jakub; Barrau, Aurelien
2014-01-01
Recent calculations in loop quantum cosmology suggest that a transition from a Lorentzian to an Euclidean space-time might take place in the very early Universe. The transition point leads to a state of silence, characterized by a vanishing speed of light. This behavior can be interpreted as a decoupling of different space points, similar to the one characterizing the BKL phase. In this study, we address the issue of imposing initial conditions for the cosmological perturbations at the transition point between the Lorentzian and Euclidean phases. Motivated by the decoupling of space points, initial conditions characterized by a lack of correlations are investigated. We show that the "white noise" initial conditions are supported by the analysis of the vacuum state in the Euclidean regime adjacent to the state of silence. Furthermore, the possibility of imposing the silent initial conditions at the trans-Planckian surface, characterized by a vanishing speed for the propagation of modes with wavelengths of the ...
Models for the Brane-Bulk Interaction: Toward Understanding Braneworld Cosmological Perturbation
Binétruy, Pierre; Carvalho, Carla
2004-01-01
Using some simple toy models, we explore the nature of the brane-bulk interaction for cosmological models with a large extra dimension. We are in particular interested in understanding the role of the bulk gravitons, which from the point of view of an observer on the brane will appear to generate dissipation and nonlocality, effects which cannot be incorporated into an effective (3+1)-dimensional Lagrangian field theoretic description. We explicitly work out the dynamics of several discrete systems consisting of a finite number of degrees of freedom on the boundary coupled to a (1+1)-dimensional field theory subject to a variety of wave equations. Systems both with and without time translation invariance are considered and moving boundaries are discussed as well. The models considered contain all the qualitative feature of quantized linearized cosmological perturbations for a Randall-Sundrum universe having an arbitrary expansion history, with the sole exception of gravitational gauge invariance, which will b...
Bogdan, V. M.; Bond, V. B.
1980-01-01
The deviation of the solution of the differential equation y' = f(t, y), y(O) = y sub O from the solution of the perturbed system z' = f(t, z) + g(t, z), z(O) = z sub O was investigated for the case where f and g are continuous functions on I x R sup n into R sup n, where I = (o, a) or I = (o, infinity). These functions are assumed to satisfy the Lipschitz condition in the variable z. The space Lip(I) of all such functions with suitable norms forms a Banach space. By introducing a suitable norm in the space of continuous functions C(I), introducing the problem can be reduced to an equivalent problem in terminology of operators in such spaces. A theorem on existence and uniqueness of the solution is presented by means of Banach space technique. Norm estimates on the rate of growth of such solutions are found. As a consequence, estimates of deviation of a solution due to perturbation are obtained. Continuity of the solution on the initial data and on the perturbation is established. A nonlinear perturbation of the harmonic oscillator is considered a perturbation of equations of the restricted three body problem linearized at libration point.
A nonlinear inversion for the velocity background and perturbation models
Wu, Zedong
2015-08-19
Reflected waveform inversion (RWI) provides a method to reduce the nonlinearity of the standard full waveform inversion (FWI) by inverting for the single scattered wavefield obtained using an image. However, current RWI methods usually neglect diving waves, which is an important source of information for extracting the long wavelength components of the velocity model. Thus, we propose a new optimization problem through breaking the velocity model into the background and the perturbation in the wave equation directly. In this case, the perturbed model is no longer the single scattering model, but includes all scattering. We optimize both components simultaneously, and thus, the objective function is nonlinear with respect to both the background and perturbation. The new introduced w can absorb the non-smooth update of background naturally. Application to the Marmousi model with frequencies that start at 5 Hz shows that this method can converge to the accurate velocity starting from a linearly increasing initial velocity. Application to the SEG2014 demonstrates the versatility of the approach.
Passive Control and ε-Bound Estimation of Singularly Perturbed Systems with Nonlinear Nonlinearities
Directory of Open Access Journals (Sweden)
Linna Zhou
2013-01-01
Full Text Available This paper considers the problems of passivity analysis and synthesis of singularly perturbed systems with nonlinear uncertainties. By a novel storage function depending on the singular perturbation parameter ε, a new method is proposed to estimate the ε-bound, such that the system is passive when the singular perturbation parameter is lower than the ε-bound. Furthermore, a controller design method is proposed to achieve a predefined ε-bound. The proposed results are shown to be less conservative than the existing ones because the adopted storage function is more general. Finally, an RLC circuit is presented to illustrate the advantages and effectiveness of the proposed methods.
Covariant Hořava-like and mimetic Horndeski gravity: cosmological solutions and perturbations
Cognola, Guido; Myrzakulov, Ratbay; Sebastiani, Lorenzo; Vagnozzi, Sunny; Zerbini, Sergio
2016-11-01
We consider a variant of the Nojiri–Odintsov covariant Hořava-like gravitational model, where diffeomorphism invariance is broken dynamically via a non-standard coupling to a perfect fluid. The theory allows one to address some of the potential instability problems present in Hořava–Lifshitz gravity due to explicit diffeomorphism invariance breaking. The fluid is instead constructed from a scalar field constrained by a Lagrange multiplier. In fact, the Lagrange multiplier construction allows for an extension of the Hořava-like model to include the scalar field of mimetic gravity, an extension which we thoroughly explore. By adding a potential for the scalar field, we show how one can reproduce a number of interesting cosmological scenarios. We then turn to the study of perturbations around a flat FLRW background, showing that the fluid in question behaves as an irrotational fluid, with zero sound speed. To address this problem, we consider a modified version of the theory, adding higher derivative terms in a way which brings us beyond the Horndeski framework. We compute the sound speed in this modified higher order mimetic Hořava-like model and show that it is non-zero, which means that perturbations therein can be sensibly defined. Caveats to our analysis, as well as comparisons to projectable Hořava–Lifshitz gravity, are also discussed. In conclusion, we present a theory of gravity which preserves diffeomorphism invariance at the level of the action but breaks it dynamically in the UV, reduces to General Relativity (GR) in the IR, allows the realization of a number of interesting cosmological scenarios, is well defined when considering perturbations around a flat FLRW background, and features cosmological dark matter emerging as an integration constant.
Composite fuzzy sliding mode control of nonlinear singularly perturbed systems.
Nagarale, Ravindrakumar M; Patre, B M
2014-05-01
This paper deals with the robust asymptotic stabilization for a class of nonlinear singularly perturbed systems using the fuzzy sliding mode control technique. In the proposed approach the original system is decomposed into two subsystems as slow and fast models by the singularly perturbed method. The composite fuzzy sliding mode controller is designed for stabilizing the full order system by combining separately designed slow and fast fuzzy sliding mode controllers. The two-time scale design approach minimizes the effect of boundary layer system on the full order system. A stability analysis allows us to provide sufficient conditions for the asymptotic stability of the full order closed-loop system. The simulation results show improved system performance of the proposed controller as compared to existing methods. The experimentation results validate the effectiveness of the proposed controller.
Geometric scaling in ultrahigh energy neutrinos and nonlinear perturbative QCD
Machado, M V T
2011-01-01
The ultrahigh energy neutrino cross section is a crucial ingredient in the calculation of the event rate in high energy neutrino telescopes. Currently there are several approaches which predict different behaviors for its magnitude for ultrahigh energies. In this contribution is presented a summary of current predictions based on the non-linear QCD evolution equations, the so-called perturbative saturation physics. In particular, predictions are shown based on the parton saturation approaches and the consequences of geometric scaling property at high energies are discussed. The scaling property allows an analytical computation of the neutrino scattering on nucleon/nucleus at high energies, providing a theoretical parameterization.
Perturbation and harmonic balance methods for nonlinear panel flutter.
Kuo, C.-C.; Morino, L.; Dugundji, J.
1972-01-01
A systematic way of applying both perturbation methods and harmonic balance methods to nonlinear panel flutter problems is developed here. Results obtained by both these methods for two-dimensional simply supported and three-dimensional clamped-clamped plates with six modes agree well with those obtained by the straightforward direct integration method, yet require less computer time and provide better insight into the solutions. Effects of viscoelastic structural damping on the flutter stability boundary are generally found to be destabilizing and the postflutter behavior becomes more explosive. The methods developed here may be of interest in related vibration problems.
Cosmological perturbation spectra from SL(4,R)-invariant effective actions
Bridgman, H A; Bridgman, Helen A.; Wands, David
2000-01-01
We investigate four-dimensional cosmological vacuum solutions derived from aneffective action invariant under global SL(n,R) transformations. We find thegeneral solutions for linear axion field perturbations about homogeneousdilaton-moduli-vacuum solutions for an SL(4,R)-invariant action and find thespectrum of super-horizon perturbations resulting from vacuum fluctuations in apre big bang scenario. We show that for SL(n,R)-invariant actions with n>3there exists a regime of parameter space of non-zero measure where all theaxion field spectra have positive spectral tilt, as required if light axionfields are to provide a seed for anisotropies in the microwave background andlarge-scale structure in the universe.
Truthing the stretch: Non-perturbative cosmological realizations with multiscale spherical collapse
Neyrinck, Mark C
2015-01-01
Here we present a simple, parameter-free, non-perturbative algorithm that gives low-redshift cosmological particle realizations accurate to few-Megaparsec scales, called muscle (MUltiscale Spherical ColLapse Evolution). It has virtually the same cost as producing N-body-simulation initial conditions, since it works with the 'stretch' parameter {\\psi}, the Lagrangian divergence of the displacement field. It promises to be useful in quickly producing mock catalogs, and to simplify computationally intensive reconstructions of galaxy surveys. muscle applies a spherical-collapse prescription on multiple Gaussian-smoothed scales. It achieves higher accuracy than perturbative schemes (Zel'dovich and 2LPT), and, by including the void-in-cloud process (voids in large-scale collapsing regions), solves problems with a single-scale spherical-collapse scheme. Additionally, we show the behavior of {\\psi} for different morphologies (voids, walls, filaments, and haloes). A Python code to produce these realizations is availab...
Shapiro, Paul R.; Iliev, Ilian T.; Raga, Alejandro C.
1999-07-01
The post-collapse structure of objects that form by gravitational condensation out of the expanding cosmological background universe is a key element in the theory of galaxy formation. Towards this end, we have reconsidered the outcome of the non-linear growth of a uniform, spherical density perturbation in an unperturbed background universe - the cosmological `top-hat' problem. We adopt the usual assumption that the collapse to infinite density at a finite time predicted by the top-hat solution is interrupted by a rapid virialization caused by the growth of small-scale inhomogeneities in the initial perturbation. We replace the standard description of the post-collapse object as a uniform sphere in virial equilibrium by a more self-consistent one as a truncated, non-singular, isothermal sphere in virial and hydrostatic equilibrium, including for the first time a proper treatment of the finite-pressure boundary condition on the sphere. The results differ significantly from both the uniform sphere and the singular isothermal sphere approximations for the post-collapse objects. The virial temperature that results is more than twice the previously used `standard value' of the post-collapse uniform sphere approximation, but 1.4 times smaller than that of the singular, truncated isothermal sphere approximation. The truncation radius is 0.554 times the radius of the top-hat at maximum expansion, and the ratio of the truncation radius to the core radius is 29.4, yielding a central density that is 514 times greater than at the surface and 1.8x10^4 times greater than that of the unperturbed background density at the epoch of infinite collapse predicted by the top-hat solution. For the top-hat fractional overdensity delta_L predicted by extrapolating the linear solution into the non-linear regime, the standard top-hat model assumes that virialization is instantaneous at delta_Ldelta_c=1.686 i.e. the epoch at which the non-linear top-hat reaches infinite density. The surface
Energy Technology Data Exchange (ETDEWEB)
Heitmann, Katrin [Los Alamos National Laboratory; Habib, Salman [Los Alamos National Laboratory; Higdon, David [Los Alamos National Laboratory; Williams, Brian J [Los Alamos National Laboratory; White, Martin [Los Alamos National Laboratory; Wagner, Christian [Los Alamos National Laboratory
2008-01-01
The power spectrum of density fluctuations is a foundational source of cosmological information. Precision cosmological probes targeted primarily at investigations of dark energy require accurate theoretical determinations of the power spectrum in the nonlinear regime. To exploit the observational power of future cosmological surveys, accuracy demands on the theory are at the one percent level or better. Numerical simulations are currently the only way to produce sufficiently error-controlled predictions for the power spectrum. The very high computational cost of (precision) N-body simulations is a major obstacle to obtaining predictions in the nonlinear regime, while scanning over cosmological parameters. Near-future observations, however, are likely to provide a meaningful constraint only on constant dark energy equation of state 'wCDM' cosmologies. In this paper we demonstrate that a limited set of only 37 cosmological models -- the 'Coyote Universe' suite -- can be used to predict the nonlinear matter power spectrum at the required accuracy over a prior parameter range set by cosmic microwave background observations. This paper is the second in a series of three, with the final aim to provide a high-accuracy prediction scheme for the nonlinear matter power spectrum for wCDM cosmologies.
Cosmological perturbations in an effective and genuinely phantom dark energy Universe
Albarran, Imanol; Morais, João
2016-01-01
We carry out an analysis of the cosmological perturbations in general relativity for three different models which are good candidates to describe the current acceleration of the Universe. These three set-ups are described classically by perfect fluids with a phantom nature and represent deviations from the most widely accepted $\\Lambda$CDM model. In addition, each of the models under study induce different future singularities or abrupt events known as (i) Big Rip, (ii) Little Rip and (iii) Little Sibling of the Big Rip. Only the first one is regarded as a true singularity since it occurs at a finite cosmic time. For this reason, we refer to the others as abrupt events. With the aim to find possible footprints of this scenario in the Universe matter distribution, we not only obtain the evolution of the cosmological scalar perturbations but also calculate the matter power spectrum for each model. Finally, we constrain observationally these models using several measurements of the growth rate function, more pre...
Cosmological Perturbations and Quasi-Static Assumption in $f(R)$ Theories
Chiu, Mu-Chen; Shu, Chenggang; Tu, Hong
2015-01-01
$f(R)$ gravity is one of the simplest theories of modified gravity to explain the accelerated cosmic expansion. Although it is usually assumed that the quasi-Newtonian approach for cosmic perturbations is good enough to describe the evolution of large scale structure in $f(R)$ models, some studies have suggested that this method is not valid for all $f(R)$ models. Here, we show that in the matter-dominated era, the pressure and shear equations alone, which can be recast into four first-order equations to solve for cosmological perturbations exactly, are sufficient to solve for the Newtonian potential, $\\Psi$, and the curvature potential, $\\Phi$. Based on these two equations, we are able to clarify how the exact linear perturbations fit into different limits. We find that in the subhorizon limit, the so called quasi-static assumption plays no role in reducing the exact linear perturbations in any viable $f(R)$ gravity. Our findings also disagree with previous studies where we find little difference between our...
Nakamura, Kouji
2008-01-01
Some formulae for the perturbations of the matter fields are summarized within the framework of the second-order gauge-invariant cosmological perturbation theory in a four dimensional homogeneous isotropic universe, which is developed in the papers [K. Nakamura, Prog. Theor. Phys. {\\bf 117} (2005), 17.]. We derive the formulae for the perturbations of the energy momentum tensors and equations of motion in the cases of a perfect fluid, an imperfect fluid, and a signle scalar field, and show that all equations are derived in terms of gauge-invariant variables without any gauge fixing.
The Early-Time Evolution of the Cosmological Perturbations in f(R) Gravity
Gu, Je-An; Wu, Yen-Ting; Chen, Pisin; Hwang, W-Y Pauchy
2011-01-01
We investigate the evolution of the linear cosmological perturbations in f(R) gravity, an alternative to dark energy for explaining the late-time cosmic acceleration. We numerically calculate the early-time evolution with an approximation we contrive to solve a problem that commonly appears when one solves the full evolution equations. With the approximate evolution equations we can fairly assess the effect of the gravity modification on the early-time evolution, thereby examining the validity of the general-relativity (GR) approximation that is widely used for the early universe. In particular, we compare the CMB photon density perturbation and the matter density perturbation obtained respectively by our approximation and the conventional GR approximation. We find that the effect of the gravity modification at early times in f(R) gravity may not be negligible. We conclude that to be self-consistent, in the f(R) theory one should employ the approximation presented in this paper instead of that of GR in the tr...
Patwardhan, Ajay; Kumar, M S R
2008-01-01
The second order perturbation calculations for gravity wave and Einstein equation for space time and matter are presented for the FRW metric cosmological model. While exact equations are found, suitable approximations are made to obtain definite results. In the gravity wave case the small wavelength case allows nearly locally flat background for obtaining a fit to the WMAP data. In the density and curvature case the FRW background is retained for the length scale of WMAP. Clustering and inhomogeneity are understood. The gravity wave ripples from Big Bang couple nonlinearly and redistribute the modes to higher values of 'l' giving consistency with the WMAP results. The order by order consistency of Einstein equations relate the second order perturbations in the curvature and density and the wrinkles in spacetime caused by the gravity wave modes reorganize these distributions. The radiation data of WMAP gives the picture of a FRW spacetime deformed and wrinkled consistent with matter distribution to one hundred...
Stability analysis for nonlinear multi－variable delay perturbation problems
Institute of Scientific and Technical Information of China (English)
WangHongshan; ZhangChengjian
2003-01-01
This paper discusses the stability of theoretical solutions for nonlinear multi-variable delay perturbation problems(MVDPP) of the form x′(t) = f(x(t),x(t - τ1(t)),…,x(t -τm(t)),y(t),y(t - τ1(t)),…,y(t - τm(t))), and gy′(t) = g(x(t),x(t- τ1(t)),…,x(t- τm(t)),y(t),y(t- τ1(t)),…,y(t- τm(t))), where 0 < ε <<1. A sufficient condition of stability for the systems is obtained. Additionally we prove the numerical solutions of the implicit Euler method are stable under this condition.
Cognola, Guido; Sebastiani, Lorenzo; Vagnozzi, Sunny; Zerbini, Sergio
2016-01-01
We consider the Nojiri-Odintsov covariant Horava-like gravitational model, where diffeomorphism invariance is broken dynamically via a non-standard coupling to a perfect fluid. The theory allows to address some of the potential instability problems present in Horava-Lifshitz gravity due to explicit diffeomorphism invariance breaking. The fluid is instead constructed from a scalar field constrained by a Lagrange multiplier. This construction allows to identify the scalar field with the mimetic field of the recently proposed mimetic gravity. Subsequently, we thoroughly explore the consequences of this identification. By adding a potential for the scalar field, we show how one can reproduce a number of interesting cosmological scenarios. We then turn to the study of perturbations around a flat FLRW background, showing that the fluid in question behaves as an irrotational fluid, with zero sound speed. To address this problem, we consider a modified version of the theory, adding higher derivative terms in a way wh...
Nandi, Debottam; Shankaranarayanan, S.
2016-10-01
In this work, we present a consistent Hamiltonian analysis of cosmological perturbations for generalized non-canonical scalar fields. In order to do so, we introduce a new phase-space variable that is uniquely defined for different non-canonical scalar fields. We also show that this is the simplest and efficient way of expressing the Hamiltonian. We extend the Hamiltonian approach of [1] to non-canonical scalar field and obtain an unique expression of speed of sound in terms of phase-space variable. In order to invert generalized phase-space Hamilton's equations to Euler-Lagrange equations of motion, we prescribe a general inversion formulae and show that our approach for non-canonical scalar field is consistent. We also obtain the third and fourth order interaction Hamiltonian for generalized non-canonical scalar fields and briefly discuss the extension of our method to generalized Galilean scalar fields.
Nandi, Debottam
2016-01-01
In this work, we present a consistent Hamiltonian analysis of cosmological perturbations for generalized non-canonical scalar fields. In order to do so, we introduce a new phase-space variable that is uniquely defined for different non-canonical scalar fields. We also show that this is the simplest and efficient way of expressing the Hamiltonian. We extend the Hamiltonian approach of [arXiv:1512.02539] to non-canonical scalar field and obtain a new definition of speed of sound in phase-space. In order to invert generalized phase-space Hamilton's equations to Euler-Lagrange equations of motion, we prescribe a general inversion formulae and show that our approach for non-canonical scalar field is consistent. We also obtain the third and fourth order interaction Hamiltonian for generalized non-canonical scalar fields and briefly discuss the extension of our method to generalized Galilean scalar fields.
Scalar-Fluid theories: cosmological perturbations and large-scale structure
Koivisto, Tomi S; Tamanini, Nicola
2015-01-01
Recently a new Lagrangian framework was introduced to describe interactions between scalar fields and relativistic perfect fluids. This allows two consistent generalizations of coupled quintessence models: non-vanishing pressures and a new type of derivative interaction. Here the implications of these to the formation of cosmological large-scale structure are uncovered at the linear order. The full perturbation equations in the two cases are derived in a unified formalism and their Newtonian, quasi-static limit is studied analytically. Requiring the absence of an effective sound speed for the coupled dark matter fluid restricts the Lagrangian to be a linear function of the matter number density. This still leaves new potentially viable classes of both algebraically and derivatively interacting models wherein the coupling may impact the background expansion dynamics and imprint signatures into the large-scale structure.
Chang, Zhe
2014-01-01
We propose the gravity's rainbow scenario as a possible alternative of the inflation paradigm to account for the flatness and horizon problems. We focus on studying the cosmological scalar perturbations which are seeded by the quantum fluctuations in the very early universe. The scalar power spectrum is expected to be nearly scale-invariant. We estimate the rainbow index $\\lambda$ and energy scale $M$ in the gravity's rainbow scenario by analyzing the Planck temperature and WMAP polarization datasets. The constraints on them are given by $\\lambda=2.933\\pm0.012$ and $\\ln (10^5M/M_p)= -0.401^{+0.457}_{-0.451}$ at the $68\\%$ confidence level.
Shapiro, Paul R.; Mao, Yi; Iliev, Ilian T.; Mellema, Garrelt; Datta, Kanan K.; Ahn, Kyungjin; Koda, Jun
2012-01-01
The 21cm background from the epoch of reionization is a promising cosmological probe: line-of-sight velocity fluctuations distort redshift, so brightness fluctuations in Fourier space depend upon angle, which linear theory shows can separate cosmological from astrophysical information. Nonlinear fluctuations in ionization, density and velocity change this, however. The validity and accuracy of the separation scheme are tested here for the first time, by detailed reionization simulations. The ...
Second-order cosmological perturbations in two-field inflation and predictions for non-Gaussianity
Tzavara, Eleftheria
2013-01-01
Inflationary predictions for the power spectrum of the curvature perturbation have been verified to an excellent degree, leaving many models compatible with observations. In this thesis we studied third-order correlations, that might allow one to further distinguish between inflationary models. From all the possible extensions of the standard inflationary model, we chose to study two-field models with canonical kinetic terms and flat field space. The new feature is the presence of the so-called isocurvature perturbation. Its interplay with the adiabatic perturbation outside the horizon gives birth to non-linearities characteristic of multiple-field models. In this context, we established the second-order gauge-invariant form of the adiabatic and isocurvature perturbation and found the third-order action that describes their interactions. Furthermore, we built on and elaborated the long-wavelength formalism in order to acquire an expression for the parameter of non-Gaussianity fNL as a function of the potentia...
Cosmological perturbations and observational constraints on non-local massive gravity
Nesseris, Savvas
2014-01-01
Non-local massive gravity can provide an interesting explanation for the late-time cosmic acceleration, with a dark energy equation of state $w_{\\rm DE}$ smaller than $-1$ in the past. We derive the equations of linear cosmological perturbations to confront such models with the observations of large-scale structures. The effective gravitational coupling to non-relativistic matter associated with galaxy clusterings is close to the Newton's gravitational constant $G$ for a mass scale $m$ slightly smaller than the today's Hubble parameter $H_0$. Taking into account the background expansion history as well as the evolution of matter perturbations $\\delta_m$, we test for these models with the Type Ia Supernovae (SnIa) from the Union 2.1, the Cosmic Microwave Background (CMB) measurements from Planck, a collection of baryon acoustic oscillations (BAO), and the growth rate data of $\\delta_m$. Using a higher value of $H_0$ derived from its direct measurement ($H_0 \\gtrsim 70$ km s$^{-1}$ Mpc$^{-1}$) the data strongly...
A general theory of linear cosmological perturbations: scalar-tensor and vector-tensor theories
Lagos, Macarena; Ferreira, Pedro G; Noller, Johannes
2016-01-01
We present a method for parametrizing linear cosmological perturbations of theories of gravity, around homogeneous and isotropic backgrounds. The method is sufficiently general and systematic that it can be applied to theories with any degrees of freedom (DoFs) and arbitrary gauge symmetries. In this paper, we focus on scalar-tensor and vector-tensor theories, invariant under linear coordinate transformations. In the case of scalar-tensor theories, we use our framework to recover the simple parametrizations of linearized Horndeski and "Beyond Horndeski" theories, and also find higher-derivative corrections. In the case of vector-tensor theories, we first construct the most general quadratic action for perturbations that leads to second-order equations of motion, which propagates two scalar DoFs. Then we specialize to the case in which the vector field is time-like (\\`a la Einstein-Aether gravity), where the theory only propagates one scalar DoF. As a result, we identify the complete forms of the quadratic act...
Conditional nonlinear optimal perturbations of the double-gyre ocean circulation
Terwisscha van Scheltinga, A.D.; Dijkstra, H.A.
2008-01-01
In this paper, we study the development of finite amplitude perturbations on linearly stable steady barotropic double-gyre flows in a rectangular basin using the concept of Conditional Nonlinear Optimal Perturbation (CNOP). The CNOPs depend on a time scale of evolution te and an initial perturbation
Ensemble prediction experiments using conditional nonlinear optimal perturbation
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Two methods for initialization of ensemble forecasts are compared, namely, singular vector (SV) and conditional nonlinear optimal perturbation (CNOP). The comparison is done for forecast lengths of up to 10 days with a three-level quasi-geostrophic (QG) atmospheric model in a perfect model scenario. Ten cases are randomly selected from 1982/1983 winter to 1993/1994 winter (from December to the following February). Anomaly correlation coefficient (ACC) is adopted as a tool to measure the quality of the predicted ensembles on the Northern Hemisphere 500 hPa geopotential height. The results show that the forecast quality of ensemble samples in which the first SV is replaced by CNOP is higher than that of samples composed of only SVs in the medium range, based on the occurrence of weather re-gime transitions in Northern Hemisphere after about four days. Besides, the reliability of ensemble forecasts is evaluated by the Rank Histograms. The above conclusions confirm and extend those reached earlier by the authors, which stated that the introduction of CNOP improves the forecast skill under the condition that the analysis error belongs to a kind of fast-growing error by using a barotropic QG model.
Ensemble prediction experiments using conditional nonlinear optimal perturbation
Institute of Scientific and Technical Information of China (English)
JIANG ZhiNa; MU Mu; WANG DongHai
2009-01-01
Two methods for initialization of ensemble forecasts are compared, namely, singular vector (SV) and conditional nonlinear optimal perturbation (CNOP). The comparison is done for forecast lengths of up to 10 days with a three-level quasi-geostrophic (QG) atmospheric model in a perfect model scenario. Ten cases are randomly selected from 1982/1983 winter to 1993/1994 winter (from 12 to the following February). Anomaly correlation coefficient (ACC) is adopted as a tool to measure the quality of the predicted ensembles on the Northern Hemisphere 500 hPa geopotential height. The results show that the forecast quality of ensemble samples in which the first SV is replaced by CNOP is higher than that of samples composed of only SVs in the medium range, based on the occurrence of weather re-gime transitions in Northern Hemisphere after about four days. Besides, the reliability of ensemble forecasts is evaluated by the Rank Histograms. The above conclusions confirm .and extend those reached earlier by the authors, which stated that the introduction of CNOP improves the forecast skill under the condition that the analysis error belongs to a kind of fast-growing error by using a barotropic QG model.
Quintin, Jerome; Sherkatghanad, Zeinab; Cai, Yi-Fu; Brandenberger, Robert H.
2015-09-01
Assuming that curvature perturbations and gravitational waves originally arise from vacuum fluctuations in a matter-dominated phase of contraction, we study the dynamics of the cosmological perturbations evolving through a nonsingular bouncing phase described by a generic single scalar field Lagrangian minimally coupled to Einstein gravity. In order for such a model to be consistent with the current upper limits on the tensor-to-scalar ratio, there must be an enhancement of the curvature fluctuations during the bounce phase. We show that, while it remains possible to enlarge the amplitude of curvature perturbations due to the nontrivial background evolution, this growth is very limited because of the conservation of curvature perturbations on super-Hubble scales. We further perform a general analysis of the evolution of primordial non-Gaussianities through the bounce phase. By studying the general form of the bispectrum we show that the non-Gaussianity parameter fNL (which is of order unity before the bounce phase) is enhanced during the bounce phase if the curvature fluctuations grow. Hence, in such nonsingular bounce models with matter given by a single scalar field, there appears to be a tension between obtaining a small enough tensor-to-scalar ratio and not obtaining a value of fNL in excess of the current upper bounds. This conclusion may be considered as a "no-go" theorem that rules out any single field matter bounce cosmology starting with vacuum initial conditions for the fluctuations.
Rahman, T.
2009-01-01
In this thesis, a finite element based perturbation approach is presented for geometrically nonlinear analysis of thin-walled structures. Geometrically nonlinear static and dynamic analyses are essential for this class of structures. Nowadays nonlinear analysis of thin-walled shell structures is oft
Exploring non-linear cosmological matter diffusion coefficients
Velten, Hermano
2014-01-01
Since microscopic velocity diffusion can be incorporated into general relativity in a consistent way, we study cosmological background solutions when the diffusion phenomena takes place in an expanding universe. Our focus here relies on the nature of the diffusion coefficient $\\sigma$ which measures the magnitude of such transport phenomena. We test dynamics where $\\sigma$ has a phenomenological dependence on the scale factor, the matter density, the dark energy and the expansion rate.
Directory of Open Access Journals (Sweden)
Yize Fan
2015-06-01
Full Text Available Cosmological perturbations of the non-minimally coupled scalar field dark energy in both the metric and Palatini formalisms are studied in this paper. We find that on the large scales with the energy density of dark energy becoming more and more important in the low redshift region, the gravitational potential becomes smaller and smaller, and the effect of non-minimal coupling becomes more and more apparent. In the metric formalism the value of the gravitational potential in the non-minimally coupled case with a positive coupling constant is less than that in the minimally coupled case, while it is larger if the coupling constant is negative. This is different from that in the Palatini formalism where the value of gravitational potential is always smaller. Based upon the quasi-static approximation on the sub-horizon scales, the linear growth of matter is also analyzed. We obtain that the effective Newton's constants in the metric and Palatini formalisms have different forms. A negative coupling constant enhances the gravitational interaction, while a positive one weakens it. Although the metric and Palatini formalisms give different linear growth rates, the difference is very small and the current observation cannot distinguish them effectively.
Two-parameter non-linear spacetime perturbations gauge transformations and gauge invariance
Bruni, M; Sopuerta, C F; Bruni, Marco; Gualtieri, Leonardo; Sopuerta, Carlos F.
2003-01-01
An implicit fundamental assumption in relativistic perturbation theory is that there exists a parametric family of spacetimes that can be Taylor expanded around a background. The choice of the latter is crucial to obtain a manageable theory, so that it is sometime convenient to construct a perturbative formalism based on two (or more) parameters. The study of perturbations of rotating stars is a good example: in this case one can treat the stationary axisymmetric star using a slow rotation approximation (expansion in the angular velocity Omega), so that the background is spherical. Generic perturbations of the rotating star (say parametrized by lambda) are then built on top of the axisymmetric perturbations in Omega. Clearly, any interesting physics requires non-linear perturbations, as at least terms lambda Omega need to be considered. In this paper we analyse the gauge dependence of non-linear perturbations depending on two parameters, derive explicit higher order gauge transformation rules, and define gaug...
Directory of Open Access Journals (Sweden)
G. Sun
2011-11-01
Full Text Available Human activities and climate change are important factors that affect grassland ecosystems. A new optimization approach, the approach of conditional nonlinear optimal perturbation (CNOP related to initial and parameter perturbations, is employed to explore the nonlinearly combined impacts of human activities and climate change on a grassland ecosystem using a theoretical grassland model. In our study, it is assumed that the initial perturbations and parameter perturbations are regarded as human activities and climate change, respectively. Numerical results indicate that the climate changes causing the maximum effect in the grassland ecosystem are different under disparate intensities of human activities. This implies the pattern of climate change is very critical to the maintenance or degradation of grassland ecosystem in light of high intensity of human activities and that the grassland ecosystem should be rationally managed when the moisture index decreases. The grassland ecosystem influenced by the nonlinear combination of human activities and climate change undergoes abrupt change, while the grassland ecosystem affected by other types of human activities and climate change fails to show the abrupt change under a certain range of perturbations with the theoretical model. The further numerical analyses also indicate that the growth of living biomass and the evaporation from soil surface shaded by the wilted biomass may be crucial factors contributing to the abrupt change of the grassland equilibrium state within the theoretical model.
Achour, Jibril Ben; Grain, Julien; Marciano, Antonino
2016-01-01
Scalar cosmological perturbations in loop quantum cosmology (LQC) is revisited in a covariant manner, using self dual Ashtekar variables. For real-valued Ashtekar-Barbero variables, this `deformed algebra' approach has been shown to implement holonomy corrections from loop quantum gravity (LQG) in a consistent manner, albeit deforming the algebra of modified constraints in the process. This deformation has serious conceptual ramifications, not the least of them being an effective `signature-change' in the deep quantum regime. In this paper, we show that working with self dual variables lead to an undeformed algebra of hypersurface deformations, even after including holonomy corrections in the effective constraints. As a necessary consequence, the diffeomorphism constraint picks up non-perturbative quantum corrections thus hinting at a modification of the underlying space-time structure, a novel ingredient compared to the usual treatment of (spatial) diffeomorphisms in LQG. This work extends a similar result o...
Nonlinear Generation of Fluting Perturbations by Kink Mode
Ruderman, M. S.
2017-08-01
We study the excitation of fluting perturbations in a magnetic tube by an initially imposed kink mode. We use the ideal magnetohydrodynamic (MHD) equations in the cold-plasma approximation. We also use the thin-tube approximation and scale the dependent and independent variables accordingly. Then we assume that the dimensionless amplitude of the kink mode is small and use it as an expansion parameter in the regular perturbation method. We obtain the expression for the tube boundary perturbation in the second-order approximation. This perturbation is a superposition of sausage and fluting perturbations. The amplitude of the fluting perturbation takes its maximum at the middle of the tube, and it monotonically decreases with the distance from the middle of the tube.
Nonlinear Vibration of Rotor Rubbing Stator Caused by Initial Perturbation
Institute of Scientific and Technical Information of China (English)
张小章; 隆锦胜; 李正光
2001-01-01
The vibration of a rotor rubbing a stator caused by an initial perturbation was studied analytically.The analytical model consists of a simple disc shaft rotor and a fixed stator. The perturbation is aninstantaneous change of the radial velocity when the rotor is operating in its normal steady state. The analysisshowed that the rotor may continue rubbing the stator for small clearance, even if the initial perturbation nolonger exists. For the interest of engineering applications, we investigated various rotating speeds,perturbation amplitudes and clearances between the rotor and the stator. Various friction coefficients on thecontact surface were also considered. The graphical results can be used for the design of rotating machines.``
Shapiro, Paul R; Mao, Yi; Iliev, Ilian T; Mellema, Garrelt; Datta, Kanan K; Ahn, Kyungjin; Koda, Jun
2013-04-12
The 21 cm background from the epoch of reionization is a promising cosmological probe: line-of-sight velocity fluctuations distort redshift, so brightness fluctuations in Fourier space depend upon angle, which linear theory shows can separate cosmological from astrophysical information. Nonlinear fluctuations in ionization, density, and velocity change this, however. The validity and accuracy of the separation scheme are tested here for the first time, by detailed reionization simulations. The scheme works reasonably well early in reionization (≲40% ionized), but not late (≳80% ionized).
Nonlinear predator-prey singularly perturbed Robin Problems for reaction diffusion systems
Institute of Scientific and Technical Information of China (English)
莫嘉琪; 韩祥临
2003-01-01
The nonlinear predator-prey reaction diffusion systems for singularly perturbed Robin Problems are considered. Under suitable conditions, the theory of differential inequalities can be used to study the asymptotic behavior of the solution for initial boundary value problems.
Institute of Scientific and Technical Information of China (English)
莫嘉琪
2003-01-01
The nonlinear predator-prey singularly perturbed Robin initial boundary value problems for reaction diffusion systems were considered. Under suitable conditions, using theory of differential inequalities the existence and asymptotic behavior of solution for initial boundary value problems were studied.
NONLINEAR PERTURBATION METHOD FOR CALCULATING AXISYMMETRIC CAVITATIONAL FLOWS
Directory of Open Access Journals (Sweden)
Vasyl Buivol
2013-12-01
Full Text Available A mathematical model of a cavity under the influence of perturbations of various origins is evaluated. The model is based on hydrodynamics of flows with free boundaries and the theory of small perturbations. Specific analysis is provided for cavitational flows behind cones
Perturbed dynamics of discrete-time switched nonlinear systems with delays and uncertainties.
Liu, Xingwen; Cheng, Jun
2016-05-01
This paper addresses the dynamics of a class of discrete-time switched nonlinear systems with time-varying delays and uncertainties and subject to perturbations. It is assumed that the nominal switched nonlinear system is robustly uniformly exponentially stable. It is revealed that there exists a maximal Lipschitz constant, if perturbation satisfies a Lipschitz condition with any Lipschitz constant less than the maximum, then the perturbed system can preserve the stability property of the nominal system. In situations where the perturbations are known, it is proved that there exists an upper bound of coefficient such that the perturbed system remains exponentially stable provided that the perturbation is scaled by any coefficient bounded by the upper bound. A numerical example is provided to illustrate the proposed theoretical results.
Simulating nonlinear cosmological structure formation with massive neutrinos
Banerjee, Arka
2016-01-01
We present a new method for simulating cosmologies that contain massive particles with thermal free streaming motion, such as massive neutrinos or warm/hot dark matter. This method combines particle and fluid descriptions of the thermal species to eliminate the shot noise known to plague conventional N-body simulations. We describe this method in detail, along with results for a number of test cases to validate our method, and check its range of applicability. Using this method, we demonstrate that massive neutrinos can produce a significant scale-dependence in the large-scale biasing of deep voids in the matter field. We show that this scale-dependence may be quantitatively understood using an extremely simple spherical expansion model which reproduces the behavior of the void bias for different neutrino parameters.
PERSISTENT HOMOCLINIC ORBITS FOR A PERTURBED CUBIC-QUINTIC NONLINEAR SCHRODINGER EQUATION
Institute of Scientific and Technical Information of China (English)
郭柏灵; 陈翰林
2002-01-01
In this paper, the existence of homoclinic orbits, for a perturbed cubicquintic nonlinear Schrodinger equation with even periodic boundary conditions, under the generalized parameters conditions is established. More specifically, we combine geometric singular perturbation theory with Melnikov analysis and integrable theory to prove the persistence of homoclinic orbits.
Indian Academy of Sciences (India)
J B ZHOU; J XU; J D WEI; X Q YANG
2017-04-01
This paper is concerned with the existence of travelling wave solutions to a singularly perturbed generalized Gardner equation with nonlinear terms of any order. By using geometric singular perturbation theory and based on the relation between solitary wave solution and homoclinic orbits of the associated ordinary differential equations, the persistence of solitary wave solutions of this equation is proved when the perturbation parameter is sufficiently small. The numerical simulations verify our theoretical analysis.
Energy Technology Data Exchange (ETDEWEB)
Astashenok, Artyom V., E-mail: artyom.art@gmail.com [Baltic Federal University of I. Kant, Department of Theoretical Physics, 236041, 14, Nevsky st., Kaliningrad (Russian Federation); Odintsov, Sergei D. [Institucio Catalana de Recerca i Estudis Avancats (ICREA), Barcelona (Spain); Institut de Ciencies de l' Espai (CSIC-IEEC), Campus UAB, Torre C5-Par-2a pl, E-08193 Bellaterra (Barcelona) (Spain); Eurasian International Center for Theor. Physics, Eurasian National University, Astana 010008 (Kazakhstan); Tomsk State Pedagogical University, Tomsk (Russian Federation)
2013-01-29
We confront dark energy models which are currently similar to {Lambda}CDM theory with observational data which include the SNe data, matter density perturbations and baryon acoustic oscillations data. DE cosmology under consideration may evolve to Big Rip, type II or type III future singularity, or to Little Rip or Pseudo-Rip universe. It is shown that matter perturbations data define more precisely the possible deviation from {Lambda}CDM model than consideration of SNe data only. The combined data analysis proves that DE models under consideration are as consistent as {Lambda}CDM model. We demonstrate that growth of matter density perturbations may occur at sufficiently small background density but still before the possible disintegration of bound objects (like clusters of galaxies, galaxies, etc.) in Big Rip, type III singularity, Little Rip or Pseudo-Rip universe. This new effect may bring the future universe to chaotic state well before disintegration or Rip.
Buchert, Thomas
2012-01-01
In this first paper we present a Lagrangian framework for the description of structure formation in general relativity, restricting attention to irrotational dust matter. As an application we present a self-contained derivation of a general-relativistic analogue of Zel'dovich's approximation for the description of structure formation in cosmology, and compare it with previous suggestions in the literature. This approximation is then investigated: paraphrasing the derivation in the Newtonian framework we provide general-relativistic analogues of the basic system of equations for a single dynamical field variable and recall the first-order perturbation solution of these equations. We then define a general-relativistic analogue of Zel'dovich's approximation and investigate consequences by functionally evaluating relevant variables. We so obtain a possibly powerful model that, although constructed through extrapolation of a perturbative solution, can be used to address non-perturbatively, e.g. problems of structu...
Farano, Mirko; Cherubini, Stefania; Robinet, Jean-Christophe; De Palma, Pietro
2016-12-01
Subcritical transition in plane Poiseuille flow is investigated by means of a Lagrange-multiplier direct-adjoint optimization procedure with the aim of finding localized three-dimensional perturbations optimally growing in a given time interval (target time). Space localization of these optimal perturbations (OPs) is achieved by choosing as objective function either a p-norm (with p\\gg 1) of the perturbation energy density in a linear framework; or the classical (1-norm) perturbation energy, including nonlinear effects. This work aims at analyzing the structure of linear and nonlinear localized OPs for Poiseuille flow, and comparing their transition thresholds and scenarios. The nonlinear optimization approach provides three types of solutions: a weakly nonlinear, a hairpin-like and a highly nonlinear optimal perturbation, depending on the value of the initial energy and the target time. The former shows localization only in the wall-normal direction, whereas the latter appears much more localized and breaks the spanwise symmetry found at lower target times. Both solutions show spanwise inclined vortices and large values of the streamwise component of velocity already at the initial time. On the other hand, p-norm optimal perturbations, although being strongly localized in space, keep a shape similar to linear 1-norm optimal perturbations, showing streamwise-aligned vortices characterized by low values of the streamwise velocity component. When used for initializing direct numerical simulations, in most of the cases nonlinear OPs provide the most efficient route to transition in terms of time to transition and initial energy, even when they are less localized in space than the p-norm OP. The p-norm OP follows a transition path similar to the oblique transition scenario, with slightly oscillating streaks which saturate and eventually experience secondary instability. On the other hand, the nonlinear OP rapidly forms large-amplitude bent streaks and skips the phases
Application of homotopy-perturbation method to nonlinear population dynamics models
Energy Technology Data Exchange (ETDEWEB)
Chowdhury, M.S.H. [School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi Selangor (Malaysia); Hashim, I. [School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi Selangor (Malaysia)], E-mail: ishak_h@ukm.my; Abdulaziz, O. [School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi Selangor (Malaysia)
2007-08-20
In this Letter, the homotopy-perturbation method (HPM) is employed to derive approximate series solutions of nonlinear population dynamics models. The nonlinear models considered are the multispecies Lotka-Volterra equations. The accuracy of this method is examined by comparison with the available exact and the fourth-order Runge-Kutta method (RK4)
A conformal approach for the analysis of the non-linear stability of radiation cosmologies
Energy Technology Data Exchange (ETDEWEB)
Luebbe, Christian, E-mail: c.luebbe@ucl.ac.uk [Department of Mathematics, University College London, Gower Street, London, WC1E 6BT (United Kingdom); Department of Mathematics, University of Leicester, University Road, LE1 8RH (United Kingdom); Valiente Kroon, Juan Antonio, E-mail: j.a.valiente-kroon@qmul.ac.uk [School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS (United Kingdom)
2013-01-15
The conformal Einstein equations for a trace-free (radiation) perfect fluid are derived in terms of the Levi-Civita connection of a conformally rescaled metric. These equations are used to provide a non-linear stability result for de Sitter-like trace-free (radiation) perfect fluid Friedman-Lemaitre-Robertson-Walker cosmological models. The solutions thus obtained exist globally towards the future and are future geodesically complete. - Highlights: Black-Right-Pointing-Pointer We study the Einstein-Euler system in General Relativity using conformal methods. Black-Right-Pointing-Pointer We analyze the structural properties of the associated evolution equations. Black-Right-Pointing-Pointer We establish the non-linear stability of pure radiation cosmological models.
Nonlinear and Perturbative Evolution of Distorted Black Holes; 2, Odd-parity Modes
Baker, J; Campanelli, M; Loustó, C O; Seidel, E; Takahashi, R
2000-01-01
We compare the fully nonlinear and perturbative evolution of nonrotating black holes with odd-parity distortions utilizing the perturbative results to interpret the nonlinear results. This introduction of the second polarization (odd-parity) mode of the system, and the systematic use of combined techniques brings us closer to the goal of studying more complicated systems like distorted, rotating black holes, such as those formed in the final inspiral stage of two black holes. The nonlinear evolutions are performed with the 3D parallel code for Numerical Relativity, {Cactus}, and an independent axisymmetric code, {Magor}. The linearized calculation is performed in two ways: (a) We treat the system as a metric perturbation on Schwarzschild, using the Regge-Wheeler equation to obtain the waveforms produced. (b) We treat the system as a curvature perturbation of a Kerr black hole (but here restricted to the case of vanishing rotation parameter a) and evolve it with the Teukolsky equation The comparisons of the wa...
Nonlinear Circuit Analysis via Perturbation Methods and Hardware Prototyping
Directory of Open Access Journals (Sweden)
K. Odame
2010-01-01
Full Text Available Nonlinear signal processing is necessary in many emerging applications where form factor and power are at a premium. In order to make such complex computation feasible under these constraints, it is necessary to implement the signal processors as analog circuits. Since analog circuit design is largely based on a linear systems perspective, new tools are being introduced to circuit designers that allow them to understand and exploit circuit nonlinearity for useful processing. This paper discusses two such tools, which represent nonlinear circuit behavior in a graphical way, making it easy to develop a qualitative appreciation for the circuits under study.
Vittorio, Nicola
2017-01-01
Modern cosmology has changed significantly over the years, from the discovery to the precision measurement era. The data now available provide a wealth of information, mostly consistent with a model where dark matter and dark energy are in a rough proportion of 3:7. The time is right for a fresh new textbook which captures the state-of-the art in cosmology. Written by one of the world's leading cosmologists, this brand new, thoroughly class-tested textbook provides graduate and undergraduate students with coverage of the very latest developments and experimental results in the field. Prof. Nicola Vittorio shows what is meant by precision cosmology, from both theoretical and observational perspectives.
INITIAL LAYER PHENOMENA FOR A CLASS OF SINGULAR PERTURBED NONLINEAR SYSTEM WITH SLOW VARIABLES
Institute of Scientific and Technical Information of China (English)
黄蔚章; 陈育森
2004-01-01
The initial layer phenomena for a class of singular perturbed nonlinear system with slow variables are studied. By introducing stretchy variables with different quantity levels and constructing the correction term of initial layer with different "thickness", the Norder approximate expansion of perturbed solution concerning small parameter is obtained,and the "multiple layer" phenomena of perturbed solutions are revealed. Using the fixed point theorem, the existence of perturbed solution is proved, and the uniformly valid asymptotic expansion of the solutions is given as well.
NONLINEAR SINGULARLY PERTURBED PREDATOR-PREY REACTION DIFFUSION SYSTEMS
Institute of Scientific and Technical Information of China (English)
MoJiaqi; TangRongrong
2004-01-01
A class of nonlinear predator-prey reaction diffusion systems for singularly perturbedproblems are considered. Under suitable conditions, by using theory of differential inequalitiesthe existence and asymptotic behavior of solution for initial boundary value problems arestudied.
Observer-Based Nonlinear Control of A Torque Motor with Perturbation Estimation
Institute of Scientific and Technical Information of China (English)
J Chen; E Prempain; Q H Wu
2006-01-01
This paper presents an observer-based nonlinear control method that was developed and implemented to provide accurate tracking control of a limited angle torque motor following a 50Hz reference waveform. The method is based on a robust nonlinear observer, which is used to estimate system states and perturbations and then employ input-output feedback linearization to compensate for the system nonlinearities and uncertainties. The estimation of system states and perturbations allows input-output linearization of the nonlinear system without an accurate mathematical model of nominal plant. The simulation results show that the observer-based nonlinear control method is superior in comparison with the conventional model-based state feedback linearizing controller.
Parabolic Perturbation of a Nonlinear Hyperbolic Problem Arising in Physiology
Colli, P.; Grasselli, M.
We study a transport-diffusion initial value problem where the diffusion codlicient is "small" and the transport coefficient is a time function depending on the solution in a nonlinear and nonlocal way. We show the existence and the uniqueness of a weak solution of this problem. Moreover we discuss its asymptotic behaviour as the diffusion coefficient goes to zero, obtaining a well-posed first-order nonlinear hyperbolic problem. These problems arise from mathematical models of muscle contraction in the framework of the sliding filament theory.
Non-linear structure formation in the `Running FLRW' cosmological model
Bibiano, Antonio; Croton, Darren J.
2016-07-01
We present a suite of cosmological N-body simulations describing the `Running Friedmann-Lemaïtre-Robertson-Walker' (R-FLRW) cosmological model. This model is based on quantum field theory in a curved space-time and extends Lambda cold dark matter (ΛCDM) with a time-evolving vacuum density, Λ(z), and time-evolving gravitational Newton's coupling, G(z). In this paper, we review the model and introduce the necessary analytical treatment needed to adapt a reference N-body code. Our resulting simulations represent the first realization of the full growth history of structure in the R-FLRW cosmology into the non-linear regime, and our normalization choice makes them fully consistent with the latest cosmic microwave background data. The post-processing data products also allow, for the first time, an analysis of the properties of the halo and sub-halo populations. We explore the degeneracies of many statistical observables and discuss the steps needed to break them. Furthermore, we provide a quantitative description of the deviations of R-FLRW from ΛCDM, which could be readily exploited by future cosmological observations to test and further constrain the model.
Directory of Open Access Journals (Sweden)
U. Filobello-Nino
2015-01-01
Full Text Available We propose an approximate solution of T-F equation, obtained by using the nonlinearities distribution homotopy perturbation method (NDHPM. Besides, we show a table of comparison, between this proposed approximate solution and a numerical of T-F, by establishing the accuracy of the results.
Exponents of non-linear clustering in scale-free one dimensional cosmological simulations
Benhaiem, David; Sicard, François
2012-01-01
One dimensional versions of cosmological N-body simulations have been shown to share many qualitative behaviours of the three dimensional problem. They can resolve a large range of time and length scales, and admit exact numerical integration. We use such models to study how non-linear clustering depends on initial conditions and cosmology. More specifically, we consider a family of models which, like the 3D EdS model, lead for power-law initial conditions to self-similar clustering characterized in the strongly non-linear regime by power-law behaviour of the two point correlation function. We study how the corresponding exponent \\gamma depends on the initial conditions, characterized by the exponent n of the power spectrum of initial fluctuations, and on a single parameter \\kappa controlling the rate of expansion. The space of initial conditions/cosmology divides very clearly into two parts: (1) a region in which \\gamma depends strongly on both n and \\kappa and where it agrees very well with a simple general...
Amin, Mustafa A; Blandford, Roger D
2007-01-01
The relationship between the metric and nonrelativistic matter distribution depends on the theory of gravity and additional fields, hence providing a possible way of distinguishing competing theories. With the assumption that the geometry and kinematics of the homogeneous universe have been measured, we present a procedure for understanding and testing the relationship between the cosmological matter distribution and metric perturbations (along with their respective evolution) using the ratio of the physical size of the perturbation to the size of the horizon as our small expansion parameter. We expand around Newtonian gravity on linear, sub-horizon scales with coefficient functions in front of the expansion parameter. Our framework relies on an ansatz which ensures that (i) the Poisson equation is recovered on small scales (ii) the metric variables (and any additional fields) are generated and supported by the nonrelativistic matter overdensity. The scales for which our framework is intended are small enough...
Delay-dependent passive control of linear systems with nonlinear perturbation
Institute of Scientific and Technical Information of China (English)
Li Caina; Cui Baotong
2008-01-01
The problem of delay-dependent passive control of a class of linear systems with nonlinear perturbation and time-varying delay in states is studied. The main idea aims at designing a state-feedback controller such that for a time-varying delay in states, the linear system with nonlinear perturbation remains robustly stable and passive.In the system, the delay is time-varying. And the derivation of delay has the maximum and minimum value. The time-varying nonlinear perturbation is allowed to be norm-bounded. Using the effective linear matrix inequality methodology, the sufficient condition is primarily obtained for the system to have robust stability and passivity.Subsequently the existent condition of a state feedback controller is given, and the explicit expression of the controller is obtained by means of the solution of linear matrix inequalities (LMIs). In the end, a numerical example is given to demonstrate the validity and applicability of the proposed approach.
Excitation of turbulence in accretion disks of binary stars by non-linear perturbations
Kurbatov, E. P.; Bisikalo, D. V.
2017-06-01
Accretion disks in binary systems can experience hydrodynamical influences at both their inner and outer edges. The former is typical for protoplanetary disks around young T Tauri stars, while the latter is typical for circumstellar disks in close binaries. This influence excites perturbations with various scales and amplitudes in the disk. The nonlinear evolution of perturbations with a finite, but small amplitude against the background of a sub-Keplerian flow is investigated. Nonlinear effects at the fronts of perturbation waves lead to the formation of discontinuities in the density and radial velocity; i.e., to formation of shocks. The tangential flow in the neighborhood of the shock becomes equivalent to a flow in a boundary layer. Due to an instability of the tangential flow, the disk becomes turbulent. The characteristics of the turbulence depend on the parameters of the perturbations, but the Shakura-Syunyaev α parameter does not exceed 0.1.
Desoer, C. A.; Kabuli, M. G.
1989-01-01
The authors consider a linear (not necessarily time-invariant) stable unity-feedback system, where the plant and the compensator have normalized right-coprime factorizations. They study two cases of nonlinear plant perturbations (additive and feedback), with four subcases resulting from: (1) allowing exogenous input to Delta P or not; 2) allowing the observation of the output of Delta P or not. The plant perturbation Delta P is not required to be stable. Using the factorization approach, the authors obtain necessary and sufficient conditions for all cases in terms of two pairs of nonlinear pseudostate maps. Simple physical considerations explain the form of these necessary and sufficient conditions. Finally, the authors obtain the characterization of all perturbations Delta P for which the perturbed system remains stable.
Adaptive Stabilization for a Class of Dynamical Systems with Nonlinear Delayed State Perturbations
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The problem of adaptive stabilization for a class of systems with nonlinear delayed state perturbations is considered. The bound of the perturbations is assumed to be unknown, by using the adaptive control method, an adaptive controller is designed. Based on the Lyapunov- Karasovskii functional, it is shown that the dynamical system can be stabilized by the adaptive controller. The effectiveness of the proposed controller is demonstrated by some simulations.
Singular perturbation methods for nonlinear dynamic systems with time delays
Energy Technology Data Exchange (ETDEWEB)
Hu, H.Y. [MOE Key Laboratory of Structure Mechanics and Control for Aircraft, Nanjing University of Aeronautics and Astronautics, 210016 Nanjing (China)], E-mail: hhyae@nuaa.edu.cn; Wang, Z.H. [MOE Key Laboratory of Structure Mechanics and Control for Aircraft, Nanjing University of Aeronautics and Astronautics, 210016 Nanjing (China)
2009-04-15
This review article surveys the recent advances in the dynamics and control of time-delay systems, with emphasis on the singular perturbation methods, such as the method of multiple scales, the method of averaging, and two newly developed methods, the energy analysis and the pseudo-oscillator analysis. Some examples are given to demonstrate the advantages of the methods. The comparisons with other methods show that these methods lead to easier computations and higher accurate prediction on the local dynamics of time-delay systems near a Hopf bifurcation.
A numerical-perturbation method for the nonlinear analysis of structural vibrations
Nayfeh, A. H.; Mook, D. T.; Lobitz, D. W.
1974-01-01
A numerical-perturbation method is proposed for the determination of the nonlinear forced response of structural elements. Purely analytical techniques are capable of determining the response of structural elements having simple geometries and simple variations in thickness and properties, but they are not applicable to elements with complicated structure and boundaries. Numerical techniques are effective in determining the linear response of complicated structures, but they are not optimal for determining the nonlinear response of even simple elements when modal interactions take place due to the complicated nature of the response. Therefore, the optimum is a combined numerical and perturbation technique. The present technique is applied to beams with varying cross sections.
Asymptotic solution for a class of weakly nonlinear singularly perturbed reaction diffusion problem
Institute of Scientific and Technical Information of China (English)
TANG Rong-rong
2009-01-01
Under appropriate conditions, with the perturbation method and the theory of differential inequalities, a class of weakly nonlinear singularly perturbed reaction diffusion problem is considered. The existence of solution of the original problem is proved by constructing the auxiliary functions. The uniformly valid asymptotic expansions of the solution for arbitrary mth order approximation are obtained through constructing the formal solutions of the original problem, expanding the nonlinear terms to the power in small parameter e and comparing the coefficient for the same powers of ε. Finally, an example is provided, resulting in the error of O(ε2).
Enhanced Multistage Homotopy Perturbation Method: Approximate Solutions of Nonlinear Dynamic Systems
Directory of Open Access Journals (Sweden)
Daniel Olvera
2014-01-01
Full Text Available We introduce a new approach called the enhanced multistage homotopy perturbation method (EMHPM that is based on the homotopy perturbation method (HPM and the usage of time subintervals to find the approximate solution of differential equations with strong nonlinearities. We also study the convergence of our proposed EMHPM approach based on the value of the control parameter h by following the homotopy analysis method (HAM. At the end of the paper, we compare the derived EMHPM approximate solutions of some nonlinear physical systems with their corresponding numerical integration solutions obtained by using the classical fourth order Runge-Kutta method via the amplitude-time response curves.
Extending the perturbation technique to the modal representation of nonlinear systems
Energy Technology Data Exchange (ETDEWEB)
Soltani, S. [Department of Electrical Engineering, Science and Research Branch, Islamic Azad University (IAU), 1477893855-14515775, Tehran (Iran); Pariz, N.; Ghazi, R. [Department of Electrical Engineering, ferdowsi University, 9177948944-1111, Mashhad (Iran)
2009-08-15
After a brief review of perturbation technique, using this method an approach is developed to represent and study the behavior of nonlinear dynamic power systems. For the first time in this field, perturbation technique is applied to obtain an approximate closed form expression for the zero input response of stressed power systems. In order to show the superiority of the proposed method, it has been applied to a typical nonlinear system which is a single machine infinite bus (SMIB) power system with unified power flow controller (UPFC). The accuracy and competency of this method in comparison with Modal Series method will also be validated. (author)
Post-inflation increase of the cosmological tensor-to-scalar perturbation ratio
Energy Technology Data Exchange (ETDEWEB)
Bartolo, N.; /ICTP, Trieste; Kolb, Edward W.; /Fermilab /Chicago U., Astron. Astrophys. Ctr. /Chicago U., EFI; Riotto, A.; /Padua U. /INFN, Padua
2005-07-01
We investigate the possibility that the amplitude of scalar density perturbations may be damped after inflation. This would imply that CMB anisotropies do not uniquely fix the amplitude of the perturbations generated during inflation and that the present tensor-to-scalar ratio might be larger than produced in inflation, increasing the prospects of detection of primordial gravitational radiation. It turns out, however, that the damping of density perturbations is hard to achieve.
A filter algorithm for multi-measurement nonlinear system with parameter perturbation
Institute of Scientific and Technical Information of China (English)
GUO Yun-fei; WEI Wei; XUE An-ke; MAO Dong-cai
2006-01-01
An improved interacting multiple models particle filter (IMM-PF) algorithm is proposed for multi-measurement nonlinear system with parameter perturbation. It divides the perturbation region into sub-regions and assigns each of them a particle filter. Hence the perturbation problem is converted into a multi-model filters problem. It combines the multiple measurements into a fusion value according to their likelihood function. In the simulation study, we compared it with the IMM-KF and the H-infinite filter; the results testify to its advantage over the other two methods.
Large-scale weakly nonlinear perturbations of convective magnetic dynamos in a rotating layer
Chertovskih, Roman
2015-01-01
We present a new mechanism for generation of large-scale magnetic field by thermal convection which does not involve the alpha-effect. We consider weakly nonlinear perturbations of space-periodic steady convective magnetic dynamos in a rotating layer that were identified in our previous work. The perturbations have a spatial scale in the horizontal direction that is much larger than the period of the perturbed convective magnetohydrodynamic state. Following the formalism of the multiscale stability theory, we have derived the system of amplitude equations governing the evolution of the leading terms in expansion of the perturbations in power series in the scale ratio. This asymptotic analysis is more involved than in the cases considered earlier, because the kernel of the operator of linearisation has zero-mean neutral modes whose origin lies in the spatial invariance of the perturbed regime, the operator reduced on the generalised kernel has two Jordan normal form blocks of size two, and simplifying symmetri...
Optical solitons in resonant and nonresonant nonlinear media in the presence of perturbations.
Piscureanu, M; Manaila-Maximean, D
2000-01-01
We studied the optical solitons in nonlinear resonant and nonresonant media in the presence of perturbations, assuming that the transient effects are stimulated by the light scanning beam. We treated a slight deviation from the exact necessary condition for the soliton existence (2betanu=1), as a small perturbation for the integrable system, studying its influence upon the soliton propagation conditions. The approximation is constructed by the help of an algebraic version of the soliton perturbation theory using a Riemann boundary problem in connection with the inverse scattering method. We have obtained the soliton equation and we have solved it in the presence of a small perturbation in the adiabatic approximation. In this case we have demonstrated that for a Lorentz profile line the amplitude of the soliton remains unchanged, the only effect of the perturbation results in a phase shift.
Inhomogeneous Cosmology with Numerical Relativity
Macpherson, Hayley J; Price, Daniel J
2016-01-01
We perform three-dimensional numerical relativity simulations of homogeneous and inhomogeneous expanding spacetimes, with a view towards quantifying non-linear effects from cosmological inhomogeneities. We demonstrate fourth-order convergence with errors less than one part in 10^6 in evolving a flat, dust Friedmann-Lemaitre-Roberston-Walker (FLRW) spacetime using the Einstein Toolkit within the Cactus framework. We also demonstrate agreement to within one part in 10^3 between the numerical relativity solution and the linear solution for density, velocity and metric perturbations in the Hubble flow over a factor of ~350 change in scale factor (redshift). We simulate the growth of linear perturbations into the non-linear regime, where effects such as gravitational slip and tensor perturbations appear. We therefore show that numerical relativity is a viable tool for investigating nonlinear effects in cosmology.
Gorbach, Andrey V
2016-01-01
We present perturbation theory for analysis of generic third-order nonlinear processes in graphene integrated photonic structures. Optical response of graphene is treated as the nonlinear boundary condition in Maxwell equations. The derived models are applied for analysis of third harmonic generation in a graphene coated dielectric micro-fibre. The efficiency of up to few percent is predicted when using sub-picosecond pump pulses with energies of the order of $0.1$nJ in a sub-millimeter long fibre, when operating near the resonance of the graphene nonlinear conductivity $\\hbar\\omega=(2/3)E_F$.
Wang, Qing; Yao, Jing-Zheng
2010-12-01
Several algorithms were proposed relating to the development of a framework of the perturbation-based stochastic finite element method (PSFEM) for large variation nonlinear dynamic problems. For this purpose, algorithms and a framework related to SFEM based on the stochastic virtual work principle were studied. To prove the validity and practicality of the algorithms and framework, numerical examples for nonlinear dynamic problems with large variations were calculated and compared with the Monte-Carlo Simulation method. This comparison shows that the proposed approaches are accurate and effective for the nonlinear dynamic analysis of structures with random parameters.
Institute of Scientific and Technical Information of China (English)
Igor Boglaev; Matthew Hardy
2008-01-01
This paper presents and analyzes a monotone domain decomposition algorithm for solving nonlinear singularly perturbed reaction-diffusion problems of parabolic type.To solve the nonlinear weighted average finite difference scheme for the partial differential equation,we construct a monotone domain decomposition algorithm based on a Schwarz alternating method and a box-domain decomposition.This algorithm needs only to solve linear discrete systems at each iterative step and converges monotonically to the exact solution of the nonlinear discrete problem. The rate of convergence of the monotone domain decomposition algorithm is estimated.Numerical experiments are presented.
A new method to obtain approximate symmetry of nonlinear evolution equation from perturbations
Institute of Scientific and Technical Information of China (English)
Zhang Zhi-Yong; Yong Xue-Lin; Chen Yu-Fu
2009-01-01
A novel method for obtaining the approximate symmetry of a partial differential equation with a small parameter is introduced. By expanding the independent variable and the dependent variable in the small parameter series, we obtain more affluent approximate symmetries. The method is applied to two perturbed nonlinear partial differential equations and new approximate solutions are derived.
Application of homotopy-perturbation to non-linear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Cveticanin, L. [Faculty of Technical Sciences, 21000 Novi Sad, Trg D. Obradovica 6 (Serbia)], E-mail: cveticanin@uns.ns.ac.yu
2009-04-15
In this paper He's homotopy perturbation method has been adopted for solving non-linear partial differential equations. An approximate solution of the differential equation which describes the longitudinal vibration of a beam is obtained. The solution is compared with that found using the variational iteration method introduced by He. The difference between the two solutions is negligible.
Directory of Open Access Journals (Sweden)
Abaker. A. Hassaballa.
2015-10-01
Full Text Available - In recent years, many more of the numerical methods were used to solve a wide range of mathematical, physical, and engineering problems linear and nonlinear. This paper applies the homotopy perturbation method (HPM to find exact solution of partial differential equation with the Dirichlet and Neumann boundary conditions.
Rahman, T.; Jansen, E.L.; Tiso, P.
2011-01-01
In this paper, a finite element-based approach for nonlinear vibration analysis of shell structures is presented. The approach makes use of a perturbation method that gives an approximation for the amplitude-frequency relation of the structure. The method is formulated using a functional notation an
SINGULARLY PERTURBED SOLUTION FOR THIRD ORDER NONLINEAR EQUATIONS WITH TWO PARAMETERS
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
A class of singularly perturbed boundary value problems for nonlinear equation of the third order with two parameters is considered. Under suitable conditions, using the theory of differential inequalities the existence and asymptotic behavior of the solution for boundary value problem are studied.
Rahman, T.; Jansen, E.L.; Tiso, P.
2011-01-01
In this paper, a finite element-based approach for nonlinear vibration analysis of shell structures is presented. The approach makes use of a perturbation method that gives an approximation for the amplitude-frequency relation of the structure. The method is formulated using a functional notation
Testing CCDM Cosmology with the Radiation Temperature-Redshift Relation
Baranov, I; Lima, J A S
2016-01-01
The standard $\\Lambda$CDM model can be mimicked at the background and perturbative levels (linear and non-linear) by a class of gravitationally induced particle production cosmology dubbed CCDM cosmology. However, the radiation component in the CCDM model follows a slightly different temperature-redshift $T(z)$-law which depends on an extra parameter, $\
Phantom expansion with non-linear Schr\\"{o}dinger-type formulation of scalar field cosmology
Phetnora, Theerakarn; Gumjudpai, Burin
2008-01-01
We describe non-flat standard Friedmann cosmology of canonical scalar field with barotropic fluid in form of non-linear Schr\\"{o}dinger-type (NLS) formulation in which all cosmological dynamical quantities are expressed in term of Schr\\"{o}dinger quantities as similar to those in time-independent quantum mechanics. We assume the expansion to be superfast, i.e. phantom expansion. We report all Schr\\"{o}dinger-analogous quantities to scalar field cosmology. Effective equation of state coefficient is analyzed and illustrated. We show that in a non-flat universe, there is no fixed $w_{\\rm eff}$ value for the phantom divide. In a non-flat universe, even $w_{\\rm eff} > -1$, the expansion can be phantom. Moreover, in open universe, phantom expansion can happen even with $w_{\\rm eff} > 0$. We also report scalar field exact solutions within frameworks of the Friedmann formulation and the NLS formulation in non-flat universe cases.
Simulating the Effect of Non-Linear Mode-Coupling in Cosmological Parameter Estimation
Kiessling, A; Heavens, A F
2011-01-01
Fisher Information Matrix methods are commonly used in cosmology to estimate the accuracy that cosmological parameters can be measured with a given experiment, and to optimise the design of experiments. However, the standard approach usually assumes both data and parameter estimates are Gaussian-distributed. Further, for survey forecasts and optimisation it is usually assumed the power-spectra covariance matrix is diagonal in Fourier-space. But in the low-redshift Universe, non-linear mode-coupling will tend to correlate small-scale power, moving information from lower to higher-order moments of the field. This movement of information will change the predictions of cosmological parameter accuracy. In this paper we quantify this loss of information by comparing naive Gaussian Fisher matrix forecasts with a Maximum Likelihood parameter estimation analysis of a suite of mock weak lensing catalogues derived from N-body simulations, based on the SUNGLASS pipeline, for a 2-D and tomographic shear analysis of a Eucl...
Non-linear structure formation in the "Running FLRW" cosmological model
Bibiano, Antonio
2016-01-01
We present a suite of cosmological N-body simulations describing the "Running Friedmann-Lema{\\"i}tre-Robertson-Walker" (R-FLRW) cosmological model. This model is based on quantum field theory in a curved space-time and extends {\\Lambda}CDM with a time-evolving vacuum density, {\\Lambda}(z), and time-evolving gravitational Newton's coupling, G(z). In this paper we review the model and introduce the necessary analytical treatment needed to adapt a reference N-body code. Our resulting simulations represent the first realisation of the full growth history of structure in the R-FLRW cosmology into the non-linear regime, and our normalisation choice makes them fully consistent with the latest cosmic microwave background data. The post-processing data products also allow, for the first time, an analysis of the properties of the halo and sub-halo populations. We explore the degeneracies of many statistical observables and discuss the steps needed to break them. Furthermore, we provide a quantitative description of the...
Numerical solving for nonlinear using higher order homotopy Taylor-perturbation
Directory of Open Access Journals (Sweden)
Nor Hanim Abd Rahman
2013-03-01
Full Text Available Rootfinding is a classical problem that still remains an interest to many researchers. A series of hybrid methods called Higher Order Homotopy Taylor-perturbation method via start-system functions (HTTPss are implemented to give approximate solutions for nonlinear equations, . The techniques serve as alternative methods for obtaining approximate solutions for different types of nonlinear equations. Thus, this paper presents an analysis on numerical comparison between the classical Newton Raphson (CNR, Homotopy Perturbation method (HTPss and Higher Order Homotopy Taylor-perturbation via start-system (HHTPss. A computational system Maple14 is used for this paper. Numerical and Illustrative results reveal that HHTPss methods are acceptably accurate and applicable.
The Nonlinear cosmological matter power spectrum with massive neutrinos. 1. The Halo model
Energy Technology Data Exchange (ETDEWEB)
Abazajian, Kevork; /Los Alamos; Switzer, Eric R.; /Princeton U.; Dodelson, Scott; /Fermilab /Chicago U., Astron. Astrophys. Ctr.; Heitmann, Katrin; Habib, Salman; /Los
2004-11-01
Measurements of the linear power spectrum of galaxies have placed tight constraints on neutrino masses. We extend the framework of the halo model of cosmological nonlinear matter clustering to include the effect of massive neutrino infall into cold dark matter (CDM) halos. The magnitude of the effect of neutrino clustering for three degenerate mass neutrinos with m{sub v{sub 1}} = 0.9 eV is of order {approx}1%, within the potential sensitivity of upcoming weak lensing surveys. In order to use these measurements to further constrain--or eventually detect--neutrino masses, accurate theoretical predictions of the nonlinear power spectrum in the presence of massive neutrinos will be needed, likely only possible through high-resolution multiple particle (neutrino, CDM and baryon) simulations.
Towards physical cosmology: focus on inhomogeneous geometry and its non-perturbative effects
Buchert, Thomas
2011-01-01
We outline the key-steps towards the construction of a physical, fully relativistic cosmology. The influence of inhomogeneities on the effective evolution history of the Universe is encoded in backreaction terms and expressed through spatially averaged geometrical invariants. These are absent and interpreted as missing dark fundamental sources in the standard model. In the inhomogeneous case they can be interpreted as energies of an emerging scalar field (the morphon). We so explain how phenomenological scalar field models for Dark Energy, Dark Matter and Inflation, that are usually added as fundamental sources to a homogeneous-geometry (FLRW) cosmology, can be traced back to inhomogeneous geometrical properties of space. We lay down a line of arguments that is qualitatively conclusive, and we outline open problems of quantitative nature, related to the interpretation of observations. We discuss within a covariant framework (i) the foliation problem and invariant definitions of backreaction effects; (ii) the ...
The Kramers-Moyal Equation of the Cosmological Comoving Curvature Perturbation
Riotto, Antonio
2011-01-01
Fluctuations of the comoving curvature perturbation with wavelengths larger than the horizon length are governed by a Langevin equation whose stochastic noise arise from the quantum fluctuations that are assumed to become classical at horizon crossing. The infrared part of the curvature perturbation performs a random walk under the action of the stochastic noise and, at the same time, it suffers a classical force caused by its self-interaction. By a path-interal approach and, alternatively, by the standard procedure in random walk analysis of adiabatic elimination of fast variables, we derive the corresponding Kramers-Moyal equation which describes how the probability distribution of the comoving curvature perturbation at a given spatial point evolves in time and is a generalization of the Fokker-Planck equation. This approach offers an alternative way to study the late time behaviour of the correlators of the curvature perturbation from infrared effects.
Nonlinear fastest growing perturbation and the first kind of predictability
Institute of Scientific and Technical Information of China (English)
MU; Mu
2001-01-01
［1］Jiao Jiujiu, Grey hydrogeologic system analysis and time series model, Survey Science and Technology (in Chinese), 1987,(10): 39-43.［2］Li Shuwen, Wang Baolai, Xiao Guoqiang, A compound model of grey and periodic scrape and its application in groundwater prediction, Journal of Hebei Institute of Architectural Science & Technology (in Chinese), 1992, (3): 246-251.［3］Wang Qingyin, Li Shuwen, Grey distributed parameter model and groundwater analog, Journal of Hebei Institute of Architectural Science & Technology (in Chinese), 1992, (3): 66-70.［4］Guo Chunqing, Xia Riyuan, Liu Zhenglin, Gray Systematic Theory and Methodological Study of Krast Groundwater Resources Evaluation (in Chinese), Beijing: Geological Publishing House, 1993, 3-60.［5］Wang Qingyin, Liu Kaidi, The Mathematical Method of Grey Systematic Theory and Its Application (in Chinese), Chengdu: Publishing House of Southwestern China University of Communication, 1990, 23-27.［6］Wang Qingyin, Wu Heqing, The concept of grey number and its property, in Proceedings of NAFIPS98, USA, 1998,45-49.［7］Givoli, D., Doukhovni, I., Finite element programming approach for contact problems with geometrical nonlinearity, Computers and Structures, 1996, (8): 31-41.［8］Li Shuwen, Wang Zhiqiang, Wu Qiang, The superiority of storage-centered finite element method in solving seepage problem, Coal Geology and Exploration (in Chinese), 1999, (5): 46-49.
Gnutzmann, Sven; Waltner, Daniel
2016-12-01
We consider exact and asymptotic solutions of the stationary cubic nonlinear Schrödinger equation on metric graphs. We focus on some basic example graphs. The asymptotic solutions are obtained using the canonical perturbation formalism developed in our earlier paper [S. Gnutzmann and D. Waltner, Phys. Rev. E 93, 032204 (2016), 10.1103/PhysRevE.93.032204]. For closed example graphs (interval, ring, star graph, tadpole graph), we calculate spectral curves and show how the description of spectra reduces to known characteristic functions of linear quantum graphs in the low-intensity limit. Analogously for open examples, we show how nonlinear scattering of stationary waves arises and how it reduces to known linear scattering amplitudes at low intensities. In the short-wavelength asymptotics we discuss how genuine nonlinear effects may be described using the leading order of canonical perturbation theory: bifurcation of spectral curves (and the corresponding solutions) in closed graphs and multistability in open graphs.
Energy Technology Data Exchange (ETDEWEB)
Wang, Sai, E-mail: wangsai@itp.ac.cn [State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, 100049, Beijing (China); Chang, Zhe [State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, 100049, Beijing (China); Institute of High Energy Physics, Chinese Academy of Sciences, 100049, Beijing (China)
2015-06-11
We propose the gravity’s rainbow scenario as a possible alternative of the inflation paradigm to account for the flatness and horizon problems. We focus on studying the cosmological scalar perturbations which are seeded by the quantum fluctuations in the very early universe. The scalar power spectrum is expected to be nearly scale-invariant. We estimate the rainbow index λ and energy scale M in the gravity’s rainbow scenario by analyzing the Planck temperature and WMAP polarization datasets. The constraints on them are given by λ=2.933±0.012 and ln(10{sup 5}M/M{sub p})=-0.401{sub -0.451}{sup +0.457} at the 68 % confidence level.
Energy Technology Data Exchange (ETDEWEB)
Wang, Sai [Chinese Academy of Sciences, State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Beijing (China); Chang, Zhe [Chinese Academy of Sciences, State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Beijing (China); Chinese Academy of Sciences, Institute of High Energy Physics, Beijing (China)
2015-06-15
We propose the gravity's rainbow scenario as a possible alternative of the inflation paradigm to account for the flatness and horizon problems. We focus on studying the cosmological scalar perturbations which are seeded by the quantum fluctuations in the very early universe. The scalar power spectrum is expected to be nearly scale-invariant. We estimate the rainbow index λ and energy scale M in the gravity's rainbow scenario by analyzing the Planck temperature and WMAP polarization datasets. The constraints on them are given by λ = 2.933 ± 0.012 and ln(10{sup 5}M/M{sub p}) = -0.401{sub -0.451}{sup +0.457} at the 68% confidence level. (orig.)
Cosmological Density and Power Spectrum from Peculiar Velocities Nonlinear Corrections and PCA
Silberman, L; Eldar, A; Zehavi, I
2001-01-01
we allow for nonlinear effects in the likelihood analysis of galaxy peculiar velocities, and obtain ~35%-lower values for the cosmological density parameter and for the amplitude of mass-density fluctuations. The power spectrum in the linear regime is assumed to be a flat LCDM model (h=0.65, n=1, COBE) with only Om_m as a free parameter. Since the likelihood is driven by the nonlinear regime, we "break" the power spectrum at k_b=0.2 h/Mpc and fit a power law at k>k_b. This allows for independent matching of the nonlinear behavior and an unbiased fit in the linear regime. The analysis assumes Gaussian fluctuations and errors, and a linear relation between velocity and density. Tests using mock catalogs that properly simulate nonlinear effects demonstrate that this procedure results in a reduced bias and a better fit. We find for the Mark3 and SFI data Om_m=0.32+-0.06 and 0.37+-0.09 respectively, with sigma_8*Om_m^0.6 =0.49+-0.06 and 0.63+-0.08, in agreement with constraints from other data. The quoted 90% erro...
Constraints on small-scale cosmological perturbations from gamma-ray searches for dark matter
Scott, Pat; Akrami, Yashar
2012-01-01
Events like inflation or phase transitions can produce large density perturbations on very small scales in the early Universe. Probes of small scales are therefore useful for e.g. discriminating between inflationary models. Until recently, the only such constraint came from non-observation of primordial black holes (PBHs), associated with the largest perturbations. Moderate-amplitude perturbations can collapse shortly after matter-radiation equality to form ultracompact minihalos (UCMHs) of dark matter, in far greater abundance than PBHs. If dark matter self-annihilates, UCMHs become excellent targets for indirect detection. Here we discuss the gamma-ray fluxes expected from UCMHs, the prospects of observing them with gamma-ray telescopes, and limits upon the primordial power spectrum derived from their non-observation by the Fermi Large Area Space Telescope.
The Kramers-Moyal Equation of the Cosmological Comoving Curvature Perturbation
DEFF Research Database (Denmark)
Riotto, Antonio; Sloth, Martin Snoager
2011-01-01
Fluctuations of the comoving curvature perturbation with wavelengths larger than the horizon length are governed by a Langevin equation whose stochastic noise arise from the quantum fluctuations that are assumed to become classical at horizon crossing. The infrared part of the curvature...... the corresponding Kramers-Moyal equation which describes how the probability distribution of the comoving curvature perturbation at a given spatial point evolves in time and is a generalization of the Fokker-Planck equation. This approach offers an alternative way to study the late time behaviour of the correlators...
Lagrangian perturbations and the matter bispectrum I: fourth-order model for non-linear clustering
Energy Technology Data Exchange (ETDEWEB)
Rampf, Cornelius [Institut für Theoretische Teilchenphysik und Kosmologie, RWTH Aachen, Physikzentrum RWTH-Melaten, D-52056 Aachen (Germany); Buchert, Thomas, E-mail: rampf@physik.rwth-aachen.de, E-mail: buchert@obs.univ-lyon1.fr [Université de Lyon, Observatoire de Lyon, Centre de Recherche Astrophysique de Lyon, CNRS UMR 5574: Université Lyon 1 and École Normale Supérieure de Lyon, 9 avenue Charles André, F-69230 Saint-Genis-Laval (France)
2012-06-01
We investigate the Lagrangian perturbation theory of a homogeneous and isotropic universe in the non-relativistic limit, and derive the solutions up to the fourth order. These solutions are needed for example for the next-to-leading order correction of the (resummed) Lagrangian matter bispectrum, which we study in an accompanying paper. We focus on flat cosmologies with a vanishing cosmological constant, and provide an in-depth description of two complementary approaches used in the current literature. Both approaches are solved with two different sets of initial conditions — both appropriate for modelling the large-scale structure. Afterwards we consider only the fastest growing mode solution, which is not affected by either of these choices of initial conditions. Under the reasonable approximation that the linear density contrast is evaluated at the initial Lagrangian position of the fluid particle, we obtain the nth-order displacement field in the so-called initial position limit: the nth order displacement field consists of 3(n-1) integrals over n linear density contrasts, and obeys self-similarity. Then, we find exact relations between the series in Lagrangian and Eulerian perturbation theory, leading to identical predictions for the density contrast and the peculiar-velocity divergence up to the fourth order.
Evolution of inhomogeneities in unstable-neutrino cosmologies
Energy Technology Data Exchange (ETDEWEB)
Doroshkevich, A.G.; Klypin, A.A.; Kotok, E.V.
1986-06-01
An attempt is made to show that many of the problems associated with the standard stable-particle pancake cosmology can be resolved by modifying the cosmological model and the spectrum of primordial irregularities. Equations describing the growth of primordial perturbations in a cosmological model initially dominated by heavy unstable neutrinos are derived. The one-dimensional approximation is used to study evolution during the nonlinear growth phase. 25 references.
ROBUST STABILITY WITH GUARANTEEING COST FOR DISCRETE TIME-DELAY SYSTEMS WITH NONLINEAR PERTURBATION
Institute of Scientific and Technical Information of China (English)
JIA Xinchun; ZHENG Nanning; LIU Yuehu
2005-01-01
The problems of robust stability and robust stability with a guaranteeing cost for discrete time-delay systems with nonlinear perturbation are discussed. A sufficient criterion for robust stability is established in an LMI framework and a linear convex optimization problem with LMI constraints for computing maximal perturbation bound is proposed. Meanwhile, a sufficient criterion for robust stability with a guaranteeing cost for such systems is obtained, and an optimal procedure for decreasing the value of guaranteeing cost is put forward. Two examples are used to illustrate the efficiency of the results.
A discrete homotopy perturbation method for non-linear Schrodinger equation
Directory of Open Access Journals (Sweden)
H. A. Wahab
2015-12-01
Full Text Available A general analysis is made by homotopy perturbation method while taking the advantages of the initial guess, appearance of the embedding parameter, different choices of the linear operator to the approximated solution to the non-linear Schrodinger equation. We are not dependent upon the Adomian polynomials and find the linear forms of the components without these calculations. The discretised forms of the nonlinear Schrodinger equation allow us whether to apply any numerical technique on the discritisation forms or proceed for perturbation solution of the problem. The discretised forms obtained by constructed homotopy provide the linear parts of the components of the solution series and hence a new discretised form is obtained. The general discretised form for the NLSE allows us to choose any initial guess and the solution in the closed form.
Sharma, Dinkar; Singh, Prince; Chauhan, Shubha
2016-01-01
In this paper, a combined form of the Laplace transform method with the homotopy perturbation method (HPTM) is applied to solve nonlinear systems of partial differential equations viz. the system of third order KdV Equations and the systems of coupled Burgers' equations in one- and two- dimensions. The nonlinear terms can be easily handled by the use of He's polynomials. The results shows that the HPTM is very efficient, simple and avoids the round-off errors. Four test examples are considered to illustrate the present scheme. Further the results are compared with Homotopy perturbation method (HPM) which shows that this method is a suitable method for solving systems of partial differential equations.
Beyond the perturbative description of the nonlinear optical response of low-index materials.
Reshef, Orad; Giese, Enno; Zahirul Alam, M; De Leon, Israel; Upham, Jeremy; Boyd, Robert W
2017-08-15
We show that standard approximations in nonlinear optics are violated for situations involving a small value of the linear refractive index. Consequently, the conventional equation for the intensity-dependent refractive index, n(I)=n0+n2I, becomes inapplicable in epsilon-near-zero and low-index media, even in the presence of only third-order effects. For the particular case of indium tin oxide, we find that the χ((3)), χ((5)), and χ((7)) contributions to refraction eclipse the linear term; thus, the nonlinear response can no longer be interpreted as a perturbation in these materials. Although the response is non-perturbative, we find no evidence that the power series expansion of the material polarization diverges.
ASYMPTOTIC THEORY OF INITIAL VALUE PROBLEMS FOR NONLINEAR PERTURBED KLEIN-GORDON EQUATIONS
Institute of Scientific and Technical Information of China (English)
GAN Zai-hui; ZHANG Jian
2005-01-01
The asymptotic theory of initial value problems for a class of nonlinear perturbed Klein-Gordon equations in two space dimensions is considered. Firstly, using the contraction mapping principle, combining some priori estimates and the convergence of Bessel function, the well-posedness of solutions of the initial value problem in twice continuous differentiable space was obtained according to the equivalent integral equation of initial value problem for the Klein-Gordon equations. Next, formal approximations of initial value problem was constructed by perturbation method and the asymptotic validity of the formal approximation is got. Finally, an application of the asymptotic theory was given, the asymptotic approximation degree of solutions for the initial value problem of a specific nonlinear Klein-Gordon equation was analyzed by using the asymptotic approximation theorem.
Spherical collapse, formation hysteresis and the deeply non-linear cosmological power spectrum
Mead, A. J.
2016-09-01
I examine differences in non-linear structure formation between cosmological models that share a z = 0 linear power spectrum in both shape and amplitude, but that differ via their growth history. N-body simulations of these models display an approximately identical large-scale-structure skeleton, but reveal deeply non-linear differences in the demographics and properties of haloes. I investigate to what extent the spherical-collapse model can help in understanding these differences, in both real and redshift space. I discuss how this is difficult to do if one attempts to identify haloes directly, because in that case one is subject to the vagaries of halo finding algorithms. However, I demonstrate that the halo model of structure formation provides an accurate non-linear response in the power spectrum, but only if results from spherical collapse that include formation hysteresis are properly incorporated. I comment on how this fact can be used to provide per cent level accurate matter power spectrum predictions for dark energy models for k ≤ 5 hMpc-1 by using the halo model as a correction to accurate ΛCDM simulations. In the appendix I provide some fitting functions for the linear-collapse threshold (δc) and virialized overdensity (Δv) that are valid for a wide range of dark energy models. I also make my spherical-collapse code available at https://github.com/alexander-mead/collapse.
Spherical collapse, formation hysteresis and the deeply non-linear cosmological power spectrum
Mead, Alexander
2016-01-01
I examine differences in non-linear structure formation between cosmological models that share a $z=0$ linear power spectrum in both shape and amplitude, but that differ via their growth history. $N$-body simulations of these models display an approximately identical large-scale-structure skeleton, but reveal deeply non-linear differences in the demographics and properties of haloes. I investigate to what extent the spherical-collapse model can help in understanding these differences, in both real and redshift space. I discuss how this is difficult to do if one attempts to identify haloes directly, because in that case one is subject to the vagaries of halo finding algorithms. However, I demonstrate that the halo model of structure formation provides an accurate non-linear response in the power spectrum, but only if results from spherical collapse that include formation hysteresis are properly incorporated. I comment on how this fact can be used to provide per cent level accurate matter power spectrum predict...
Spherical collapse, formation hysteresis and the deeply non-linear cosmological power spectrum
Mead, A. J.
2017-01-01
I examine differences in non-linear structure formation between cosmological models that share a z = 0 linear power spectrum in both shape and amplitude, but that differ via their growth history. N-body simulations of these models display an approximately identical large-scale-structure skeleton, but reveal deeply non-linear differences in the demographics and properties of haloes. I investigate to what extent the spherical-collapse model can help in understanding these differences, in both real and redshift space. I discuss how this is difficult to do if one attempts to identify haloes directly, because in that case one is subject to the vagaries of halo-finding algorithms. However, I demonstrate that the halo model of structure formation provides an accurate non-linear response in the power spectrum, but only if results from spherical collapse that include formation hysteresis are properly incorporated. I comment on how this fact can be used to provide per cent level accurate matter power-spectrum predictions for dark energy models for k ≤ 5 h Mpc-1 by using the halo model as a correction to accurate ΛCDM simulations. In the Appendix, I provide some fitting functions for the linear-collapse threshold (δc) and virialized overdensity (Δv) that are valid for a wide range of dark energy models. I also make my spherical-collapse code available at https://github.com/alexander-mead/collapse.
Abate, Alexandra; Teodoro, Luis F A; Warren, Michael S; Hendry, Martin
2008-01-01
We investigate methods to best estimate the normalisation of the mass density fluctuation power spectrum (sigma_8) using peculiar velocity data from a survey like the Six degree Field Galaxy Velocity Survey (6dFGSv). We focus on two potential problems (i) biases from nonlinear growth of structure and (ii) the large number of velocities in the survey. Simulations of LambdaCDM-like models are used to test the methods. We calculate the likelihood from a full covariance matrix of velocities averaged in grid cells. This simultaneously reduces the number of data points and smooths out nonlinearities which tend to dominate on small scales. We show how the averaging can be taken into account in the predictions in a practical way, and show the effect of the choice of cell size. We find that a cell size can be chosen that significantly reduces the nonlinearities without significantly increasing the error bars on cosmological parameters. We compare our results with those from a principal components analysis following Wa...
Ambiguities in second-order cosmological perturbations for non-canonical scalar fields
Appignani, Corrado; Shankaranarayanan, S
2010-01-01
Over the last few years, it was realised that non-canonical scalar fields can lead to the accelerated expansion in the early universe. The primordial spectrum in these scenarios not only shows near scale-invariance consistent with CMB observations,but also large primordial non-Gaussianity. Second-order perturbation theory is the primary theoretical tool to investigate such non-Gaussianity. However, it is still uncertain which quantities are gauge-invariant at second-order and their physical understanding therefore remains unclear. As an attempt to understand second order quantities, we consider a general non-canonical scalar field, minimally coupled to gravity, on the unperturbed FRW background where metric fluctuations are neglected a priori. In this simplified set-up, we show that there arise ambiguities in the expressions of physically relevant quantities, such as the effective speeds of the perturbations. Further, the stress tensor and energy density display a potential instability which is not present at...
Cosmological perturbations in warm-tachyon inflationary universe model with viscous pressure
Directory of Open Access Journals (Sweden)
M.R. Setare
2014-09-01
Full Text Available We study the warm-tachyon inflationary universe model with viscous pressure in high-dissipation regime. General conditions which are required for this model to be realizable are derived in the slow-roll approximation. We present analytic expressions for density perturbation and amplitude of tensor perturbation in longitudinal gauge. Expressions of tensor-to-scalar ratio, scalar spectral index and its running are obtained. We develop our model by using exponential potential, the characteristics of this model are calculated for two specific cases in great details: 1. Dissipative parameter Γ and bulk viscous parameter ζ are constant parameters. 2. Dissipative parameter is a function of tachyon field ϕ and bulk viscous parameter is a function of matter-radiation mixture energy density ρ. The parameters of the model are restricted by recent observational data from the nine-year Wilkinson microwave anisotropy probe (WMAP9, Planck and BICEP2 data.
Cosmological perturbations in warm-tachyon inflationary universe model with viscous pressure
Energy Technology Data Exchange (ETDEWEB)
Setare, M.R., E-mail: rezakord@ipm.ir [Department of Science, Campus of Bijar, University of Kurdistan, Bijar (Iran, Islamic Republic of); Kamali, V., E-mail: vkamali1362@gmail.com [Department of Physics, Faculty of Science, Bu-Ali Sina University, Hamedan, 65178 (Iran, Islamic Republic of)
2014-09-07
We study the warm-tachyon inflationary universe model with viscous pressure in high-dissipation regime. General conditions which are required for this model to be realizable are derived in the slow-roll approximation. We present analytic expressions for density perturbation and amplitude of tensor perturbation in longitudinal gauge. Expressions of tensor-to-scalar ratio, scalar spectral index and its running are obtained. We develop our model by using exponential potential, the characteristics of this model are calculated for two specific cases in great details: 1. Dissipative parameter Γ and bulk viscous parameter ζ are constant parameters. 2. Dissipative parameter is a function of tachyon field ϕ and bulk viscous parameter is a function of matter-radiation mixture energy density ρ. The parameters of the model are restricted by recent observational data from the nine-year Wilkinson microwave anisotropy probe (WMAP9), Planck and BICEP2 data.
Non-Gaussianities in the Cosmological Perturbation Spectrum due to Primordial Anisotropy
Dey, Anindya
2011-01-01
We investigate possible signatures of a pre-inflationary anisotropic phase in two-point and three-point correlation functions of the curvature perturbation for high-momentum modes which exit the horizon after isotropization. In this momentum regime, the early time dynamics admits a WKB description and the late time dynamics can be described in terms of a non-Bunch Davies vacuum state which encodes the information of the initial anisotropy in the background spacetime. We compute the bi-spectrum for the curvature perturbation for a canonical single-field action with and without higher derivative operators. We show that the bi-spectrum at late times, in the former case, is enhanced for a flattened triangle configuration and compute the corresponding $f_{NL}$ parameter. The angular dependence of the $f_{NL}$ parameter appears as a distinctive feature of the background anisotropy at early times.
Non-Gaussianities in the Cosmological Perturbation Spectrum due to Primordial Anisotropy II
Dey, Anindya
2012-01-01
We continue to investigate possible signatures of a pre-inflationary anisotropic phase in two-point and three point correlation functions of the curvature perturbation for high-momentum modes which exit the horizon well after isotropization. The late time dynamics of these modes is characterized by a non-Bunch Davies vacuum state which encodes all the information about initial anisotropy in the background space-time. We observe that, unlike the non-planar momenta, there exist regimes of planar momenta for which scale invariance of the power spectrum is strongly broken. This regime of planar momenta gives rise to enhanced non-Gaussianity in certain squeezed triangle configurations, although the enhancement of the $f_{NL}$ parameter is limited by the breakdown of linear perturbation theory at "exact planarity". Finally, we demonstrate that for the range of planar modes for which scale invariance of the power spectrum is preserved, non-Gaussianity in the curvature perturbation spectrum is naturally constrained t...
Delay-dependent robust stabilization for a class of neutral systems with nonlinear perturbations
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
This note deals with the problem of stabilization/stability for neutral systems with nonlinear perturbations.A new stabilization/stability scheme is presented.Using improved Lyapunov functionals.less conservative stabilization/stability conditions are derived for such systems based on linear matrix inequalities(LMI).Numerical examples are provided to show that the proposed results significantly improve the allowed upper bounds of the delay size over some existing ones in the literature.
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Considering the limitation of the linear theory of singular vector (SV), the authors and their collaborators proposed conditional nonlinear optimal perturbation (CNOP) and then applied it in the predictability study and the sensitivity analysis of weather and climate system. To celebrate the 20th anniversary of Chinese National Committee for World Climate Research Programme (WCRP), this paper is devoted to reviewing the main results of these studies. First, CNOP represents the initial perturbation that has largest nonlinear evolution at prediction time, which is different from linear singular vector (LSV) for the large magnitude of initial perturbation or/and the long optimization time interval. Second, CNOP,rather than linear singular vector (LSV), represents the initial anomaly that evolves into ENSO events most probably. It is also the CNOP that induces the most prominent seasonal variation of error growth for ENSO predictability; furthermore, CNOP was applied to investigate the decadal variability of ENSO asymmetry. It is demonstrated that the changing nonlinearity causes the change of ENSO asymmetry.Third, in the studies of the sensitivity and stability of ocean's thermohaline circulation (THC), the non-linear asymmetric response of THC to finite amplitude of initial perturbations was revealed by CNOP.Through this approach the passive mechanism of decadal variation of THC was demonstrated; Also the authors studies the instability and sensitivity analysis of grassland ecosystem by using CNOP and show the mechanism of the transitions between the grassland and desert states. Finally, a detailed discussion on the results obtained by CNOP suggests the applicability of CNOP in predictability studies and sensitivity analysis.
Homotopy perturbation method for nonlinear partial differential equations of fractional order
Energy Technology Data Exchange (ETDEWEB)
Momani, Shaher [Department of Mathematics and Physics, Qatar University (Qatar)]. E-mail: shahermm@yahoo.com; Odibat, Zaid [Prince Abdullah Bin Ghazi Faculty of Science and IT, Al-Balqa' Applied University, Salt (Jordan)]. E-mail: odibat@bau.edu.jo
2007-06-11
The aim of this Letter is to present an efficient and reliable treatment of the homotopy perturbation method (HPM) for nonlinear partial differential equations with fractional time derivative. The fractional derivative is described in the Caputo sense. The modified algorithm provides approximate solutions in the form of convergent series with easily computable components. The obtained results are in good agreement with the existing ones in open literature and it is shown that the technique introduced here is robust, efficient and easy to implement.
Adaptive Third-Order Leader-Following Consensus of Nonlinear Multi-agent Systems with Perturbations
Institute of Scientific and Technical Information of China (English)
SUN Mei; CHEN Ying; CAO Long; WANG Xiao-Fang
2012-01-01
We investigate the third-order leader-following consensus problem of nonlinear multi-agent systems in undirected network topologies. Based on graph theory and Lyapunov stability theory, the adaptive control method is employed to achieve leader-following consensus in an undirected network of agents with nonlinear third-order dynamics against the perturbations. Simulation examples validate the correctness of the results and show that the control gains have a great influence on the convergence performance of errors for a short time.%We investigate the third-order leader-following consensus problem of nonlinear multi-agent systems in undirected network topologies.Based on graph theory and Lyapunov stability theory,the adaptive control method is employed to achieve leader-following consensus in an undirected network of agents with nonlinear third-order dynamics against the perturbations.Simulation examples validate the correctness of the results and show that the control gains have a great influence on the convergence performance of errors for a short time.
Zhang, Tian-Ping; Zhu, Qing; Yang, Yue-Quan
2012-04-01
In this article, two robust adaptive control schemes are investigated for a class of completely non-affine pure-feedback non-linear systems with input non-linearity and perturbed uncertainties using radial basis function neural networks (RBFNNs). Based on the dynamic surface control (DSC) technique and using the quadratic Lyapunov function, the explosion of complexity in the traditional backstepping design is avoided when the gain signs are known. In addition, the unknown virtual gain signs are dealt with using the Nussbaum functions. Using the mean value theorem and Young's inequality, only one learning parameter needs to be tuned online at each step of recursion. It is proved that the proposed design method is able to guarantee semi-global uniform ultimate boundedness (SGUUB) of all signals in the closed-loop system. Simulation results verify the effectiveness of the proposed approach.
Analytical solitons for Langmuir waves in plasma physics with cubic nonlinearity and perturbations
Energy Technology Data Exchange (ETDEWEB)
Zhou, Qin [Wuhan Donghu Univ. (China). School of Electronics and Information Engineering; Mirzazadeh, M. [Guilan Univ. (Iran, Islamic Republic of). Dept. of Engineering Sciences
2016-07-01
We presented an analytical study on dynamics of solitons for Langmuir waves in plasma physics. The mathematical model is given by the perturbed nonlinear Schroedinger equation with full nonlinearity and Kerr law nonlinearity. There are three techniques of integrability were employed to extract exact solutions along with the integrability conditions. The topological 1-soliton solutions, singular 1-soliton solutions, and plane wave solution were reported by Ricatti equation expansion approach and then the bright 1-soliton solution, singular 1-soliton solution, periodic singular solutions, and plane wave solution were derived with the help of trial solution method. Finally, based on the G'/G-expansion scheme, we obtained the hyperbolic function travelling wave solution, trigonometric function travelling wave solution, and plane wave solution.
Analytical Solitons for Langmuir Waves in Plasma Physics with Cubic Nonlinearity and Perturbations
Zhou, Qin; Mirzazadeh, M.
2016-09-01
We presented an analytical study on dynamics of solitons for Langmuir waves in plasma physics. The mathematical model is given by the perturbed nonlinear Schrödinger equation with full nonlinearity and Kerr law nonlinearity. There are three techniques of integrability were employed to extract exact solutions along with the integrability conditions. The topological 1-soliton solutions, singular 1-soliton solutions, and plane wave solution were reported by Ricatti equation expansion approach and then the bright 1-soliton solution, singular 1-soliton solution, periodic singular solutions, and plane wave solution were derived with the help of trial solution method. Finally, based on the G'/G-expansion scheme, we obtained the hyperbolic function travelling wave solution, trigonometric function travelling wave solution, and plane wave solution.
Zhang, Huayong; Huang, Tousheng; Dai, Liming
2015-05-01
Predator-prey interaction widely exists in nature and the research on predator-prey systems is an important field in ecology. The nonlinear dynamic characteristics of a seasonally perturbed predator-prey system are studied in this research. To study the nonlinear characteristics affected by a wide variety of system parameters, the PR approach is employed and periodic, quasiperiodic, chaotic behaviors and the behaviors between period and quasiperiod are found in the system. Periodic-quasiperiodic-chaotic region diagrams are generated for analyzing the global characteristics of the predator-prey system with desired ranges of system parameters. The ecological significances of the dynamical characteristics are discussed and compared with the theoretical research results existing in the literature. The approach of this research demonstrates effectiveness and efficiency of PR method in analyzing the complex dynamical characteristics of nonlinear ecological systems.
Nungesser, Ernesto
2014-01-01
We show future global non-linear stability of surface symmetric solutions of the Einstein-Vlasov system with a positive cosmological constant. Estimates of higher derivatives of the metric and the matter terms are obtained using an inductive argument. In a recent research monograph Ringstr\\"{o}m shows future non-linear stability of (not necessarily symmetric) solutions of the Einstein-Vlasov system with a non-linear scalar field if certain local estimates on the geometry and the matter terms are fulfilled. We show that these assumptions are satisfied at late times for the case under consideration here which together with Cauchy stability leads to our main conclusion.
Evolution of Cosmological Perturbations in the Presence of Primordial Magnetic Fields
Kojima, Kazuhiko
2009-01-01
Possible existence of the primordial magnetic fields has affected the structure formation of the universe. In the numerical calculations for the evolution of density perturbations with primordial magnetic fields, there has been a difficulty in solving the Einstein-Boltzmann equations which arises due to the unwanted cancellation of contributions from the magnetic fields and primordial radiations. Here this problem is solved by newly taking into account a non-relativistic matter contribution in the radiation dominated era. A complete set of equations and appropriate initial conditions in the long wavelength limit are derived in a courteous manner in the covariant approach with CDM frame. By solving these equations numerically, we derive the angular spectrum of cosmic microwave background anisotropies and the matter power spectrum with magnetic fields. We find that the amplitude of the angular power spectrum of CMB anisotropies can alter at most a order of magnitude at $l \\lesssim 3000$ compared with the previo...
Conformal Symmetries of Adiabatic Modes in Cosmology
Hinterbichler, Kurt; Khoury, Justin
2012-01-01
We remark on the existence of non-linearly realized conformal symmetries for scalar adiabatic perturbations in cosmology. These conformal symmetries are present for any cosmological background, beyond any slow-roll or quasi-de Sitter approximation. The dilatation transformation shifts the curvature perturbation by a constant, and corresponds to the well-known symmetry under spatial rescaling. We argue that the scalar sector is also invariant under special conformal transformations, which shift the curvature perturbation by a term linear in the spatial coordinates. We discuss whether these conformal symmetries can be extended to include tensor perturbations. Tensor modes introduce their own set of non-linearly realized symmetries. We identify an infinite set of large gauge transformations which maintain the transverse, traceless gauge condition, while shifting the tensor mode non-trivially.
Variational principle and a perturbative solution of non-linear string equations in curved space
Roshchupkin, S N
1999-01-01
String dynamics in a curved space-time is studied on the basis of an action functional including a small parameter of rescaled tension constant. A rescaled slow worldsheet time $T=\\epsilon\\tau$ is introduced, and general covariant non-linear string equation are derived. It is shown that in the first order of an $\\epsilon $-expansion these equations are reduced to the known equation for geodesic derivation but complemented by a string oscillatory term. These equations are solved for the de Sitter and Friedmann -Robertson-Walker spaces. The primary string constraints are found to be split into a chain of perturbative constraints and their conservation and consistency are proved. It is established that in the proposed realization of the perturbative approach the string dynamics in the de Sitter space is stable for a large Hubble constant $H
Apparently non-invariant terms of nonlinear sigma models in lattice perturbation theory
Harada, Koji; Kubo, Hirofumi; Yamamoto, Yuki
2009-01-01
Apparently non-invariant terms (ANTs) which appear in loop diagrams for nonlinear sigma models (NLSs) are revisited in lattice perturbation theory. The calculations have been done mostly with dimensional regularization so far. In order to establish that the existence of ANTs is independent of the regularization scheme, and of the potential ambiguities in the definition of the Jacobian of the change of integration variables from group elements to "pion" fields, we employ lattice regularization, in which everything (including the Jacobian) is well-defined. We show explicitly that lattice perturbation theory produces ANTs in the four-point functions of the "pion" fields at one-loop and the Jacobian does not play an important role in generating ANTs.
Indian Academy of Sciences (India)
Zaiyun Zhang; Jianhua Huang; Juan Zhong; Sha-Sha Dou; Jiao Liu; Dan Peng; Ting Gao
2014-06-01
In this paper, we construct the travelling wave solutions to the perturbed nonlinear Schrödinger’s equation (NLSE) with Kerr law non-linearity by the extended (′/)-expansion method. Based on this method, we obtain abundant exact travelling wave solutions of NLSE with Kerr law nonlinearity with arbitrary parameters. The travelling wave solutions are expressed by the hyperbolic functions, trigonometric functions and rational functions.
Comparisons of linear and nonlinear plasma response models for non-axisymmetric perturbations
Energy Technology Data Exchange (ETDEWEB)
Turnbull, A. D.; Ferraro, N. M.; Lao, L. L.; Lanctot, M. J. [General Atomics, P.O. Box 85608, San Diego, California 92186-5608 (United States); Izzo, V. A. [University of California-San Diego, 9500 Gilman Dr., La Jolla, California 92093-0417 (United States); Lazarus, E. A.; Hirshman, S. P. [Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, Tennessee 37831 (United States); Park, J.-K.; Lazerson, S.; Reiman, A. [Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton, New Jersey 08543-0451 (United States); Cooper, W. A. [Association Euratom-Confederation Suisse, Centre de Recherches en Physique des Plasmas, Ecole Polytechnique Federale de Lausanne, Lausanne (Switzerland); Liu, Y. Q. [Culham Centre for Fusion Energy, Culham Science Centre, Abingdon, Oxfordshire, OX14 3DB (United Kingdom); Turco, F. [Columbia University, 116th St and Broadway, New York, New York 10027 (United States)
2013-05-15
With the installation of non-axisymmetric coil systems on major tokamaks for the purpose of studying the prospects of ELM-free operation, understanding the plasma response to the applied fields is a crucial issue. Application of different response models, using standard tools, to DIII-D discharges with applied non-axisymmetric fields from internal coils, is shown to yield qualitatively different results. The plasma response can be treated as an initial value problem, following the system dynamically from an initial unperturbed state, or from a nearby perturbed equilibrium approach, and using both linear and nonlinear models [A. D. Turnbull, Nucl. Fusion 52, 054016 (2012)]. Criteria are discussed under which each of the approaches can yield a valid response. In the DIII-D cases studied, these criteria show a breakdown in the linear theory despite the small 10{sup −3} relative magnitude of the applied magnetic field perturbations in this case. For nonlinear dynamical evolution simulations to reach a saturated nonlinear steady state, appropriate damping mechanisms need to be provided for each normal mode comprising the response. Other issues arise in the technical construction of perturbed flux surfaces from a displacement and from the presence of near nullspace normal modes. For the nearby equilibrium approach, in the absence of a full 3D equilibrium reconstruction with a controlled comparison, constraints relating the 2D system profiles to the final profiles in the 3D system also need to be imposed to assure accessibility. The magnetic helicity profile has been proposed as an appropriate input to a 3D equilibrium calculation and tests of this show the anticipated qualitative behavior.
Energy Technology Data Exchange (ETDEWEB)
Olazabal-Loume, M; Breil, J; Hallo, L; Ribeyre, X [CELIA, UMR 5107 Universite Bordeaux 1-CNRS-CEA, 351 cours de la Liberation, 33405 Talence (France); Sanz, J, E-mail: olazabal@celia.u-bordeaux1.f [ETSI Aeronauticos, Universidad Politecnica de Madrid, Madrid 28040 (Spain)
2011-01-15
The linear and non-linear sensitivity of the 180 kJ baseline HiPER target to high-mode perturbations, i.e. surface roughness, is addressed using two-dimensional simulations and a complementary analysis by linear and non-linear ablative Rayleigh-Taylor models. Simulations provide an assessment of an early non-linear stage leading to a significant deformation of the ablation surface for modes of maximum linear growth factor. A design using a picket prepulse evidences an improvement in the target stability inducing a delay of the non-linear behavior. Perturbation evolution and shape, evidenced by simulations of the non-linear stage, are analyzed with existing self-consistent non-linear theory.
Robust adaptive fuzzy control for a class of perturbed pure-feedback nonlinear systems
Institute of Scientific and Technical Information of China (English)
Jianjiang YU; Tianping ZHANG; Haijun GU
2004-01-01
A new design scheme of direct adaptive fuzzy controller for a class of perturbed pure-feedback nonlinear systems is proposed. The design is based on backstepping and the approximation capability of the first type fuzzy systems. A continuous robust term is adopted to minif-y the influence of modeling errors or disturbances. By introducing the modified integral-type Lyapunov function, the approach is able to avoid the requirement of the upper bound of the first time derivation of the high frequency control gain. Through theoretical analysis, the closed-loop control system is proven to be semi-globally uniformly ultimately bounded, with tracking error converging to a residual set.
Adaptive neural control for a class of perturbed strict-feedback nonlinear time-delay systems.
Wang, Min; Chen, Bing; Shi, Peng
2008-06-01
This paper proposes a novel adaptive neural control scheme for a class of perturbed strict-feedback nonlinear time-delay systems with unknown virtual control coefficients. Based on the radial basis function neural network online approximation capability, an adaptive neural controller is presented by combining the backstepping approach and Lyapunov-Krasovskii functionals. The proposed controller guarantees the semiglobal boundedness of all the signals in the closed-loop system and contains minimal learning parameters. Finally, three simulation examples are given to demonstrate the effectiveness and applicability of the proposed scheme.
Directory of Open Access Journals (Sweden)
Kanit Mukdasai
2012-01-01
Full Text Available This paper investigates the problem of robust exponential stability for linear parameter-dependent (LPD systems with discrete and distributed time-varying delays and nonlinear perturbations. Parameter dependent Lyapunov-Krasovskii functional, Leibniz-Newton formula, and linear matrix inequality are proposed to analyze the stability. On the basis of the estimation and by utilizing free-weighting matrices, new delay-dependent exponential stability criteria are established in terms of linear matrix inequalities (LMIs. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.
Directory of Open Access Journals (Sweden)
Xia Zhou
2013-01-01
Full Text Available The problem of bounded-input bounded-output (BIBO stabilization in mean square for a class of discrete-time stochastic control systems with mixed time-varying delays and nonlinear perturbations is investigated. Some novel delay-dependent stability conditions for the previously mentioned system are established by constructing a novel Lyapunov-Krasovskii function. These conditions are expressed in the forms of linear matrix inequalities (LMIs, whose feasibility can be easily checked by using MATLAB LMI Toolbox. Finally, a numerical example is given to illustrate the validity of the obtained results.
On properties of nonlinear second order systems under nonlinear impulse perturbations
Directory of Open Access Journals (Sweden)
John R. Graef
1998-11-01
Full Text Available In this paper, we consider the impulsive second order system [ ddot{x}+f(x=0quad (teq t_{n};quad dot{x}(t_{n}+0=b_{n}dot{x}(t_{n} quad (t=t_{n} ] where $t_n=t_0+n,p$ $(p>0, n=1,2dots $. In a previous paper, the authors proved that if $f(x$ is strictly nonlinear, then this system has infinitely many periodic solutions. The impulses account for the main differences in the attractivity properties of the zero solution. Here, we prove that these periodic solutions are attractive in some sense, and we give good estimates for the attractivity region.
Orain, François; Bécoulet, M.; Morales, J.; Huijsmans, G. T. A.; Dif-Pradalier, G.; Hoelzl, M.; Garbet, X.; Pamela, S.; Nardon, E.; Passeron, C.; Latu, G.; Fil, A.; Cahyna, P.
2015-01-01
The dynamics of a multi-edge localized mode (ELM) cycle as well as the ELM mitigation by resonant magnetic perturbations (RMPs) are modeled in realistic tokamak X-point geometry with the non-linear reduced MHD code JOREK. The diamagnetic rotation is found to be a key parameter enabling us to reproduce the cyclical dynamics of the plasma relaxations and to model the near-symmetric ELM power deposition on the inner and outer divertor target plates consistently with experimental measurements. Moreover, the non-linear coupling of the RMPs with unstable modes are found to modify the edge magnetic topology and induce a continuous MHD activity in place of a large ELM crash, resulting in the mitigation of the ELMs. At larger diamagnetic rotation, a bifurcation from unmitigated ELMs—at low RMP current—towards fully suppressed ELMs—at large RMP current—is obtained.
Directory of Open Access Journals (Sweden)
Hong Qin
2000-08-01
Full Text Available Collective processes in intense charged particle beams described self-consistently by the Vlasov-Maxwell equations are studied using a 3D multispecies nonlinear perturbative particle simulation method. The newly developed beam equilibrium, stability, and transport (BEST code is used to simulate the nonlinear stability properties of intense beam propagation, surface eigenmodes in a high-intensity beam, and the electron-proton (e-p two-stream instability observed in the Proton Storage Ring (PSR experiment. Detailed simulations in a parameter regime characteristic of the PSR experiment show that the dipole-mode two-stream instability is stabilized by a modest spread (about 0.1% in axial momentum of the beam particles.
Chang, Wen-Jer; Huang, Bo-Jyun
2014-11-01
The multi-constrained robust fuzzy control problem is investigated in this paper for perturbed continuous-time nonlinear stochastic systems. The nonlinear system considered in this paper is represented by a Takagi-Sugeno fuzzy model with perturbations and state multiplicative noises. The multiple performance constraints considered in this paper include stability, passivity and individual state variance constraints. The Lyapunov stability theory is employed to derive sufficient conditions to achieve the above performance constraints. By solving these sufficient conditions, the contribution of this paper is to develop a parallel distributed compensation based robust fuzzy control approach to satisfy multiple performance constraints for perturbed nonlinear systems with multiplicative noises. At last, a numerical example for the control of perturbed inverted pendulum system is provided to illustrate the applicability and effectiveness of the proposed multi-constrained robust fuzzy control method.
Mead, Alexander; Heymans, Catherine; Joudaki, Shahab; Heavens, Alan
2015-01-01
We present an optimised variant of the halo model, designed to produce accurate matter power spectra well into the non-linear regime for a wide range of cosmological models. To do this, we introduce physically-motivated free parameters into the halo-model formalism and fit these to data from high-resolution N-body simulations. For a variety of $\\Lambda$CDM and $w$CDM models the halo-model power is accurate to $\\simeq 5$ per cent for $k\\leq 10h\\,\\mathrm{Mpc}^{-1}$ and $z\\leq 2$. We compare our results with recent revisions of the popular HALOFIT model and show that our predictions are more accurate. An advantage of our new halo model is that it can be adapted to account for the effects of baryonic feedback on the power spectrum. We demonstrate this by fitting the halo model to power spectra from the OWLS hydrodynamical simulation suite via parameters that govern halo internal structure. We are able to fit all feedback models investigated at the 5 per cent level using only two free parameters, and we place limi...
Zhang, Xing; Mu, Mu; Wang, Qiang; Pierini, Stefano
2017-06-01
In this study, the initial perturbations that are the easiest to trigger the Kuroshio Extension (KE) transition connecting a basic weak jet state and a strong, fairly stable meandering state, are investigated using a reduced-gravity shallow water ocean model and the CNOP (Conditional Nonlinear Optimal Perturbation) approach. This kind of initial perturbation is called an optimal precursor (OPR). The spatial structures and evolutionary processes of the OPRs are analyzed in detail. The results show that most of the OPRs are in the form of negative sea surface height (SSH) anomalies mainly located in a narrow band region south of the KE jet, in basic agreement with altimetric observations. These negative SSH anomalies reduce the meridional SSH gradient within the KE, thus weakening the strength of the jet. The KE jet then becomes more convoluted, with a high-frequency and large-amplitude variability corresponding to a high eddy kinetic energy level; this gradually strengthens the KE jet through an inverse energy cascade. Eventually, the KE reaches a high-energy state characterized by two well defined and fairly stable anticyclonic meanders. Moreover, sensitivity experiments indicate that the spatial structures of the OPRs are not sensitive to the model parameters and to the optimization times used in the analysis.
Non-linear curvature perturbation in multi-field inflation models with non-minimal coupling
Energy Technology Data Exchange (ETDEWEB)
White, Jonathan; Minamitsuji, Masato; Sasaki, Misao, E-mail: jwhite@yukawa.kyoto-u.ac.jp, E-mail: masato.minamitsuji@ist.utl.pt, E-mail: misao@yukawa.kyoto-u.ac.jp [Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan)
2013-09-01
Using the δN formalism we consider the non-linear curvature perturbation in multi-field models of inflation with non-minimal coupling. In particular, we focus on the relation between the δN formalism as applied in the conformally related Jordan and Einstein frames. Exploiting results already known in the Einstein frame, we give expressions for the power spectrum, spectral tilt and non-gaussianity associated with the Jordan frame curvature perturbation. In the case that an adiabatic limit has not been reached, we find that in general these quantities differ from those associated with the Einstein frame curvature perturbation, and also confirm their equivalence in the absence of isocurvature modes. We then proceed to consider two analytically soluble examples, the first involving a non-minimally coupled 'spectator' field and the second being a non-minimally coupled extension of the multi-brid inflation model. In the first model we find that predictions can easily be brought into agreement with the recent Planck results, as the tensor-to-scalar ratio is generally small, the spectral tilt tuneable and the non-gaussianity suppressed. In the second model we find that predictions for all three parameters can differ substantially from those predicted in the minimally coupled case, and that the recent Planck results for the spectral tilt can be used to constrain the non-minimal coupling parameters.
Energy Technology Data Exchange (ETDEWEB)
Somogyi, Gabor [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Zurich Univ. (Switzerland). Inst. for Theoretical Physics; Smith, Robert E. [Zurich Univ. (Switzerland). Inst. for Theoretical Physics
2009-10-15
We generalize the ''renormalized'' perturbation theory (RPT) formalism of M. Crocce and R. Scoccimarro (2006) to deal with multiple fluids in the Universe and here we present the complete calculations up to the one-loop level in the RPT. We apply this approach to the problem of following the nonlinear evolution of baryon and cold dark matter (CDM) perturbations, evolving from the distinct sets of initial conditions, from the high redshift post-recombination Universe right through to the present day. In current theoretical and numerical models of structure formation, it is standard practice to treat baryons and CDM as an effective single matter fluid - the so called dark matter only modeling. In this approximation, one uses a weighed sum of late time baryon and CDM transfer functions to set initial mass fluctuations. In this paper we explore whether this approach can be employed for high precision modeling of structure formation. We show that, even if we only follow the linear evolution, there is a large-scale scale-dependent bias between baryons and CDM for the currently favored WMAP5 {lambda}CDM model. This time evolving bias is significant (> 1%) until the present day, when it is driven towards unity through gravitational relaxation processes. Using the RPT formalism we test this approximation in the non-linear regime. We show that the non-linear CDM power spectrum in the 2-component fluid differs from that obtained from an effective mean-mass 1-component fluid by {proportional_to} 3% on scales of order k {proportional_to} 0.05 h Mpc{sup -1} at z = 10, and by {proportional_to} 0.5% at z = 0. However, for the case of the non-linear evolution of the baryons the situation is worse and we find that the power spectrum is suppressed, relative to the total matter, by {proportional_to} 15% on scales k {proportional_to} 0.05 hMpc{sup -1} at z = 10, and by {proportional_to} 3 - 5% at z = 0. Importantly, besides the suppression of the spectrum, the
Nourazar, S. S.; Nazari-Golshan, A.
2015-01-01
A hybrid of Fourier transform and new modified homotopy perturbation method based on the Adomian method is developed to solve linear and nonlinear partial differential equations. The Taylor series expansion is used to expand nonlinear term of partial differential equation and the Adomian polynomial incorporated into homotopy perturbation method combined with Fourier transform, is used to solve partial differential equations. Three case study problems, partial differential equations, are handled using homotopy perturbation method and Fourier transform modified homotopy perturbation method (FTMHPM). Results obtained are compared with exact solution. The comparison reveals that for same components of recursive sequences, errors associated with Fourier transform modified method are much less than the other and are valid for a large range of x-axis coordinates.
Pavarini, C.
1974-01-01
Work in two somewhat distinct areas is presented. First, the optimal system design problem for a Mars-roving vehicle is attacked by creating static system models and a system evaluation function and optimizing via nonlinear programming techniques. The second area concerns the problem of perturbed-optimal solutions. Given an initial perturbation in an element of the solution to a nonlinear programming problem, a linear method is determined to approximate the optimal readjustments of the other elements of the solution. Then, the sensitivity of the Mars rover designs is described by application of this method.
New results on stability analysis for time-varying delay systems with non-linear perturbations.
Liu, Pin-Lin
2013-05-01
The problem of stability for linear time-varying delay systems under nonlinear perturbation is discussed, with delay assumed as time-varying. Delay decomposition approach allows information of the delayed plant states to be fully considered. A less conservative delay-dependent robust stability condition is derived, using integral inequality approach to express the relationship of Leibniz-Newton formula terms in the within the framework of linear matrix inequalities (LMIs). Merits of the proposed results lie in lesser conservatism, which are realized by choosing different Lyapunov matrices in the decomposed integral intervals and estimating the upper bound of some cross term more exactly. Numerical examples are given to illustrate the effectiveness and lesser conservatism of the proposed method.
Georgievskii, D. V.
2007-06-01
Material functions are necessary element of the constitutive relations determining any model of continuum. These functions can be defined as a collection of objects from which the operator of constitutive relations can be reconstructed completely. The material functions are found in test experiments and show the differences between a given medium and other media in the framework of the same model [1]. The "test experiment theory" is an important part of modern experimental mechanics. Just as in any experiment, from determining the viscosity coefficient by using the rotational viscosimeters to constructing the yield surface by using machines combined loading, the material functions are determined with an unavoidable error. For example, experimenters know that, in experiments with arbitrary accuracy, the moduli of elasticity can only be measured with an unimprovable tolerance of about 7%. Starting already from [2], the investigators' attention has been repeatedly drawn to the fact that it is necessary to take into account this tolerance in determining the material constants, functions, and functionals in problems of mechanics and especially in analyzing the stability of deformation processes. Mathematically, this means that problems of stability under perturbations of the initial data, external constantly acting forces, domain boundaries, etc. should be supplemented with the assumption that the material functions have unknown perturbations of a certain class [3]. The variations of material functions in the framework of the linearized stability theory were considered in [2, 4, 5]. In what follows, we study isotropic tensor functions in the most general case of scalar and tensor nonlinearity. These functions are assigned the meaning of constitutive relations between the stress and strain rate tensors in continuum. These constitutive relations contain scalar material functions of invariants on which, as follows from the above, some variations proportional to a small
Sopuerta, C F; Gualtieri, L; Sopuerta, Carlos F.; Bruni, Marco; Gualtieri, Leonardo
2003-01-01
We present a new way of deriving gauge transformations in non--linear relativistic perturbation theory. The main ingredient in this formulation is the use of the Baker-Campbell-Hausdorff formula. The associated formal machinery allows us to generalize one-parameter perturbation theory to an arbitrary number of parameters, and to prove the main results concerning the consistency of the scheme to any order in the perturbations. Gauge transformations at any required order can then be directly derived from a generating exponential formula via a simple Taylor expansion. We outline the relation between our novel formulation and previous results.
Moen, Erick K.; Beier, Hope T.; Thompson, Gary L.; Roth, Caleb C.; Ibey, Bennett L.
2014-03-01
Nonlinear optical probes, especially those involving second harmonic generation (SHG), have proven useful as sensors for near-instantaneous detection of alterations to orientation or energetics within a substance. This has been exploited to some success for observing conformational changes in proteins. SHG probes, therefore, hold promise for reporting rapid and minute changes in lipid membranes. In this report, one of these probes is employed in this regard, using nanosecond electric pulses (nsEPs) as a vehicle for instigating subtle membrane perturbations. The result provides a useful tool and methodology for the observation of minute membrane perturbation, while also providing meaningful information on the phenomenon of electropermeabilization due to nsEP. The SHG probe Di- 4-ANEPPDHQ is used in conjunction with a tuned optical setup to demonstrate nanoporation preferential to one hemisphere, or pole, of the cell given a single square shaped pulse. The results also confirm a correlation of pulse width to the amount of poration. Furthermore, the polarity of this event and the membrane physics of both hemispheres, the poles facing either electrode, were tested using bipolar pulses consisting of two pulses of opposite polarity. The experiment corroborates findings by other researchers that these types of pulses are less effective in causing repairable damage to the lipid membrane of cells.
Application of He's homotopy perturbation method to conservative truly nonlinear oscillators
Energy Technology Data Exchange (ETDEWEB)
Belendez, A. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es; Belendez, T.; Marquez, A.; Neipp, C. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2008-08-15
We apply He's homotopy perturbation method to find improved approximate solutions to conservative truly nonlinear oscillators. This approach gives us not only a truly periodic solution but also the period of the motion as a function of the amplitude of oscillation. We find that this method works very well for the whole range of parameters in the case of the cubic oscillator, and excellent agreement of the approximate frequencies with the exact one has been demonstrated and discussed. For the second order approximation we have shown that the relative error in the analytical approximate frequency is approximately 0.03% for any parameter values involved. We also compared the analytical approximate solutions and the Fourier series expansion of the exact solution. This has allowed us to compare the coefficients for the different harmonic terms in these solutions. The most significant features of this method are its simplicity and its excellent accuracy for the whole range of oscillation amplitude values and the results reveal that this technique is very effective and convenient for solving conservative truly nonlinear oscillatory systems.
Quintin, Jerome; Cai, Yi-Fu; Brandenberger, Robert H
2015-01-01
Assuming that curvature perturbations and gravitational waves originally arise from vacuum fluctuations in a matter-dominated phase of contraction, we study the dynamics of the cosmological perturbations evolving through a nonsingular bouncing phase described by a generic single scalar field Lagrangian minimally coupled to Einstein gravity. In order for such a model to be consistent with the current upper limits on the tensor-to-scalar ratio, there must be an enhancement of the curvature fluctuations during the bounce phase. We show that, while it remains possible to enlarge the amplitude of curvature perturbations due to the non-trivial background evolution, this growth is very limited because of the conservation of curvature perturbations on super-Hubble scales. We further perform a general analysis of the evolution of primordial non-Gaussianities through the bounce phase. By studying the general form of the bispectrum we show that the non-Gaussianity parameter $f_{\\mathrm{NL}}$ (which is of order unity bef...
奇摄动非线性边值问题%THE SINGULARLY PERTURBED NONLINEAR BOUNDARY VALUE PROBLEMS
Institute of Scientific and Technical Information of China (English)
莫嘉琪
2000-01-01
The singularly perturbed nonlinear boundary value problems are considered.Using the stretched variable and the method of boundary layer correction,the formal asymptotic expansion of solution is obtained.And then the uniform validity of solution is proved by using the differential inequalities.
Liu, Gang; Jayathilake, Pahala Gedara; Khoo, Boo Cheong
2014-02-01
Two nonlinear models are proposed to investigate the focused acoustic waves that the nonlinear effects will be important inside the liquid around the scatterer. Firstly, the one dimensional solutions for the widely used Westervelt equation with different coordinates are obtained based on the perturbation method with the second order nonlinear terms. Then, by introducing the small parameter (Mach number), a dimensionless formulation and asymptotic perturbation expansion via the compressible potential flow theory is applied. This model permits the decoupling between the velocity potential and enthalpy to second order, with the first potential solutions satisfying the linear wave equation (Helmholtz equation), whereas the second order solutions are associated with the linear non-homogeneous equation. Based on the model, the local nonlinear effects of focused acoustic waves on certain volume are studied in which the findings may have important implications for bubble cavitation/initiation via focused ultrasound called HIFU (High Intensity Focused Ultrasound). The calculated results show that for the domain encompassing less than ten times the radius away from the center of the scatterer, the non-linear effect exerts a significant influence on the focused high intensity acoustic wave. Moreover, at the comparatively higher frequencies, for the model of spherical wave, a lower Mach number may result in stronger nonlinear effects.
Beigy, Hamid; Ahmad, Ashar; Masoudi-Nejad, Ali; Fröhlich, Holger
2017-01-01
Inferring the structure of molecular networks from time series protein or gene expression data provides valuable information about the complex biological processes of the cell. Causal network structure inference has been approached using different methods in the past. Most causal network inference techniques, such as Dynamic Bayesian Networks and ordinary differential equations, are limited by their computational complexity and thus make large scale inference infeasible. This is specifically true if a Bayesian framework is applied in order to deal with the unavoidable uncertainty about the correct model. We devise a novel Bayesian network reverse engineering approach using ordinary differential equations with the ability to include non-linearity. Besides modeling arbitrary, possibly combinatorial and time dependent perturbations with unknown targets, one of our main contributions is the use of Expectation Propagation, an algorithm for approximate Bayesian inference over large scale network structures in short computation time. We further explore the possibility of integrating prior knowledge into network inference. We evaluate the proposed model on DREAM4 and DREAM8 data and find it competitive against several state-of-the-art existing network inference methods. PMID:28166542
Non-linear magnetohydrodynamic modeling of plasma response to resonant magnetic perturbations
Energy Technology Data Exchange (ETDEWEB)
Orain, F.; Bécoulet, M.; Dif-Pradalier, G.; Nardon, E.; Passeron, C.; Latu, G.; Grandgirard, V.; Fil, A.; Ratnani, A. [CEA, IRFM, F-13108 Saint-Paul-Lez-Durance (France); Huijsmans, G. [ITER Organization, Route de Vinon, F-13115 Saint-Paul-Lez-Durance (France); Pamela, S. [IIFS-PIIM. Aix Marseille Université - CNRS, 13397 Marseille Cedex20 (France); Chapman, I.; Kirk, A.; Thornton, A. [EURATOM/CCFE Fusion Association, Culham Science Centre, Oxon OX14 3DB (United Kingdom); Hoelzl, M. [Max-Planck-Institut für Plasmaphysik, EURATOM Association, Garching (Germany); Cahyna, P. [Association EURATOM/IPP.CR, Prague (Czech Republic)
2013-10-15
The interaction of static Resonant Magnetic Perturbations (RMPs) with the plasma flows is modeled in toroidal geometry, using the non-linear resistive MHD code JOREK, which includes the X-point and the scrape-off-layer. Two-fluid diamagnetic effects, the neoclassical poloidal friction and a source of toroidal rotation are introduced in the model to describe realistic plasma flows. RMP penetration is studied taking self-consistently into account the effects of these flows and the radial electric field evolution. JET-like, MAST, and ITER parameters are used in modeling. For JET-like parameters, three regimes of plasma response are found depending on the plasma resistivity and the diamagnetic rotation: at high resistivity and slow rotation, the islands generated by the RMPs at the edge resonant surfaces rotate in the ion diamagnetic direction and their size oscillates. At faster rotation, the generated islands are static and are more screened by the plasma. An intermediate regime with static islands which slightly oscillate is found at lower resistivity. In ITER simulations, the RMPs generate static islands, which forms an ergodic layer at the very edge (ψ≥0.96) characterized by lobe structures near the X-point and results in a small strike point splitting on the divertor targets. In MAST Double Null Divertor geometry, lobes are also found near the X-point and the 3D-deformation of the density and temperature profiles is observed.
Non-linear magnetohydrodynamic modeling of plasma response to resonant magnetic perturbations
Orain, F.; Bécoulet, M.; Dif-Pradalier, G.; Huijsmans, G.; Pamela, S.; Nardon, E.; Passeron, C.; Latu, G.; Grandgirard, V.; Fil, A.; Ratnani, A.; Chapman, I.; Kirk, A.; Thornton, A.; Hoelzl, M.; Cahyna, P.
2013-10-01
The interaction of static Resonant Magnetic Perturbations (RMPs) with the plasma flows is modeled in toroidal geometry, using the non-linear resistive MHD code JOREK, which includes the X-point and the scrape-off-layer. Two-fluid diamagnetic effects, the neoclassical poloidal friction and a source of toroidal rotation are introduced in the model to describe realistic plasma flows. RMP penetration is studied taking self-consistently into account the effects of these flows and the radial electric field evolution. JET-like, MAST, and ITER parameters are used in modeling. For JET-like parameters, three regimes of plasma response are found depending on the plasma resistivity and the diamagnetic rotation: at high resistivity and slow rotation, the islands generated by the RMPs at the edge resonant surfaces rotate in the ion diamagnetic direction and their size oscillates. At faster rotation, the generated islands are static and are more screened by the plasma. An intermediate regime with static islands which slightly oscillate is found at lower resistivity. In ITER simulations, the RMPs generate static islands, which forms an ergodic layer at the very edge (ψ ≥0.96) characterized by lobe structures near the X-point and results in a small strike point splitting on the divertor targets. In MAST Double Null Divertor geometry, lobes are also found near the X-point and the 3D-deformation of the density and temperature profiles is observed.
Gasperini, Maurizio
2011-03-01
Preface; Acknowledgements; Notation, units and conventions; 1. A short review of standard and inflationary cosmology; 2. The basic string cosmology equations; 3. Conformal invariance and string effective action; 4. Duality symmetries and cosmological solutions; 5. Inflationary kinematics; 6. The string phase; 7. The cosmic background of relic gravitational waves; 8. Scalar perturbations and the anisotropy of the CMB radiation; 9. Dilaton phenomenology; 10. Elements of brane cosmology; Index.
Hwang, J.; Noh, H.
2004-01-01
The dynamic world model and its linear perturbations were first studied in Einstein's gravity. In the system without pressure the relativistic equations coincide exactly with the later known ones in Newton's gravity. Here we prove that, except for the gravitational wave contribution, even to the second-order perturbations, equations for the relativistic irrotational zero-pressure fluid in a flat Friedmann background coincide exactly with the previously known Newtonian equations. Thus, to the ...
Energy Technology Data Exchange (ETDEWEB)
Mihalache, D.; Panoiu, N.-C.; Moldoveanu, F.; Baboiu, D.-M. [Dept. of Theor. Phys., Inst. of Atomic Phys., Bucharest (Romania)
1994-09-21
We used the Riemann problem method with a 3*3 matrix system to find the femtosecond single soliton solution for a perturbed nonlinear Schroedinger equation which describes bright ultrashort pulse propagation in properly tailored monomode optical fibres. Compared with the Gel'fand-Levitan-Marchenko approach, the major advantage of the Riemann problem method is that it provides the general single soliton solution in a simple and compact form. Unlike the standard nonlinear Schroedinger equation, here the single soliton solution exhibits periodic evolution patterns. (author)
Composite control of a class of nonlinear singularly perturbed discrete-time systems via D-SDRE
Zhang, Yan; Subbaram Naidu, D.; Cai, Chenxiao; Zou, Yun
2016-08-01
In this paper, the regulation problem of a class of nonlinear singularly perturbed discrete-time systems is investigated. Using the theory of singular perturbations and time scales, the nonlinear system is decoupled into reduced-order slow and fast (boundary layer) subsystems. Then, a composite controller consisting of two sub-controllers for the slow and fast subsystems is developed using the discrete-time state-dependent Riccati equation (D-SDRE). It is proved that the equilibrium point of the original closed-loop system with a composite controller is locally asymptotically stable. Moreover, the region of attraction of the closed-loop system is estimated by using linear matrix inequality. One example is given to illustrate the effectiveness of the results obtained.
Sun, Y; Liang, Y; Liu, Y Q; Gu, S; Yang, X; Guo, W; Shi, T; Jia, M; Wang, L; Lyu, B; Zhou, C; Liu, A; Zang, Q; Liu, H; Chu, N; Wang, H H; Zhang, T; Qian, J; Xu, L; He, K; Chen, D; Shen, B; Gong, X; Ji, X; Wang, S; Qi, M; Song, Y; Yuan, Q; Sheng, Z; Gao, G; Fu, P; Wan, B
2016-09-01
Evidence of a nonlinear transition from mitigation to suppression of the edge localized mode (ELM) by using resonant magnetic perturbations (RMPs) in the EAST tokamak is presented. This is the first demonstration of ELM suppression with RMPs in slowly rotating plasmas with dominant radio-frequency wave heating. Changes of edge magnetic topology after the transition are indicated by a gradual phase shift in the plasma response field from a linear magneto hydro dynamics modeling result to a vacuum one and a sudden increase of three-dimensional particle flux to the divertor. The transition threshold depends on the spectrum of RMPs and plasma rotation as well as perturbation amplitude. This means that edge topological changes resulting from nonlinear plasma response plays a key role in the suppression of ELM with RMPs.
Hu, Weipeng; Deng, Zichen; Yin, Tingting
2017-01-01
Exploring the dynamic behaviors of the damping nonlinear Schrödinger equation (NLSE) with periodic perturbation is a challenge in the field of nonlinear science, because the numerical approaches available for damping-driven dynamic systems may exhibit the artificial dissipation in different degree. In this paper, based on the generalized multi-symplectic idea, the local energy/momentum loss expressions as well as the approximate symmetric form of the linearly damping NLSE with periodic perturbation are deduced firstly. And then, the local energy/momentum losses are separated from the simulation results of the NLSE with small linear damping rate less than the threshold to insure structure-preserving properties of the scheme. Finally, the breakup process of the multisoliton state is simulated and the bifurcation of the discrete eigenvalues of the associated Zakharov-Shabat spectral problem is obtained to investigate the variation of the velocity as well as the amplitude of the solitons during the splitting process.
Energy Technology Data Exchange (ETDEWEB)
Boudesocque-Dubois, C.; Clarisse, J.M
2007-07-01
In the context of linear perturbation computations of planar or spherically symmetric flows, we propose numerical methods, in Lagrangian coordinates, for integrating the one-dimensional gas dynamics equations with nonlinear heat conduction and their linear perturbations. Numerical results are presented for different configurations, with or without flow motion. (authors)
Institute of Scientific and Technical Information of China (English)
ZHENGChun-Long; ZHANGJie-Fang; CHENLi-Qun
2003-01-01
Starting from a special Baecklund transform and a variable separation approach, a quite general variable separation solution of the generalized ( 2 + 1 )-dimensional perturbed nonlinear Schroedinger system is obtained. In addition to the single-valued localized coherent soliron excitations like dromions, breathers, instantons, peakons, and previously revealed chaotic localized solution, a new type of multi-valued (folded) localized excitation is derived by introducing some appropriate lower-dimensional multiple valued functions.
Directory of Open Access Journals (Sweden)
Ohanyan G.G.
2010-09-01
Full Text Available The quasi-adiabatic and quasi-isotherm regimes of propagation of high-frequency perturbation are considered in a thermal relaxing gas–fluid mixture. The simplified non-linear equations are obtained. It is shown that in the absence of heat transfer and under the quasi-adiabatic regime the form of propagation is soliton, or the shock wave in quasi-isotherm regime.
Ohanyan G.G.
2010-01-01
The quasi-adiabatic and quasi-isotherm regimes of propagation of high-frequency perturbation are considered in a thermal relaxing gas–fluid mixture. The simplified non-linear equations are obtained. It is shown that in the absence of heat transfer and under the quasi-adiabatic regime the form of propagation is soliton, or the shock wave in quasi-isotherm regime.
Abate, Alexandra; Bridle, Sarah; Teodoro, Luis F. A.; Warren, Michael S.; Hendry, Martin
2008-10-01
We investigate methods to best estimate the normalization of the mass density fluctuation power spectrum (σ8) using peculiar velocity data from a survey like the six-degree Field Galaxy Velocity Survey (6dFGSv). We focus on two potential problems: (i) biases from non-linear growth of structure and (ii) the large number of velocities in the survey. Simulations of ΛCDM-like models are used to test the methods. We calculate the likelihood from a full covariance matrix of velocities averaged in grid cells. This simultaneously reduces the number of data points and smoothes out non-linearities which tend to dominate on small scales. We show how the averaging can be taken into account in the predictions in a practical way, and show the effect of the choice of cell size. We find that a cell size can be chosen that significantly reduces the non-linearities without significantly increasing the error bars on cosmological parameters. We compare our results with those from a principal components analysis following Watkins et al. and Feldman et al. to select a set of optimal moments constructed from linear combinations of the peculiar velocities that are least sensitive to the non-linear scales. We conclude that averaging in grid cells performs equally well. We find that for a survey such as 6dFGSv we can estimate σ8 with less than 3 per cent bias from non-linearities. The expected error on σ8 after marginalizing over Ωm is approximately 16 per cent.
Institute of Scientific and Technical Information of China (English)
JIANG Zhina; MU Mu
2009-01-01
The authors apply the technique of conditional nonlinear optimal perturbations (CNOPs) as a means of providing initial perturbations for ensemble forecasting by using a barotropic quasi-gcostrophic (QG) model in a perfect-model scenario. Ensemble forecasts for the medium range (14 days) are made from the initial states perturbed by CNOPs and singular vectors (SVs). 13 different cases have been chosen when analysis error is a kind of fast growing error. Our experiments show that the introduction of CNOP provides better forecast skill than the SV method. Moreover, the spread-skill relationship reveals that the ensemble samples in which the first SV is replaced by CNOP appear supcrior to those obtained by SVs from day 6 to day 14. Rank diagrams are adopted to compare the new method with the SV approach. The results illustrate that the introduction of CNOP has higher reliability for medium-range ensemble forecasts.
Energy Technology Data Exchange (ETDEWEB)
Belendez, A. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es; Hernandez, A.; Belendez, T.; Neipp, C.; Marquez, A. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2008-03-17
He's homotopy perturbation method is used to calculate higher-order approximate periodic solutions of a nonlinear oscillator with discontinuity for which the elastic force term is proportional to sgn(x). We find He's homotopy perturbation method works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. Only one iteration leads to high accuracy of the solutions with a maximal relative error for the approximate period of less than 1.56% for all values of oscillation amplitude, while this relative error is 0.30% for the second iteration and as low as 0.057% when the third-order approximation is considered. Comparison of the result obtained using this method with those obtained by different harmonic balance methods reveals that He's homotopy perturbation method is very effective and convenient.
Institute of Scientific and Technical Information of China (English)
WANG Bo; HUO Zhenhua
2013-01-01
An extension of the conditional nonlinear optimal parameter perturbation (CNOP-P) method is applied to the parameter optimization of the Common Land Model (CoLM) for the North China Plain with the differential evolution (DE) method.Using National Meteorological Center (NMC) Reanalysis 6-hourly surface flux data and National Center for Environmental Prediction/Department of Energy (NCEP/DOE)Atmospheric Model Intercomparison Project II (AMIP-II) 6-hourly Reanalysis Gaussian Grid data,two experiments (I and II) were designed to investigate the impact of the percentages of sand and clay in the shallow soil in CoLM on its ability to simulate shallow soil moisture.A third experiment (III) was designed to study the shallow soil moisture and latent heat flux simultaneously.In all the three experiments,after the optimization stage,the percentages of sand and clay of the shallow soil were used to predict the shallow soil moisture in the following month.The results show that the optimal parameters can enable CoLM to better simulate shallow soil moisture,with the simulation results of CoLM after the double-parameter optimal experiment being better than the single-parameter optimal experiment in the optimization slot.Furthermore,the optimal parameters were able to significantly improve the prediction results of CoLM at the prediction stage.In addition,whether or not the atmospheric forcing and observational data are accurate can seriously affect the results of optimization,and the more accurate the data are,the more significant the results of optimization may be.
Initial conditions, Discreteness and non-linear structure formation in cosmology
Sylos-Labini, F; Gabrielli, A; Joyce, M; Labini, Francesco Sylos; Baertschiger, Thierry; Gabrielli, Andrea; Joyce, Michael
2002-01-01
In this lecture we address three different but related aspects of the initial continuous fluctuation field in standard cosmological models. Firstly we discuss the properties of the so-called Harrison-Zeldovich like spectra. This power spectrum is a fundamental feature of all current standard cosmological models. In a simple classification of all stationary stochastic processes into three categories, we highlight with the name ``super-homogeneous'' the properties of the class to which models like this, with $P(0)=0$, belong. In statistical physics language they are well described as glass-like. Secondly, the initial continuous density field with such small amplitude correlated Gaussian fluctuations must be discretised in order to set up the initial particle distribution used in gravitational N-body simulations. We discuss the main issues related to the effects of discretisation, particularly concerning the effect of particle induced fluctuations on the statistical properties of the initial conditions and on th...
Nonlinear description of Yang-Mills cosmology: cosmic inflation and the accompanying Hannay’s angle
Bouguerra, Yacine; Maamache, Mustapha; Ryeol Choi, Jeong
2017-06-01
Hannay’s angle is a classical analogue of the “geometrical phase factor” found by Berry in his research on the quantum adiabatic theorem. This classical analogue is defined if closed curves of constant action variables return to the same curves in phase space after an adaibatic evolution. Adiabatic evolution of Yang-Mills cosmology, which is described by a time-dependent quartic oscillator, is investigated. Phase properties of the Yang-Mills fields are analyzed and the corresponding Hannay’s angle is derived from a rigorous evaluation. The obtained Hannay’s angle shift is represented in terms of several observable parameters associated with such an angle shift. The time evolution of Hannay’s angle in Yang-Mills cosmology is examined from an illustration plotted on the basis of numerical evaluation, and its physical nature is addressed. Hannay’s angle, together with its quantum counterpart Berry’s phase, plays a pivotal role in conceptual understanding of several cosmological problems and indeed can be used as a supplementary probe for cosmic inflation. Supported by Basic Science Research Program through National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2016R1D1A1A09919503)
Axions : Theory and Cosmological Role
Kawasaki, Masahiro; Nakayama, Kazunori
2013-01-01
We review recent developments on axion cosmology. Topics include : axion cold dark matter, axions from topological defects, axion isocurvature perturbation and its non-Gaussianity and axino/saxion cosmology in supersymmetric axion model.
Luo, Xiaochun; Schramm, David N.
1993-01-01
One of the crucial aspects of density perturbations that are produced by the standard inflation scenario is that they are Gaussian where seeds produced by topological defects tend to be non-Gaussian. The three-point correlation function of the temperature anisotropy of the cosmic microwave background radiation (CBR) provides a sensitive test of this aspect of the primordial density field. In this paper, this function is calculated in the general context of various allowed non-Gaussian models. It is shown that the Cosmic Background Explorer and the forthcoming South Pole and balloon CBR anisotropy data may be able to provide a crucial test of the Gaussian nature of the perturbations.
Relativistic cosmological hydrodynamics
Hwang, J
1997-01-01
We investigate the relativistic cosmological hydrodynamic perturbations. We present the general large scale solutions of the perturbation variables valid for the general sign of three space curvature, the cosmological constant, and generally evolving background equation of state. The large scale evolution is characterized by a conserved gauge invariant quantity which is the same as a perturbed potential (or three-space curvature) in the comoving gauge.
Covariant Bardeen perturbation formalism
Vitenti, S. D. P.; Falciano, F. T.; Pinto-Neto, N.
2014-05-01
In a previous work we obtained a set of necessary conditions for the linear approximation in cosmology. Here we discuss the relations of this approach with the so-called covariant perturbations. It is often argued in the literature that one of the main advantages of the covariant approach to describe cosmological perturbations is that the Bardeen formalism is coordinate dependent. In this paper we will reformulate the Bardeen approach in a completely covariant manner. For that, we introduce the notion of pure and mixed tensors, which yields an adequate language to treat both perturbative approaches in a common framework. We then stress that in the referred covariant approach, one necessarily introduces an additional hypersurface choice to the problem. Using our mixed and pure tensors approach, we are able to construct a one-to-one map relating the usual gauge dependence of the Bardeen formalism with the hypersurface dependence inherent to the covariant approach. Finally, through the use of this map, we define full nonlinear tensors that at first order correspond to the three known gauge invariant variables Φ, Ψ and Ξ, which are simultaneously foliation and gauge invariant. We then stress that the use of the proposed mixed tensors allows one to construct simultaneously gauge and hypersurface invariant variables at any order.
Directory of Open Access Journals (Sweden)
Hong Qin
2003-01-01
Full Text Available Two-stream instabilities in intense charged particle beams, described self-consistently by the nonlinear Vlasov-Maxwell equations, are studied using a 3D multispecies perturbative particle simulation method. The recently developed Beam Equilibrium, Stability and Transport code is used to simulate the linear and nonlinear properties of the electron-proton (e-p two-stream instability observed in the Proton Storage Ring (PSR experiment for a long, coasting beam. Simulations in a parameter regime characteristic of the PSR experiment show that the e-p instability has a dipole-mode structure, and that the growth rate is an increasing function of beam intensity, but a decreasing function of the longitudinal momentum spread. It is also shown that the instability threshold decreases with increasing fractional charge neutralization and increases with increasing axial momentum spread of the beam particles. In the nonlinear phase, the simulations show that the proton density perturbation first saturates at a relatively low level and subsequently grows to a higher level. Finally, the nonlinear space-charge-induced transverse tune spread, which introduces a major growth-rate reduction effect on the e-p instability, is studied for self-consistent equilibrium populations of protons and electrons.
Akbarzade, M.; Langari, J.
2011-02-01
In this paper a new approach combining the features of the homotopy concept with variational approach is proposed to find accurate analytical solutions for nonlinear oscillators with and without a fractional power restoring force. Since the first-order approximation leads to very accurate results, comparisons with other results are presented to show the effectiveness of this method. The validity of the method is independent of whether or not there exist small or large parameters in the considered nonlinear equations; the obtained results prove the validity and efficiency of the method, which can be easily extended to other strongly nonlinear problems. At the end we compare our procedure with the optimal homotopy perturbation method.
National Research Council Canada - National Science Library
Zhou, Xiao Ping; Lee, Victoria S; Wang, Emily Q; Jiang, Jack J
2009-01-01
...) and levodopa on patients with Parkinson's disease (PD). Methods: In this study, the effects of DBS and levodopa treatment on patients with PD were measured using perturbation, nonlinear dynamic, and perceptual analysis...
Cosmological tests of modified gravity
Koyama, Kazuya
2016-04-01
We review recent progress in the construction of modified gravity models as alternatives to dark energy as well as the development of cosmological tests of gravity. Einstein’s theory of general relativity (GR) has been tested accurately within the local universe i.e. the Solar System, but this leaves the possibility open that it is not a good description of gravity at the largest scales in the Universe. This being said, the standard model of cosmology assumes GR on all scales. In 1998, astronomers made the surprising discovery that the expansion of the Universe is accelerating, not slowing down. This late-time acceleration of the Universe has become the most challenging problem in theoretical physics. Within the framework of GR, the acceleration would originate from an unknown dark energy. Alternatively, it could be that there is no dark energy and GR itself is in error on cosmological scales. In this review, we first give an overview of recent developments in modified gravity theories including f(R) gravity, braneworld gravity, Horndeski theory and massive/bigravity theory. We then focus on common properties these models share, such as screening mechanisms they use to evade the stringent Solar System tests. Once armed with a theoretical knowledge of modified gravity models, we move on to discuss how we can test modifications of gravity on cosmological scales. We present tests of gravity using linear cosmological perturbations and review the latest constraints on deviations from the standard Λ CDM model. Since screening mechanisms leave distinct signatures in the non-linear structure formation, we also review novel astrophysical tests of gravity using clusters, dwarf galaxies and stars. The last decade has seen a number of new constraints placed on gravity from astrophysical to cosmological scales. Thanks to on-going and future surveys, cosmological tests of gravity will enjoy another, possibly even more, exciting ten years.
Cosmological tests of modified gravity.
Koyama, Kazuya
2016-04-01
We review recent progress in the construction of modified gravity models as alternatives to dark energy as well as the development of cosmological tests of gravity. Einstein's theory of general relativity (GR) has been tested accurately within the local universe i.e. the Solar System, but this leaves the possibility open that it is not a good description of gravity at the largest scales in the Universe. This being said, the standard model of cosmology assumes GR on all scales. In 1998, astronomers made the surprising discovery that the expansion of the Universe is accelerating, not slowing down. This late-time acceleration of the Universe has become the most challenging problem in theoretical physics. Within the framework of GR, the acceleration would originate from an unknown dark energy. Alternatively, it could be that there is no dark energy and GR itself is in error on cosmological scales. In this review, we first give an overview of recent developments in modified gravity theories including f(R) gravity, braneworld gravity, Horndeski theory and massive/bigravity theory. We then focus on common properties these models share, such as screening mechanisms they use to evade the stringent Solar System tests. Once armed with a theoretical knowledge of modified gravity models, we move on to discuss how we can test modifications of gravity on cosmological scales. We present tests of gravity using linear cosmological perturbations and review the latest constraints on deviations from the standard [Formula: see text]CDM model. Since screening mechanisms leave distinct signatures in the non-linear structure formation, we also review novel astrophysical tests of gravity using clusters, dwarf galaxies and stars. The last decade has seen a number of new constraints placed on gravity from astrophysical to cosmological scales. Thanks to on-going and future surveys, cosmological tests of gravity will enjoy another, possibly even more, exciting ten years.
Energy Technology Data Exchange (ETDEWEB)
De Felice, Antonio, E-mail: antoniod@nu.ac.th [Department of Physics, Faculty of Science, Tokyo University of Science, 1-3, Kagurazaka, Shinjuku-ku, Tokyo 162-8601 (Japan); TPTP and NEP, The Institute for Fundamental Study, Naresuan University, Phitsanulok, 65000 (Thailand); Thailand Center of Excellence in Physics, Ministry of Education, Bangkok 10400 (Thailand); Kobayashi, Tsutomu [Hakubi Center, Kyoto University, Kyoto 606-8302 (Japan); Department of Physics, Kyoto University, Kyoto 606-8502 (Japan); Tsujikawa, Shinji [Department of Physics, Faculty of Science, Tokyo University of Science, 1-3, Kagurazaka, Shinjuku-ku, Tokyo 162-8601 (Japan)
2011-12-06
In the Horndeski's most general scalar-tensor theories the equations of scalar density perturbations are derived in the presence of non-relativistic matter minimally coupled to gravity. Under a quasi-static approximation on sub-horizon scales we obtain the effective gravitational coupling G{sub eff} associated with the growth rate of matter perturbations as well as the effective gravitational potential {Phi}{sub eff} relevant to the deviation of light rays. We then apply our formulas to a number of modified gravitational models of dark energy - such as those based on f(R) theories, Brans-Dicke theories, kinetic gravity braidings, covariant Galileons, and field derivative couplings with the Einstein tensor. Our results are useful to test the large-distance modification of gravity from the future high-precision observations of large-scale structure, weak lensing, and cosmic microwave background.
De Felice, Antonio; Tsujikawa, Shinji
2011-01-01
In the Horndeski's most general scalar-tensor theories the equations of scalar density perturbations are derived in the presence of non-relativistic matter minimally coupled to gravity. Under a quasi-static approximation on sub-horizon scales we obtain the effective gravitational coupling $G_{eff}$ associated with the growth rate of matter perturbations as well as the effective gravitational potential $\\Phi_{eff}$ relevant to the deviation of light rays. We then apply our formulas to a number of modified gravitational models of dark energy--such as those based on f(R) theories, Brans-Dicke theories, kinetic gravity braidings, covariant Galileons, and field derivative couplings with the Einstein tensor. Our results are useful to test the large-distance modification of gravity from the future high-precision observations of large-scale structure, weak lensing, and cosmic microwave background.
Nakamura, Kouji
2010-01-01
We derived the second-order perturbations of the Einstein equations and the Klein-Gordon equation for a generic situation in terms of gauge-invariant variables. The consistency of all the equations is confirmed. This confirmation implies that all the derived equations of the second order are self-consistent and these equations are correct in this sense. We also discuss the physical implication of these equations.
Zheng, Qin; Yang, Zubin; Sha, Jianxin; Yan, Jun
2017-02-01
In predictability problem research, the conditional nonlinear optimal perturbation (CNOP) describes the initial perturbation that satisfies a certain constraint condition and causes the largest prediction error at the prediction time. The CNOP has been successfully applied in estimation of the lower bound of maximum predictable time (LBMPT). Generally, CNOPs are calculated by a gradient descent algorithm based on the adjoint model, which is called ADJ-CNOP. This study, through the two-dimensional Ikeda model, investigates the impacts of the nonlinearity on ADJ-CNOP and the corresponding precision problems when using ADJ-CNOP to estimate the LBMPT. Our conclusions are that (1) when the initial perturbation is large or the prediction time is long, the strong nonlinearity of the dynamical model in the prediction variable will lead to failure of the ADJ-CNOP method, and (2) when the objective function has multiple extreme values, ADJ-CNOP has a large probability of producing local CNOPs, hence making a false estimation of the LBMPT. Furthermore, the particle swarm optimization (PSO) algorithm, one kind of intelligent algorithm, is introduced to solve this problem. The method using PSO to compute CNOP is called PSO-CNOP. The results of numerical experiments show that even with a large initial perturbation and long prediction time, or when the objective function has multiple extreme values, PSO-CNOP can always obtain the global CNOP. Since the PSO algorithm is a heuristic search algorithm based on the population, it can overcome the impact of nonlinearity and the disturbance from multiple extremes of the objective function. In addition, to check the estimation accuracy of the LBMPT presented by PSO-CNOP and ADJ-CNOP, we partition the constraint domain of initial perturbations into sufficiently fine grid meshes and take the LBMPT obtained by the filtering method as a benchmark. The result shows that the estimation presented by PSO-CNOP is closer to the true value than the
Non-Linearly Interacting Ghost Dark Energy in Brans-Dicke Cosmology
Ebrahimi, E
2016-01-01
In this paper we extend the form of interaction term into the non-linear regime in the ghost dark energy model. A general form of non-linear interaction term is presented and cosmic dynamic equations are obtained. Next, the model is detailed for two special choice of the non-linear interaction term. According to this the universe transits at suitable time ($z\\sim 0.8$) from deceleration to acceleration phase which alleviate the coincidence problem. Squared sound speed analysis revealed that for one class of non-linear interaction term $v_s^2$ can gets positive. This point is an impact of the non-linear interaction term and we never find such behavior in non interacting and linearly interacting ghost dark energy models. Also statefinder parameters are introduced for this model and we found that for one class the model meets the $\\Lambda CDM$ while in the second choice although the model approaches the $\\Lambda CDM$ but never touch that.
Cosmology emerging as the gauge structure of a nonlinear quantum system
Kam, Chon-Fai
2016-01-01
Berry phases and gauge structures in parameter spaces of quantum systems are the foundation of a broad range of quantum effects such as quantum Hall effects and topological insulators. The gauge structures of interacting many-body systems, which often present exotic features, are particularly interesting. While quantum systems are intrinsically linear due to the superposition principle, nonlinear quantum mechanics can arise as an effective theory for interacting systems (such as condensates of interacting bosons). Here we show that gauge structures similar to curved spacetime can arise in nonlinear quantum systems where the superposition principle breaks down. In the canonical formalism of the nonlinear quantum mechanics, the geometric phases of quantum evolutions can be formulated as the classical geometric phases of a harmonic oscillator that represents the Bogoliubov excitations. We find that the classical geometric phase can be described by a de Sitter universe. The fundamental frequency of the harmonic o...
Braneworld cosmology and noncommutative inflation
Calcagni, G
2005-01-01
In this work we develop the patch formalism, an approach providing a very simple and compact description of braneworld-motivated cosmologies with nonstandard effective Friedmann equations. In particular, the Hubble parameter is assumed to depend on some power of the brane energy density, H^2 \\propto \\rho^q. The high-energy limit of Randall-Sundrum (q=2) and Gauss-Bonnet (q=2/3) braneworlds are considered, during an accelerating era triggered by a single ordinary or tachyonic scalar field. The inflationary dynamics, solutions, and spectra are provided. Using the latest results from WMAP and other experiments for estimates of cosmological observables, it is shown that future data and missions can in principle discriminate between standard four-dimensional and braneworld scenarios. The issue of non-Gaussianity is also studied within nonlinear perturbation theory. The introduction of a fundamental energy scale reinforces these results. Several classes of noncommutative inflationary models are considered and their...
Massive neutrinos in nonlinear large scale structure: A consistent perturbation theory
Levi, Michele
2016-01-01
A consistent formulation to incorporate massive neutrinos in the perturbation theory of the effective CDM+baryons fluid is introduced. In this formulation all linear k dependence in the growth functions of CDM+baryons perturbations, as well as all consequent additional mode coupling at higher orders, are taken into account to any desirable accuracy. Our formulation regards the neutrino fraction, which is constant in time after the non-relativistic transition of neutrinos, and much smaller than unity, as the coupling constant of the theory. Then the "bare" perturbations are those in the massless neutrino case when the neutrino fraction vanishes, and we consider the backreaction corrections due to the gravitational coupling of neutrinos. We derive the general equations for the "bare" perturbations, and backrecation corrections. Then, by employing exact time evolution with the proper analytic Green's function we explicitly derive the leading backreaction effect, and find precise agreement at the linear level. We...
Institute of Scientific and Technical Information of China (English)
Jia-qi Mo; Wan-tao Lin
2006-01-01
In this paper the singularly perturbed initial boundary value problems for the nonlocal reaction diffusion system are considered. Using the iteration method and the comparison theorem, the existence and its asymptotic behavior of the solution for the problem are studied.
Yin, J. L.; Xing, Q. Q.; Tian, L. X.
2015-03-01
The behavior of non-smooth solitary waves switching to chaos is studied. Firstly, we present some singular homoclinic orbits of an unperturbed system. These singular homoclinic orbits correspond to non-smooth solutions. Secondly, we find that the peculiar solitary waves are more likely to be chaos by using the Melnikov theory. Finally, chaos thresholds under different amplitudes and frequencies of a periodic perturbation are given. One interesting finding is that there exists a peculiar perturbation frequency, which has significant effect on the system. The system is not well-controlled under this frequency. However, the system can be well controlled, when the frequency of the perturbation surpasses the peculiar perturbation frequency with fixed parameters of the unperturbed system.
The correlation function for density perturbations in an expanding universe. II - Nonlinear theory
Mcclelland, J.; Silk, J.
1977-01-01
A formalism is developed to find the two-point and higher-order correlation functions for a given distribution of sizes and shapes of perturbations which are randomly placed in three-dimensional space. The perturbations are described by two parameters such as central density and size, and the two-point correlation function is explicitly related to the luminosity function of groups and clusters of galaxies
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
A two-layer quasi-geostrophic model is used to study the stability and sensitivity of motions on small-scale vortices in Jupiter's atmosphere. Conditional nonlinear optimal perturbations (CNOPs) and linear singular vectors (LSVs) are both obtained numerically and compared in this paper. The results show that CNOPs can capture the nonlinear characteristics of motions in small-scale vortices in Jupiter's atmosphere and show great difference from LSVs under the condition that the initial constraint condition is large or the optimization time is not very short or both. Besides, in some basic states, local CNOPs are found.The pattern of LSV is more similar to local CNOP than global CNOP in some cases. The elementary application of the method of CNOP to the Jovian atmosphere helps us to explore the stability of variousscale motions of Jupiter's atmosphere and to compare the stability of motions in Jupiter's atmosphere and Earth's atmosphere further.
Perturbative Treatment of the Non-Linear q-Schrödinger and q-Klein–Gordon Equations
Directory of Open Access Journals (Sweden)
Javier Zamora
2016-12-01
Full Text Available Interesting non-linear generalization of both Schrödinger’s and Klein–Gordon’s equations have been recently advanced by Tsallis, Rego-Monteiro and Tsallis (NRT in Nobre et al. (Phys. Rev. Lett. 2011, 106, 140601. There is much current activity going on in this area. The non-linearity is governed by a real parameter q. Empiric hints suggest that the ensuing non-linear q-Schrödinger and q-Klein–Gordon equations are a natural manifestations of very high energy phenomena, as verified by LHC-experiments. This happens for q − values close to unity (Plastino et al. (Nucl. Phys. A 2016, 955, 16–26, Nucl. Phys. A 2016, 948, 19–27. It might thus be difficult for q-values close to unity to ascertain whether one is dealing with solutions to the ordinary Schrödinger equation (whose free particle solutions are exponentials and for which q = 1 or with its NRT non-linear q-generalizations, whose free particle solutions are q-exponentials. In this work, we provide a careful analysis of the q ∼ 1 instance via a perturbative analysis of the NRT equations.
Concordance cosmology without dark energy
Rácz, Gábor; Dobos, László; Beck, Róbert; Szapudi, István; Csabai, István
2017-07-01
According to the separate universe conjecture, spherically symmetric sub-regions in an isotropic universe behave like mini-universes with their own cosmological parameters. This is an excellent approximation in both Newtonian and general relativistic theories. We estimate local expansion rates for a large number of such regions, and use a scale parameter calculated from the volume-averaged increments of local scale parameters at each time step in an otherwise standard cosmological N-body simulation. The particle mass, corresponding to a coarse graining scale, is an adjustable parameter. This mean field approximation neglects tidal forces and boundary effects, but it is the first step towards a non-perturbative statistical estimation of the effect of non-linear evolution of structure on the expansion rate. Using our algorithm, a simulation with an initial Ωm = 1 Einstein-de Sitter setting closely tracks the expansion and structure growth history of the Λ cold dark matter (ΛCDM) cosmology. Due to small but characteristic differences, our model can be distinguished from the ΛCDM model by future precision observations. Moreover, our model can resolve the emerging tension between local Hubble constant measurements and the Planck best-fitting cosmology. Further improvements to the simulation are necessary to investigate light propagation and confirm full consistency with cosmic microwave background observations.
Braneworld cosmology and noncommutative inflation
Calcagni, Gianluca
2005-03-01
In this work we develop the patch formalism, an approach providing a very simple and compact description of braneworld-motivated cosmologies with nonstandard effective Friedmann equations. In particular, the Hubble parameter is assumed to depend on some power of the brane energy density, H^2 propto rho^q. The high-energy limit of Randall-Sundrum (q=2) and Gauss-Bonnet (q=2/3) braneworlds are considered, during an accelerating era triggered by a single ordinary or tachyonic scalar field. The inflationary dynamics, solutions, and spectra are provided. Using the latest results from WMAP and other experiments for estimates of cosmological observables, it is shown that future data and missions can in principle discriminate between standard four-dimensional and braneworld scenarios. The issue of non-Gaussianity is also studied within nonlinear perturbation theory. The introduction of a fundamental energy scale reinforces these results. Several classes of noncommutative inflationary models are considered and their features analyzed in a number of ways and energy regimes. Finally, we establish dual relations between inflationary, cyclic/ekpyrotic and phantom cosmologies, as well as between scalar-driven and tachyon-driven cosmologies. The exact dualities relating the four-dimensional spectra are broken in favour of their braneworld counterparts. The dual solutions display new interesting features because of the modification of the effective Friedmann equation on the brane.
Regular Black Holes with Cosmological Constant
Institute of Scientific and Technical Information of China (English)
MO Wen-Juan; CAI Rong-Gen; SU Ru-Keng
2006-01-01
We present a class of regular black holes with cosmological constant Λ in nonlinear electrodynamics. Instead of usual singularity behind black hole horizon, all fields and curvature invariants are regular everywhere for the regular black holes. Through gauge invariant approach, the linearly dynamical stability of the regular black hole is studied. In odd-parity sector, we find that the Λ term does not appear in the master equations of perturbations, which shows that the regular black hole is stable under odd-parity perturbations. On the other hand, for the even-parity sector, the master equations are more complicated than the case without the cosmological constant. We obtain the sufficient conditions for stability of the regular black hole. We also investigate the thermodynamic properties of the regular black hole, and find that those thermodynamic quantities do not satisfy the differential form of first law of black hole thermodynamics. The reason for violating the first law is revealed.
Characterization of the cosmological nonlinear path of single galaxies in N-body Simulations
Stalder Díaz, Diego Herbin; Rosa, Reinaldo; Clua, Esteban; Campanharo, Andriana
Turbulent-like behaviour is an important and recent ingredient in the investigation of large scale structure formation in the observable universe [1,2]. Recently, an established statistical method was used to demonstrate the importance of considering chaotic advection (or Lagrange turbulence) in combination with gravitational instabilities in the LambdaCDM simulations performed from the Virgo Consortium (VC). However, the Hubble volumes simulated from GADGET-VC algoritm have some limitations for direct lagrangian data analysis due to the large amount of data and no real time computation for particle kinetic velocity along the dark matter structure evolution. We use our COsmic LAgrangian TUrbulence Simulator (COLATUS) [3], based on GPU/CUDA technology, to perform gravitational Cosmological N-body simulations and tracking the particles paths. In this work we discuss the chaotic advection behavior of tracers galaxies based on the angular velocity fluctuation analysis of single particles during its trajectory to the gravitational collapse of super clusters at low redshifts. [1] Caretta et al., A&A doi:10.1051/0004-6361:20079105 [2] Rosa et al., CCP doi: 10.1016/j.cpc.2008.11.018 [3] Stalder et al., AIP doi: 10.1063/1.4756992
Stability analysis of nonlinear systems by multiple time scaling. [using perturbation methods
Morino, L.
1974-01-01
The asymptotic solution for the transient analysis of a general nonlinear system in the neighborhood of the stability boundary was obtained by using the multiple-time-scaling asymptotic-expansion method. The nonlinearities are assumed to be of algebraic nature. Terms of order epsilon to the 3rd power (where epsilon is the order of amplitude of the unknown) are included in the solution. The solution indicates that there is always a limit cycle which is stable (unstable) and exists above (below) the stability boundary if the nonlinear terms are stabilizing (destabilizing). Extension of the solution to include fifth order nonlinear terms is also presented. Comparisons with harmonic balance and with multiple-time-scaling solution of panel flutter equations are also included.
Time-Sliced Perturbation Theory for Large Scale Structure I: General Formalism
Blas, Diego; Ivanov, Mikhail M; Sibiryakov, Sergey
2016-01-01
We present a new analytic approach to describe large scale structure formation in the mildly non-linear regime. The central object of the method is the time-dependent probability distribution function generating correlators of the cosmological observables at a given moment of time. Expanding the distribution function around the Gaussian weight we formulate a perturbative technique to calculate non-linear corrections to cosmological correlators, similar to the diagrammatic expansion in a three-dimensional Euclidean quantum field theory, with time playing the role of an external parameter. For the physically relevant case of cold dark matter in an Einstein--de Sitter universe, the time evolution of the distribution function can be found exactly and is encapsulated by a time-dependent coupling constant controlling the perturbative expansion. We show that all building blocks of the expansion are free from spurious infrared enhanced contributions that plague the standard cosmological perturbation theory. This pave...
Scalar Perturbations on the background of Linearly and Nonlinearly Charged BTZ Black Holes
Tang, Zi-Yu; Zangeneh, Mahdi Kord; Wang, Bin; Saavedra, Joel
2016-01-01
We investigate the spacetime properties of BTZ black holes in Maxwell field and BornInfeld field and find rich properties in the spacetime structures when the model parameters vary. Employing the Landau-Lifshitz theory, we examine the thermodynamical phase transition in the charged BTZ holes. We further study the dynamical perturbation in the background of the charged BTZ black holes and find different properties of dynamical perturbations for the extreme and nonextreme charged BTZ black holes, which can serve as a new physical signal to indicate the phase transition between them.
Cosmological diagrammatic rules
Giddings, Steven B
2010-01-01
A simple set of diagrammatic rules is formulated for perturbative evaluation of ``in-in" correlators, as is needed in cosmology and other nonequilibrium problems. These rules are both intuitive, and efficient for calculational purposes.
Cosmological diagrammatic rules
Energy Technology Data Exchange (ETDEWEB)
Giddings, Steven B. [Department of Physics, University of California, Santa Barbara, CA 93106 (United States); Sloth, Martin S., E-mail: giddings@physics.ucsb.edu, E-mail: sloth@cern.ch [CERN, Physics Department, Theory Unit, CH-1211 Geneva 23 (Switzerland)
2010-07-01
A simple set of diagrammatic rules is formulated for perturbative evaluation of ''in-in'' correlators, as is needed in cosmology and other nonequilibrium problems. These rules are both intuitive, and efficient for calculational purposes.
Lucio Rapoport, Diego
2013-04-01
We present a unified principle for science that surmounts dualism, in terms of torsion fields and the non-orientable surfaces, notably the Klein Bottle and its logic, the Möbius strip and the projective plane. We apply it to the complex numbers and cosmology, to non-linear systems integrating the issue of hyperbolic divergences with the change of orientability, to the biomechanics of vision and the mammal heart, to the morphogenesis of crustal shapes on Earth in connection to the wavefronts of gravitation, elasticity and electromagnetism, to pattern recognition of artificial images and visual recognition, to neurology and the topographic maps of the sensorium, to perception, in particular of music. We develop it in terms of the fundamental 2:1 resonance inherent to the Möbius strip and the Klein Bottle, the minimal surfaces representation of the wavefronts, and the non-dual Klein Bottle logic inherent to pattern recognition, to the harmonic functions and vector fields that lay at the basis of geophysics and physics at large. We discuss the relation between the topographic maps of the sensorium, and the issue of turning inside-out of the visual world as a general principle for cognition, topological chemistry, cell biology and biological morphogenesis in particular in embryology
Mirus, Kevin Andrew
In this thesis, the possibility of controlling low- and high-dimensional chaotic systems by periodically driving an accessible system parameter is examined. This method has been carried out on several numerical systems and the MST Reversed Field Pinch. The numerical systems investigated include the logistic equation, the Lorenz equations, the Rossler equations, a coupled lattice of logistic equations, a coupled lattice of Lorenz equations, the Yoshida equations, which model tearing mode fluctuations in a plasma, and a neural net model for magnetic fluctuations on MST. This method was tested on the MST by sinusoidally driving a magnetic flux through the toroidal gap of the device. Numerically, periodic drives were found to be most effective at producing limit cycle behavior or significantly reducing the dimension of the system when the perturbation frequency was near natural frequencies of unstable periodic orbits embedded in the attractor of the unperturbed system. Several different unstable periodic orbits have been stabilized in this way for the low-dimensional numerical systems, sometimes with perturbation amplitudes that were less than 5% of the nominal value of the parameter being perturbed. In high- dimensional systems, limit cycle behavior and significant decreases in the system dimension were also achieved using perturbations with frequencies near the natural unstable periodic orbit frequencies. Results for the MST were not this encouraging, most likely because of an insufficient drive amplitude, the extremely high dimension of the plasma behavior, large amounts of noise, and a lack of stationarity in the transient plasma pulses.
Institute of Scientific and Technical Information of China (English)
鲁世平
2003-01-01
By employing the theory of differential inequality and some analysis methods, a nonlinear boundary value problem subject to a general kind of second-order Volterra functional differential equation was considered first. Then, by constructing the right-side layer function and the outer solution, a nonlinear boundary value problem subject to a kind of second- order Volterra functional differential equation with a small parameter was studied further. By using the differential mean value theorem and the technique of upper and lower solution, a new result on the existence of the solutions to the boundary value problem is obtained, and a uniformly valid asymptotic expansions of the solution is given as well.
Propagation of Weakly Guided Waves in a Kerr Nonlinear Medium using a Perturbation Approach
Energy Technology Data Exchange (ETDEWEB)
Dacles-Mariani, J; Rodrigue, G
2004-10-06
The equations are represented in a simplified format with only a few leading terms needed in the expansion. The set of equations are then solved numerically using vector finite element method. To validate the algorithm, they analyzed a two-dimensional rectangular waveguide consisting of a linear core and nonlinear identical cladding. The exact nonlinear solutions for three different modes of propagations, TE0, TE1, and TE2 modes are generated and compared with the computed solutions. Next, they investigate the effect of a more intense monochromatic field on the propagation of a 'weak' optical field in a fully three-dimensional cylindrical waveguide.
Directory of Open Access Journals (Sweden)
Teffera M. Asfaw
2016-01-01
Full Text Available Let X be a real reflexive locally uniformly convex Banach space with locally uniformly convex dual space X⁎. Let T:X⊇DT→2X⁎ be maximal monotone of type Γdϕ (i.e., there exist d≥0 and a nondecreasing function ϕ:0,∞→0,∞ with ϕ(0=0 such that 〈v⁎,x-y〉≥-dx-ϕy for all x∈DT, v⁎∈Tx, and y∈X,L:X⊃D(L→X⁎ be linear, surjective, and closed such that L-1:X⁎→X is compact, and C:X→X⁎ be a bounded demicontinuous operator. A new degree theory is developed for operators of the type L+T+C. The surjectivity of L can be omitted provided that RL is closed, L is densely defined and self-adjoint, and X=H, a real Hilbert space. The theory improves the degree theory of Berkovits and Mustonen for L+C, where C is bounded demicontinuous pseudomonotone. New existence theorems are provided. In the case when L is monotone, a maximality result is included for L and L+T. The theory is applied to prove existence of weak solutions in X=L20,T;H01Ω of the nonlinear equation given by ∂u/∂t-∑i=1N(∂/∂xiAix,u,∇u+Hλx,u,∇u=fx,t, x,t∈QT; ux,t=0, x,t∈∂QT; and ux,0=ux,T, x∈Ω, where λ>0, QT=Ω×0,T, ∂QT=∂Ω×0,T, Aix,u,∇u=∂/∂xiρx,u,∇u+aix,u,∇u (i=1,2,…,N, Hλx,u,∇u=-λΔu+gx,u,∇u, Ω is a nonempty, bounded, and open subset of RN with smooth boundary, and ρ,ai,g:Ω¯×R×RN→R satisfy suitable growth conditions. In addition, a new existence result is given concerning existence of weak solutions for nonlinear wave equation with nonmonotone nonlinearity.
Cosmology and the Korteweg-de Vries Equation
Lidsey, James E
2012-01-01
The Korteweg-de Vries (KdV) equation is a non-linear wave equation that has played a fundamental role in diverse branches of mathematical and theoretical physics. In the present paper, we consider its significance to cosmology. It is found that the KdV equation arises in a number of important scenarios, including inflationary cosmology, the cyclic universe, loop quantum cosmology and braneworld models. Analogies can be drawn between cosmic dynamics and the propagation of the solitonic wave solution to the equation, whereby quantities such as the speed and amplitude profile of the wave can be identified with cosmological parameters such as the spectral index of the density perturbation spectrum and the energy density of the universe. The unique mathematical properties of the Schwarzian derivative operator are important to the analysis. A connection with dark solitons in Bose-Einstein condensates is briefly discussed.
Nonlinear Phenomena and Resonant Parametric Perturbation Control in QR-ZCS Buck DC-DC Converters
Hsieh, Fei-Hu; Liu, Feng-Shao; Hsieh, Hui-Chang
The purpose of this study is to investigate the chaotic phenomena and to control in current-mode controlled quasi-resonant zero-current-switching (QR-ZCS) DC-DC buck converters, and to present control of chaos by resonant parametric perturbation control methods. First of all, MATLAB/SIMULINK is used to derive a mathematical model for QR-ZCS DC-DC buck converters, and to simulate the converters to observe the waveform of output voltages, inductance currents and phase-plane portraits from the period-doubling bifurcation to chaos by changing the load resistances. Secondly, using resonant parametric perturbation control in QR-ZCS buck DC-DC converters, the simulation results of the chaotic converter form chaos state turn into stable state period 1, and improve ripple amplitudes of converters under the chaos, to verify the validity of the proposes method.
Nonlinear perturbations of systems of partial differential equations with constant coefficients
Directory of Open Access Journals (Sweden)
Carmen J. Vanegas
2000-01-01
Full Text Available In this article, we show the existence of solutions to boundary-value problems, consisting of nonlinear systems of partial differential equations with constant coefficients. For this purpose, we use the right inverse of an associated operator and a fix point argument. As illustrations, we apply this method to Helmholtz equations and to second order systems of elliptic equations.
Energy Technology Data Exchange (ETDEWEB)
Doroshkevich, A.G.; Zel' dovich, Y.B.; Syunyaev, R.A.; Khlopov, M.Y.
1980-07-01
A discussion is given of the influence that a finite rest mass for the neutrino would have on the phenomenon of ''missing mass'' in galaxies and clusters of galaxies, on the nonlinear stage in the evolution of primordial irregularities, and on the problem of observing neutral hydrogen in the spectrum of distant quasars.
Institute of Scientific and Technical Information of China (English)
CHENGYan
2003-01-01
In this paper,the fixed-point theorem is used to estimated an asymptotic solution of intial val-ue problems for a class of third nonlinear differential equations which has double initial-layer properties.We obtain the uniformly valid asymptotic expansion of any orders including boundary layers.
A Bohmian approach to the perturbations of non-linear Klein--Gordon equation
Indian Academy of Sciences (India)
FARAMARZ RAHMANI; MEHDI GOLSHANI; MOHSEN SARBISHEI
2016-08-01
In the framework of Bohmian quantum mechanics, the Klein--Gordon equation can be seen as representing a particle with mass m which is guided by a guiding wave $\\phi(x)$ in a causal manner. Here a relevant question is whether Bohmian quantum mechanics is applicable to a non-linear Klein--Gordon equation? We examine this approach for $\\phi_{4}(x)$ and sine-Gordon potentials. It turns out that this method leads to equations for quantum states which are identical to those derived by field theoretical methods used for quantum solitons. Moreover, the quantum force exerted on the particle can be determined. This method can be used for other non-linear potentials as well.
Short-lived two-soliton bound states in weakly perturbed nonlinear Schrodinger equation.
Dmitriev, Sergey V.; Shigenari, Takeshi
2002-06-01
Resonant soliton collisions in the weakly discrete nonlinear Schrodinger equation are studied numerically. The fractal nature of the soliton scattering, described in our previous works, is investigated in detail. We demonstrate that the fractal scattering pattern is related to the existence of the short-lived two-soliton bound states. The bound state can be regarded as a two-soliton quasiparticle of a new type, different from the breather. We establish that the probability P of a bound state with the lifetime L follows the law P approximately L(-3). In the frame of a simple two-particle model, we derive the nonlinear map, which generates the fractal pattern similar to that observed in the numerical study of soliton collisions. (c) 2002 American Institute of Physics.
2010-07-01
Henson, M. 1998. "Nonlinear model predictive control: current status and future directions." Computers and Chemical Engineering , 23: 187-202. Ikhouane...Eichhorn2, Ralph Smith3 1Florida Center for Advanced Aero Propulsion (FCAAP), Department of Mechanical Engineering , Florida State University...collected using (AE Techron 7780 linear amplifier, DS1003 dSpace processor board, Matlab V5.2/ Simulink V2.2.1, Schaevitz 025MHR LVDT). The experimental
Kehagias, Alex
2016-01-01
Symmetries play an interesting role in cosmology. They are useful in characterizing the cosmological perturbations generated during inflation and lead to consistency relations involving the soft limit of the statistical correlators of large-scale structure dark matter and galaxies overdensities. On the other hand, in observational cosmology the carriers of the information about these large-scale statistical distributions are light rays traveling on null geodesics. Motivated by this simple consideration, we study the structure of null infinity and the associated BMS symmetry in a cosmological setting. For decelerating Friedmann-Robertson-Walker backgrounds, for which future null infinity exists, we find that the BMS transformations which leaves the asymptotic metric invariant to leading order. Contrary to the asymptotic flat case, the BMS transformations in cosmology generate Goldstone modes corresponding to both scalar and tensor degrees of freedom which may exist at null infinity and perturb the asymptotic d...
Directory of Open Access Journals (Sweden)
Ching-Hung Lee
2011-01-01
Full Text Available This paper proposes a new type fuzzy neural systems, denoted IT2RFNS-A (interval type-2 recurrent fuzzy neural system with asymmetric membership function, for nonlinear systems identification and control. To enhance the performance and approximation ability, the triangular asymmetric fuzzy membership function (AFMF and TSK-type consequent part are adopted for IT2RFNS-A. The gradient information of the IT2RFNS-A is not easy to obtain due to the asymmetric membership functions and interval valued sets. The corresponding stable learning is derived by simultaneous perturbation stochastic approximation (SPSA algorithm which guarantees the convergence and stability of the closed-loop systems. Simulation and comparison results for the chaotic system identification and the control of Chua's chaotic circuit are shown to illustrate the feasibility and effectiveness of the proposed method.
Directory of Open Access Journals (Sweden)
Zhaohui Chen
2013-01-01
Full Text Available The delay-dependent exponential L2-L∞ performance analysis and filter design are investigated for stochastic systems with mixed delays and nonlinear perturbations. Based on the delay partitioning and integral partitioning technique, an improved delay-dependent sufficient condition for the existence of the L2-L∞ filter is established, by choosing an appropriate Lyapunov-Krasovskii functional and constructing a new integral inequality. The full-order filter design approaches are obtained in terms of linear matrix inequalities (LMIs. By solving the LMIs and using matrix decomposition, the desired filter gains can be obtained, which ensure that the filter error system is exponentially stable with a prescribed L2-L∞ performance γ. Numerical examples are provided to illustrate the effectiveness and significant improvement of the proposed method.
Directory of Open Access Journals (Sweden)
Hamid Reza Karimi
2009-01-01
Full Text Available The problem of stability analysis for a class of neutral systems with mixed time-varying neutral, discrete and distributed delays and nonlinear parameter perturbations is addressed. By introducing a novel Lyapunov-Krasovskii functional and combining the descriptor model transformation, the Leibniz-Newton formula, some free-weighting matrices, and a suitable change of variables, new sufficient conditions are established for the stability of the considered system, which are neutral-delay-dependent, discrete-delay-range-dependent, and distributed-delay-dependent. The conditions are presented in terms of linear matrix inequalities (LMIs and can be efficiently solved using convex programming techniques. Two numerical examples are given to illustrate the efficiency of the proposed method.
Wang, Qiang; Mu, Mu; Dijkstra, Henk A.
2012-01-01
A reduced-gravity barotropic shallow-water model was used to simulate the Kuroshio path variations. The results show that the model was able to capture the essential features of these path variations. We used one simulation of the model as the reference state and investigated the effects of errors in model parameters on the prediction of the transition to the Kuroshio large meander (KLM) state using the conditional nonlinear optimal parameter perturbation (CNOP-P) method. Because of their relatively large uncertainties, three model parameters were considered: the interfacial friction coefficient, the wind-stress amplitude, and the lateral friction coefficient. We determined the CNOP-Ps optimized for each of these three parameters independently, and we optimized all three parameters simultaneously using the Spectral Projected Gradient 2 (SPG2) algorithm. Similarly, the impacts caused by errors in initial conditions were examined using the conditional nonlinear optimal initial perturbation (CNOP-I) method. Both the CNOP-I and CNOP-Ps can result in significant prediction errors of the KLM over a lead time of 240 days. But the prediction error caused by CNOP-I is greater than that caused by CNOP-P. The results of this study indicate not only that initial condition errors have greater effects on the prediction of the KLM than errors in model parameters but also that the latter cannot be ignored. Hence, to enhance the forecast skill of the KLM in this model, the initial conditions should first be improved, the model parameters should use the best possible estimates.
Institute of Scientific and Technical Information of China (English)
WANG Qiang; MU Mu; Henk A. DIJKSTRA
2012-01-01
A reduced-gravity barotropic shallow-water model was used to simulate the Kuroshio path variations.The results show that the model was able to capture the essential features of these path variations.We used one simulation of the model as the reference state and investigated the effects of errors in model parameters on the prediction of the transition to the Kuroshio large meander (KLM) state using the conditional nonlinear optimal parameter perturbation (CNOP-P) method.Because of their relatively large uncertainties,three model parameters were considcred:the interfacial friction coefficient,the wind-stress amplitude,and the lateral friction coefficient.We determined the CNOP-Ps optimized for each of these three parameters independently,and we optimized all three parameters simultaneously using the Spectral Projected Gradient 2 (SPG2) algorithm.Similarly,the impacts caused by errors in initial conditions were examined using the conditional nonlinear optimal initial perturbation (CNOP-I) method.Both the CNOP-I and CNOP-Ps can result in significant prediction errors of the KLM over a lead time of 240 days.But the prediction error caused by CNOP-I is greater than that caused by CNOP-P.The results of this study indicate not only that initial condition errors have greater effects on the prediction of the KLM than errors in model parameters but also that the latter cannot be ignored.Hence,to enhance the forecast skill of the KLM in this model,the initial conditions should first be improved,the model parameters should use the best possible estimates.
Bartelmann, Matthias; Berg, Daniel; Kozlikin, Elena; Lilow, Robert; Viermann, Celia
2014-01-01
We use the non-equlibrium statistical field theory for classical particles, recently developed by Mazenko and Das and Mazenko, together with the free generating functional we have previously derived for point sets initially correlated in phase space, to calculate the time evolution of power spectra in the free theory, i.e. neglecting particle interactions. We provide expressions taking linear and quadratic momentum correlations into account. Up to this point, the expressions are general with respect to the free propagator of the microscopic degrees of freedom. We then specialise the propagator to that expected for particles in cosmology treated within the Zel'dovich approximation and show that, to linear order in the momentum correlations, the linear growth of the cosmological power spectrum is reproduced. Quadratic momentum correlations return a first contribution to the non-linear evolution of the power spectrum, for which we derive a simple closed expression valid for arbitrary wave numbers. This expressio...
Nishimichi, Takahiro; Nakamichi, Masashi; Taruya, Atsushi; Yahata, Kazuhiro; Shirata, Akihito; Saito, Shun; Nomura, Hidenori; Yamamoto, Kazuhiro; Suto, Yasushi
2007-01-01
An acoustic oscillation of the primeval photon-baryon fluid around the decoupling time imprints a characteristic scale in the galaxy distribution today, known as the baryon acoustic oscillation (BAO) scale. Several on-going and/or future galaxy surveys aim at detecting and precisely determining the BAO scale so as to trace the expansion history of the universe. We consider nonlinear and redshift-space distortion effects on the shifts of the BAO scale in $k$-space using perturbation theory. The resulting shifts are indeed sensitive to different choices of the definition of the BAO scale, which needs to be kept in mind in the data analysis. We present a toy model to explain the physical behavior of the shifts. We find that the BAO scale defined as in Percival et al. (2007) indeed shows very small shifts ($\\lesssim$ 1%) relative to the prediction in {\\it linear theory} in real space. The shifts can be predicted accurately for scales where the perturbation theory is reliable.
Ardema, M. D.
1979-01-01
Singular perturbation techniques are studied for dealing with singular arc problems by analyzing a relatively low-order but otherwise general system. This system encompasses many flight mechanic problems including Goddard's problem and a version of the minimum time-to-climb problem. Boundary layer solutions are constructed which are stable and reach the outer solution in a finite time. A uniformly valid composite solution is then formed from the reduced and boundary layer solutions. The value of the approximate solution is that it is relatively easy to obtain and does not involve singular arcs. To illustrate the utility of the results, the technique is used to obtain an approximate solution of a simplified version of the aircraft minimum time-to-climb problem.
Energy Technology Data Exchange (ETDEWEB)
Nishimura, Seiya, E-mail: n-seiya@kobe-kosen.ac.jp [Kobe City College of Technology, Kobe, Hyogo 651-2194 (Japan)
2014-12-15
Resonant magnetic perturbations (RMPs) produce magnetic islands in toroidal plasmas. Self-healing (annihilation) of RMP-induced magnetic islands has been observed in helical systems, where a possible mechanism of the self-healing is shielding of RMP penetration by plasma flows, which is well known in tokamaks. Thus, fundamental physics of RMP shielding is commonly investigated in both tokamaks and helical systems. In order to check this mechanism, detailed informations of magnetic island phases are necessary. In experiments, measurement of radial magnetic responses is relatively easy. In this study, based on a theoretical model of rotating magnetic islands, behavior of radial magnetic fields during the self-healing is investigated. It is confirmed that flips of radial magnetic fields are typically observed during the self-healing. Such behavior of radial magnetic responses is also observed in LHD experiments.
NONLINEAR COMPLEX DYNAMIC PHENOMENA OF THE PERTURBED METALLIC BAR CONSIDERING DISSIPATING EFFECT
Institute of Scientific and Technical Information of China (English)
ZHAO Guang-hui; ZHANG Nian-mei; YANG Gui-tong
2005-01-01
Considering Peierls-Nabarro effect, one-dimensional finite metallic bar subjected with periodic field was researched under Neumann boundary condition. Dynamics of this system was described with displacement by perturbed sine-Gordon type equation.Finite difference scheme with fourth-order central differences in space and second-order central differences in time was used to simulate dynamic responses of this system. For the metallic bar with specified sizes and physical features, effect of amplitude of external driving on dynamic behavior of the bar was investigated under initial "breather" condition. Four kinds of typical dynamic behaviors are shown: x-independent simple harmonic motion;harmonic motion with single wave; quasi-periodic motion with single wave; temporal determine dynamic features.
Weakly nonlinear dynamics and the σ{sub 8} parameter
Energy Technology Data Exchange (ETDEWEB)
Juszkiewicz, Roman [Department of Physics and Astronomy, Zielona Góra University, Lubuska 2, 65-265 Zielona Góra (Poland); Feldman, Hume A. [Department of Physics and Astronomy, University of Kansas, Lawrence KS 66045 (United States); Fry, J.N. [Department of Physics, University of Florida, Gainesville FL 32611-8440 (United States); Jaffe, Andrew H., E-mail: roman@camk.edu.pl, E-mail: feldman@ku.edu, E-mail: fry@phys.ufl.edu, E-mail: a.jaffe@imperial.ac.uk [Astrophysics, Blackett Laboratory, Imperial College, London SW7 2AZ (United Kingdom)
2010-02-01
The amplitude of cosmological density fluctuations, σ{sub 8}, has been studied and estimated by analysing many cosmological observations. The values of the estimates vary considerably between the various probes. However, different estimators probe the value of σ{sub 8} in different cosmological scales and do not take into account the nonlinear evolution of the parameter at late times. We show that estimates of the amplitude of cosmological density fluctuations derived from cosmic flows are systematically higher than those inferred at early epochs from the CMB because of nonlinear evolution at later times. We discuss the past and future evolution of linear and nonlinear perturbations, derive corrections to the value of σ{sub 8} and compare amplitudes after accounting for these differences.
Fabris, J C; Rodrigues, D C; Batista, C E M; Daouda, M H
2012-01-01
We review the difficulties of the generalized Chaplygin gas model to fit observational data, due to the tension between background and perturbative tests. We argue that such issues may be circumvented by means of a self-interacting scalar field representation of the model. However, this proposal seems to be successful only if the self-interacting scalar field has a non-canonical form. The latter can be implemented in Rastall's theory of gravity, which is based on a modification of the usual matter conservation law. We show that, besides its application to the generalized Chaplygin gas model, other cosmological models based on Rastall's theory have many interesting and unexpected new features.
Institute of Scientific and Technical Information of China (English)
莫嘉琪
2006-01-01
A class of nonlinear nonlocal singularly perturbed Robin initial boundary value problems for reaction diffusion equations with boundary perturbation is considered. Under suitable conditions, firstly, the outer solution of the original problem is obtained; secondly, by using the stretched variable, the composing expansion method and the expanding theory of power series, the initial layer is constructed; and finally,by using the theory of differential inequalities the asymptotic behavior of solutions for initial boundary value problems is studied, and including some relational inequalities the existence and uniqueness of solutions for the original problem and the uniformly valid asymptotic estimation are discussed.
Post-Newtonian cosmological models
Sanghai, Viraj A A
2015-01-01
We construct a framework to probe the effect of non-linear structure formation on the large-scale expansion of the universe. We take a bottom-up approach to cosmological modelling by splitting our universe into cells. The matter content within each cell is described by the post-Newtonian formalism. We assume that most of the cell is in the vicinity of weak gravitational fields, so that it can be described using a perturbed Minkowski metric. Our cells are patched together using the Israel junction conditions. We impose reflection symmetry across the boundary of these cells. This allows us to calculate the equation of motion for the boundary of the cell and, hence, the expansion rate of the universe. At Newtonian order, we recover the standard Friedmann-like equations. At post-Newtonian orders, we obtain a correction to the large-scale expansion of the universe. Our framework does not depend on the process of averaging in cosmology. As an example, we use this framework to investigate the cosmological evolution ...
Impact of resonant magnetic perturbations on nonlinearly driven modes in drift-wave turbulence
Energy Technology Data Exchange (ETDEWEB)
Leconte, M. [WCI Center for Fusion Theory, NFRI (Korea, Republic of); Diamond, P. H. [WCI Center for Fusion Theory, NFRI (Korea, Republic of); CMTFO and CASS, UCSD, California 92093 (United States)
2012-05-15
In this work, we study the effects of resonant magnetic perturbations (RMPs) on turbulence, flows, and confinement in the framework of resistive drift wave turbulence. We extend the Hasegawa-Wakatani model to include RMP fields. The effect of the RMPs is to induce a linear coupling between the zonal electric field and the zonal density gradient, which drives the system to a state of electron radial force balance for large ({delta}B{sub r}/B{sub 0}). Both the vorticity flux (Reynolds stress) and particle flux are modulated. We derive an extended predator prey model which couples zonal potential and density dynamics to the evolution of turbulence intensity. This model has both turbulence drive and RMP amplitude as control parameters and predicts a novel type of transport bifurcation in the presence of RMPs. We find states that are similar to the ZF-dominated state of the standard predator-prey model, but for which the power threshold is now a function of the RMP strength. For small RMP amplitude, the energy of zonal flows decreases and the turbulence energy increases with ({delta}B{sub r}/B{sub 0}), corresponding to a damping of zonal flows.
Institute of Scientific and Technical Information of China (English)
牛晓花; 潘祖梁
2006-01-01
A new method based on Lie-B(a)cklund symmetry method to solve the perturbed nonlinear evolution equations is presented. New approximate solutions of perturbed nonlinear evolution equations stemming from the exact solutions of unperturbed equations are obtained.This method is a generalization of Burde's Lie point symmetry technique.
Brax, Philippe
2016-01-01
We investigate scalar-tensor theories where matter couples to the scalar field via a kinetically dependent conformal coupling. These models can be seen as the low-energy description of invariant field theories under a global Abelian symmetry. The scalar field is then identified with the Goldstone mode of the broken symmetry. It turns out that the properties of these models are very similar to the ones of ultralocal theories where the scalar-field value is directly determined by the local matter density. This leads to a complete screening of the fifth force in the Solar System and between compact objects, through the ultralocal screening mechanism. On the other hand, the fifth force can have large effects in extended structures with large-scale density gradients, such as galactic halos. Interestingly, it can either amplify or damp Newtonian gravity, depending on the model parameters. We also study the background cosmology and the linear cosmological perturbations. The background cosmology is hardly different f...
Solomon, Adam R
2015-01-01
The accelerating expansion of the Universe poses a major challenge to our understanding of fundamental physics. One promising avenue is to modify general relativity and obtain a new description of the gravitational force. Because gravitation dominates the other forces mostly on large scales, cosmological probes provide an ideal testing ground for theories of gravity. In this thesis, we describe two complementary approaches to the problem of testing gravity using cosmology. In the first part, we discuss the cosmological solutions of massive gravity and its generalisation to a bimetric theory. These theories describe a graviton with a small mass, and can potentially explain the late-time acceleration in a technically-natural way. We describe these self-accelerating solutions and investigate the cosmological perturbations in depth, beginning with an investigation of their linear stability, followed by the construction of a method for solving these perturbations in the quasistatic limit. This allows the predictio...
Testing loop quantum cosmology
Wilson-Ewing, Edward
2017-03-01
Loop quantum cosmology predicts that quantum gravity effects resolve the big-bang singularity and replace it by a cosmic bounce. Furthermore, loop quantum cosmology can also modify the form of primordial cosmological perturbations, for example by reducing power at large scales in inflationary models or by suppressing the tensor-to-scalar ratio in the matter bounce scenario; these two effects are potential observational tests for loop quantum cosmology. In this article, I review these predictions and others, and also briefly discuss three open problems in loop quantum cosmology: its relation to loop quantum gravity, the trans-Planckian problem, and a possible transition from a Lorentzian to a Euclidean space-time around the bounce point.
Scalar and vector perturbations in a universe with discrete and continuous matter sources
Eingorn, Maxim; Zhuk, Alexander
2016-01-01
We study a universe filled with dust-like matter in the form of discrete inhomogeneities (e.g., galaxies and their groups and clusters) and two sets of perfect fluids with linear and nonlinear equations of state, respectively. The background spacetime geometry is defined by the FLRW metric. In the weak gravitational field limit, we develop the first-order scalar and vector cosmological perturbation theory. Our approach works at all cosmological scales (i.e. sub-horizon and super-horizon ones) and incorporates linear and nonlinear effects with respect to energy density fluctuations. We demonstrate that the scalar perturbation (i.e. the gravitational potential) as well as the vector perturbation can be split into individual contributions from each matter source. Each of these contributions satisfies its own equation. The velocity-independent parts of the individual gravitational potentials are characterized by a finite time-dependent Yukawa interaction range being the same for each individual contribution. We a...
Marsh, David J. E.
2016-07-01
Axions comprise a broad class of particles that can play a major role in explaining the unknown aspects of cosmology. They are also well-motivated within high energy physics, appearing in theories related to CP-violation in the standard model, supersymmetric theories, and theories with extra-dimensions, including string theory, and so axion cosmology offers us a unique view onto these theories. I review the motivation and models for axions in particle physics and string theory. I then present a comprehensive and pedagogical view on the cosmology and astrophysics of axion-like particles, starting from inflation and progressing via BBN, the CMB, reionization and structure formation, up to the present-day Universe. Topics covered include: axion dark matter (DM); direct and indirect detection of axions, reviewing existing and future experiments; axions as dark radiation; axions and the cosmological constant problem; decays of heavy axions; axions and stellar astrophysics; black hole superradiance; axions and astrophysical magnetic fields; axion inflation, and axion DM as an indirect probe of inflation. A major focus is on the population of ultralight axions created via vacuum realignment, and its role as a DM candidate with distinctive phenomenology. Cosmological observations place robust constraints on the axion mass and relic density in this scenario, and I review where such constraints come from. I next cover aspects of galaxy formation with axion DM, and ways this can be used to further search for evidence of axions. An absolute lower bound on DM particle mass is established. It is ma > 10-24eV from linear observables, extending to ma ≳ 10-22eV from non-linear observables, and has the potential to reach ma ≳ 10-18eV in the future. These bounds are weaker if the axion is not all of the DM, giving rise to limits on the relic density at low mass. This leads to the exciting possibility that the effects of axion DM on structure formation could one day be detected
Variable speed of light cosmology, primordial fluctuations and gravitational waves
Energy Technology Data Exchange (ETDEWEB)
Moffat, J.W. [Perimeter Institute for Theoretical Physics, Waterloo, Ontario (Canada); University of Waterloo, Department of Physics and Astronomy, Waterloo, Ontario (Canada)
2016-03-15
A variable speed of light (VSL) cosmology is described in which the causal mechanism of generating primordial perturbations is achieved by varying the speed of light in a primordial epoch. This yields an alternative to inflation for explaining the formation of the cosmic microwave background (CMB) and the large scale structure (LSS) of the universe. The initial value horizon and flatness problems in cosmology are solved. The model predicts primordial scalar and tensor fluctuation spectral indices n{sub s} = 0.96 and n{sub t} = - 0.04, respectively. We make use of the δN formalism to identify signatures of primordial nonlinear fluctuations, and this allows the VSL model to be distinguished from inflationary models. In particular, we find that the parameter f{sub NL} = 5 in the variable speed of light cosmology. The value of the parameter g{sub NL} evolves during the primordial era and shows a running behavior. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Kehagias, A. [Physics Division, National Technical University of Athens, 15780 Zografou Campus, Athens (Greece); Riotto, A. [Department of Theoretical Physics,24 quai E. Ansermet, CH-1211 Geneva 4 (Switzerland); Center for Astroparticle Physics (CAP),24 quai E. Ansermet, CH-1211 Geneva 4 (Switzerland)
2016-05-25
Symmetries play an interesting role in cosmology. They are useful in characterizing the cosmological perturbations generated during inflation and lead to consistency relations involving the soft limit of the statistical correlators of large-scale structure dark matter and galaxies overdensities. On the other hand, in observational cosmology the carriers of the information about these large-scale statistical distributions are light rays traveling on null geodesics. Motivated by this simple consideration, we study the structure of null infinity and the associated BMS symmetry in a cosmological setting. For decelerating Friedmann-Robertson-Walker backgrounds, for which future null infinity exists, we find that the BMS transformations which leaves the asymptotic metric invariant to leading order. Contrary to the asymptotic flat case, the BMS transformations in cosmology generate Goldstone modes corresponding to scalar, vector and tensor degrees of freedom which may exist at null infinity and perturb the asymptotic data. Therefore, BMS transformations generate physically inequivalent vacua as they populate the universe at null infinity with these physical degrees of freedom. We also discuss the gravitational memory effect when cosmological expansion is taken into account. In this case, there are extra contribution to the gravitational memory due to the tail of the retarded Green functions which are supported not only on the light-cone, but also in its interior. The gravitational memory effect can be understood also from an asymptotic point of view as a transition among cosmological BMS-related vacua.
Kehagias, A.; Riotto, A.
2016-05-01
Symmetries play an interesting role in cosmology. They are useful in characterizing the cosmological perturbations generated during inflation and lead to consistency relations involving the soft limit of the statistical correlators of large-scale structure dark matter and galaxies overdensities. On the other hand, in observational cosmology the carriers of the information about these large-scale statistical distributions are light rays traveling on null geodesics. Motivated by this simple consideration, we study the structure of null infinity and the associated BMS symmetry in a cosmological setting. For decelerating Friedmann-Robertson-Walker backgrounds, for which future null infinity exists, we find that the BMS transformations which leaves the asymptotic metric invariant to leading order. Contrary to the asymptotic flat case, the BMS transformations in cosmology generate Goldstone modes corresponding to scalar, vector and tensor degrees of freedom which may exist at null infinity and perturb the asymptotic data. Therefore, BMS transformations generate physically inequivalent vacua as they populate the universe at null infinity with these physical degrees of freedom. We also discuss the gravitational memory effect when cosmological expansion is taken into account. In this case, there are extra contribution to the gravitational memory due to the tail of the retarded Green functions which are supported not only on the light-cone, but also in its interior. The gravitational memory effect can be understood also from an asymptotic point of view as a transition among cosmological BMS-related vacua.
Feng, Jie; Ding, Ruiqiang; Li, Jianping; Liu, Deqiang
2016-09-01
The breeding method has been widely used to generate ensemble perturbations in ensemble forecasting due to its simple concept and low computational cost. This method produces the fastest growing perturbation modes to catch the growing components in analysis errors. However, the bred vectors (BVs) are evolved on the same dynamical flow, which may increase the dependence of perturbations. In contrast, the nonlinear local Lyapunov vector (NLLV) scheme generates flow-dependent perturbations as in the breeding method, but regularly conducts the Gram-Schmidt reorthonormalization processes on the perturbations. The resulting NLLVs span the fast-growing perturbation subspace efficiently, and thus may grasp more components in analysis errors than the BVs. In this paper, the NLLVs are employed to generate initial ensemble perturbations in a barotropic quasi-geostrophic model. The performances of the ensemble forecasts of the NLLV method are systematically compared to those of the random perturbation (RP) technique, and the BV method, as well as its improved version—the ensemble transform Kalman filter (ETKF) method. The results demonstrate that the RP technique has the worst performance in ensemble forecasts, which indicates the importance of a flow-dependent initialization scheme. The ensemble perturbation subspaces of the NLLV and ETKF methods are preliminarily shown to catch similar components of analysis errors, which exceed that of the BVs. However, the NLLV scheme demonstrates slightly higher ensemble forecast skill than the ETKF scheme. In addition, the NLLV scheme involves a significantly simpler algorithm and less computation time than the ETKF method, and both demonstrate better ensemble forecast skill than the BV scheme.
Institute of Scientific and Technical Information of China (English)
朱卫平; 黄黔
2002-01-01
In order to analyze bellows effectively and practically, the finite-element-displacement-perturbation method (FEDPM) is proposed for the geometric nonlinearbehaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes. The formulations are mainly based upon the idea of perturba-tion that the nodal displacement vector and the nodal force vector of each finite elementare expanded by taking root-mean-square value of circumferential strains of the shells as aperturbation parameter. The load steps and the iteration times are not cs arbitrary andunpredictable as in usual nonlinear analysis. Instead, there are certain relations betweenthe load steps and the displacement increments, and no need of iteration for each loadstep. Besides, in the formulations, the shell is idealized into a series of conical frusta for the convenience of practice, Sander' s nonlinear geometric equations of moderate smallrotation are used, and the shell made of more than one material ply is also considered.
On the cosmology of massive gravity
De Felice, Antonio; Lin, Chunshan; Mukohyama, Shinji
2013-01-01
We present a review of cosmological solutions in non-linear massive gravity, focusing on the stability of perturbations. Although homogeneous and isotropic solutions have been found, these are now known to suffer from either Higuchi ghost or a new non-linear ghost instability. We discuss two approaches to alleviate this issue. By relaxing the symmetry of the background by e.g. breaking isotropy in the hidden sector, it is possible to accommodate a stable cosmological solution. Alternatively, extending the theory to allow for new dynamical degrees of freedom can also remove the conditions which lead to the instability. As examples for this case, we study the stability of self-accelerating solutions in the quasi-dilatonic extension and generic cosmological solutions in the varying mass extension. While the quasi-dilaton case turns out to be unstable, the varying mass case allows stable regimes of parameters. Viable self-accelerating solutions in the varying mass theory yet remain to be found.
Directory of Open Access Journals (Sweden)
Xudong Yin
2014-02-01
Full Text Available The authors propose to implement conditional non-linear optimal perturbation related to model parameters (CNOP-P through an ensemble-based approach. The approach was first used in our earlier study and is improved to be suitable for calculating CNOP-P. Idealised experiments using the Lorenz-63 model are conducted to evaluate the performance of the improved ensemble-based approach. The results show that the maximum prediction error after optimisation has been multiplied manifold compared with the initial-guess prediction error, and is extremely close to, or greater than, the maximum value of the exhaustive attack method (a million random samples. The calculation of CNOP-P by the ensemble-based approach is capable of maintaining a high accuracy over a long prediction time under different constraints and initial conditions. Further, the CNOP-P obtained by the approach is applied to sensitivity analysis of the Lorenz-63 model. The sensitivity analysis indicates that when the prediction time is set to 0.2 time units, the Lorenz-63 model becomes extremely insensitive to one parameter, which leaves the other two parameters to affect the uncertainty of the model. Finally, a serial of parameter estimation experiments are performed to verify sensitivity analysis. It is found that when the three parameters are estimated simultaneously, the insensitive parameter is estimated much worse, but the Lorenz-63 model can still generate a very good simulation thanks to the relatively accurate values of the other two parameters. When only two sensitive parameters are estimated simultaneously and the insensitive parameter is left to be non-optimised, the outcome is better than the case when the three parameters are estimated simultaneously. With the increase of prediction time and observation, however, the model sensitivity to the insensitive parameter increases accordingly and the insensitive parameter can also be estimated successfully.
Gonçalves, P. B.; Silva, F. M. A.; Del Prado, Z. J. G. N.
2008-08-01
In formulating mathematical models for dynamical systems, obtaining a high degree of qualitative correctness (i.e. predictive capability) may not be the only objective. The model must be useful for its intended application, and models of reduced complexity are attractive in many cases where time-consuming numerical procedures are required. This paper discusses the derivation of discrete low-dimensional models for the nonlinear vibration analysis of thin cylindrical shells. In order to understand the peculiarities inherent to this class of structural problems, the nonlinear vibrations and dynamic stability of a circular cylindrical shell subjected to static and dynamic loads are analyzed. This choice is based on the fact that cylindrical shells exhibit a highly nonlinear behavior under both static and dynamic loads. Geometric nonlinearities due to finite-amplitude shell motions are considered by using Donnell's nonlinear shallow-shell theory. A perturbation procedure, validated in previous studies, is used to derive a general expression for the nonlinear vibration modes and the discretized equations of motion are obtained by the Galerkin method using modal expansions for the displacements that satisfy all the relevant boundary and symmetry conditions. Next, the model is analyzed via the Karhunen-Loève expansion to investigate the relative importance of each mode obtained by the perturbation solution on the nonlinear response and total energy of the system. The responses of several low-dimensional models are compared. It is shown that rather low-dimensional but properly selected models can describe with good accuracy the response of the shell up to very large vibration amplitudes.
Ishikawa, Takashi; Nishimichi, Takahiro; Takahashi, Ryuichi; Yoshida, Naoki; Tonegawa, Motonari
2013-01-01
Redshift space distortion (RSD) observed in galaxy redshift surveys is a powerful tool to test gravity theories on cosmological scales, but the systematic uncertainties must carefully be examined for future surveys with large statistics. Here we employ various analytic models of RSD and estimate the systematic errors on measurements of the structure growth-rate parameter, f\\sigma_8, induced by non-linear effects and the halo bias with respect to the dark matter distribution, by using halo catalogues from 40 realisations of 3.4 \\times 10^8 comoving h^{-3}Mpc^3 cosmological N-body simulations. We consider hypothetical redshift surveys at redshifts z=0.5, 1.35 and 2, and different minimum halo mass thresholds in the range of 5.0 \\times 10^{11} -- 2.0 \\times 10^{13} h^{-1} M_\\odot. We find that the systematic error of f\\sigma_8 is greatly reduced to ~4 per cent level, when a recently proposed analytical formula of RSD that takes into account the higher-order coupling between the density and velocity fields is ado...
Ishikawa, Takashi; Totani, Tomonori; Nishimichi, Takahiro; Takahashi, Ryuichi; Yoshida, Naoki; Tonegawa, Motonari
2014-10-01
Redshift-space distortion (RSD) observed in galaxy redshift surveys is a powerful tool to test gravity theories on cosmological scales, but the systematic uncertainties must carefully be examined for future surveys with large statistics. Here we employ various analytic models of RSD and estimate the systematic errors on measurements of the structure growth-rate parameter, fσ8, induced by non-linear effects and the halo bias with respect to the dark matter distribution, by using halo catalogues from 40 realizations of 3.4 × 108 comoving h-3 Mpc3 cosmological N-body simulations. We consider hypothetical redshift surveys at redshifts z = 0.5, 1.35 and 2, and different minimum halo mass thresholds in the range of 5.0 × 1011-2.0 × 1013 h-1 M⊙. We find that the systematic error of fσ8 is greatly reduced to ˜5 per cent level, when a recently proposed analytical formula of RSD that takes into account the higher order coupling between the density and velocity fields is adopted, with a scale-dependent parametric bias model. Dependence of the systematic error on the halo mass, the redshift and the maximum wavenumber used in the analysis is discussed. We also find that the Wilson-Hilferty transformation is useful to improve the accuracy of likelihood analysis when only a small number of modes are available in power spectrum measurements.
Cosmological 3-point correlators from holography
McFadden, P.; Skenderis, K.
2011-01-01
We investigate the non-Gaussianity of primordial cosmological perturbations using holographic methods. In particular, we derive holographic formulae that relate all cosmological 3-point correlation functions, including both scalar and tensor perturbations, to stress-energy correlation functions of a
Institute of Scientific and Technical Information of China (English)
朱卫平; 黄黔
2002-01-01
The finite-element-displacement-perturbation method (FEDPM)for thegeometric nonlinear behaviors of shells of revolution subjected to pure bending moments orlateral forces in one of their meridional planes ( Ⅰ ) was employed to calculate the stressdistributions and the stiffness of the bellows. Firstly, by applying the first-orderperturbation solution ( the linear solution ) of the FEDPM to the bellows, the obtainedresults were compared with those of the general solution and the initial parameter integrationsolution proposed by the present authors earlier, as well as of the experiments and the FEAby others. It is shown that the FEDPM is with good precision and reliability, and as it waspointed out in ( Ⅰ ) the abrupt changes of the meridian curvature of bellows would not affectthe use of the usual straight element. Then the nonlinear behaviors of the bellows werediscussed. As expected, the nonlinear effects mainly come from the bellows ring plate, andthe wider the ring plate is, the stronger the nonlinear effects are. Contrarily, the vanishingof the ring plate, like the C-shaped bellows, the nonlinear effects almost vanish. Inaddition, when the pure bending moments act on the bellows, each convolution has thesame stress distributions calculated by the linear solution and other linear theories, but bythe present nonlinear solution they vary with respect to the convolutions of the bellows. Yetfor most bellows, the linear solutions are valid in practice.
Stornaiolo, C
2002-01-01
In this letter we propose the existence of low density black holes and discuss its compatibility with the cosmological observations. The origin of these black holes can be traced back to the collapse of long wavelength cosmological perturbations during the matter dominated era, when the densities are low enough to neglect any internal and thermal pressure. By introducing a threshold density $\\hat{\\rho}$ above which pressure and non-gravitational interactions become effective, we find the highest wavelength for the perturbations that can reach an equilibrium state instead of collapsing to a black hole. The low density black holes introduced here, if they exist, can be observed through weak and strong gravitational lensing effects. Finally we observe that we obtained here a cosmological model which is capable to explain in a qualitative way the void formation together with the value $\\Omega=1$. But we remark that it needs to be improved by considering non spherical symmetric black holes.
Gibbons, Gary W
2013-01-01
In this paper we lay down the foundations for a purely Newtonian theory of cosmology, valid at scales small compared with the Hubble radius, using only Newtonian point particles acted on by gravity and a possible cosmological term. We describe the cosmological background which is given by an exact solution of the equations of motion in which the particles expand homothetically with their comoving positions constituting a central configuration. We point out, using previous work, that an important class of central configurations are homogeneous and isotropic, thus justifying the usual assumptions of elementary treatments. The scale factor is shown to satisfy the standard Raychaudhuri and Friedmann equations without making any fluid dynamic or continuum approximations. Since we make no commitment as to the identity of the point particles, our results are valid for cold dark matter, galaxies, or clusters of galaxies. In future publications we plan to discuss perturbations of our cosmological background from the p...
Energy Technology Data Exchange (ETDEWEB)
Miles, A
2004-04-27
In core-collapse supernovae, strong blast waves drive interfaces susceptible to Rayleigh-Taylor (RT), Richtmyer-Meshkov (RM), and Kelvin-Helmholtz (KH) instabilities. In addition, perturbation growth can result from material expansion in large-scale velocity gradients behind the shock front. Laser-driven experiments are designed to produce a strongly shocked interface whose evolution is a scaled version of the unstable hydrogen-helium interface in core-collapse supernovae such as SN 1987A. The ultimate goal of this research is to develop an understanding of the effect of hydrodynamic instabilities and the resulting transition to turbulence on supernovae observables that remain as yet unexplained. In this dissertation, we present a computational study of unstable systems driven by high Mach number shock and blast waves. Using multi-physics radiation hydrodynamics codes and theoretical models, we consider the late nonlinear instability evolution of single mode, few mode, and multimode interfaces. We rely primarily on 2D calculations but present recent 3D results as well. For planar multimode systems, we show that compressibility effects preclude the emergence of a regime of self-similar instability growth independent of the initial conditions (IC's) by allowing for memory of the initial conditions to be retained in the mix-width at all times. The loss of transverse spectral information is demonstrated, however, along with the existence of a quasi-self-similar regime over short time intervals. Aspects of the IC's are shown to have a strong effect on the time to transition to the quasi-self-similar regime. With higher-dimensional blast waves, divergence restores the properties necessary for establishment of the self-similar state, but achieving it requires very high initial characteristic mode number and high Mach number for the incident blast wave. We point to recent stellar calculations that predict IC's we find incompatible with self-similarity, and
Energy Technology Data Exchange (ETDEWEB)
Miles, Aaron R. [Univ. of Maryland, College Park, MD (United States)
2004-01-01
In core-collapse supernovae, strong blast waves drive interfaces susceptible to Rayleigh-Taylor (RT), Richtmyer-Meshkov (RM), and Kelvin-Helmholtz (KH) instabilities. In addition, perturbation growth can result from material expansion in large-scale velocity gradients behind the shock front. Laser-driven experiments are designed to produce a strongly shocked interface whose evolution is a scaled version of the unstable hydrogen-helium interface in core-collapse supernovae such as SN 1987A. The ultimate goal of this research is to develop an understanding of the effect of hydrodynamic instabilities and the resulting transition to turbulence on supernovae observables that remain as yet unexplained. In this dissertation, we present a computational study of unstable systems driven by high Mach number shock and blast waves. Using multi-physics radiation hydrodynamics codes and theoretical models, we consider the late nonlinear instability evolution of single mode, few mode, and multimode interfaces. We rely primarily on 2D calculations but present recent 3D results as well. For planar multimode systems, we show that compressibility effects preclude the emergence of a regime of self-similar instability growth independent of the initial conditions (IC's) by allowing for memory of the initial conditions to be retained in the mix-width at all times. The loss of transverse spectral information is demonstrated, however, along with the existence of a quasi-self-similar regime over short time intervals. Aspects of the IC's are shown to have a strong effect on the time to transition to the quasi-self-similar regime. With higher-dimensional blast waves, divergence restores the properties necessary for establishment of the self-similar state, but achieving it requires very high initial characteristic mode number and high Mach number for the incident blast wave. We point to recent stellar calculations that predict IC's we find incompatible with self-similarity, and
Viable cosmology in bimetric theory
De Felice, Antonio; Mukohyama, Shinji; Tanahashi, Norihiro; Tanaka, Takahiro
2014-01-01
We study cosmological perturbations in bimetric theory with two fluids each of which is coupled to one of the two metrics. Focusing on a healthy branch of background solutions, we clarify the stability of the cosmological perturbations. For this purpose, we extend the condition for the absence of the so-called Higuchi ghost, and show that the condition is guaranteed to be satisfied on the healthy branch. We also calculate the squared propagation speeds of perturbations and derive the conditions for the absence of the gradient instability. To avoid the gradient instability, we find that the model parameters are weakly constrained.
Classical and Quantum Theory of Perturbations in Inflationary Universe Models
Brandenberger, R H; Mukhanov, V
1993-01-01
A brief introduction to the gauge invariant classical and quantum theory of cosmological perturbations is given. The formalism is applied to inflationary Universe models and yields a consistent and unified description of the generation and evolution of fluctuations. A general formula for the amplitude of cosmological perturbations in inflationary cosmology is derived.
The joint statistics of mildly non-linear cosmological densities and slopes in count-in-cells
Bernardeau, Francis; Pichon, Christophe
2015-01-01
In the context of count-in-cells statistics, the joint probability distribution of the density in two concentric spherical shells is predicted from first first principle for sigmas of the order of one. The agreement with simulation is found to be excellent. This statistics allows us to deduce the conditional one dimensional probability distribution function of the slope within under dense (resp. overdense) regions, or of the density for positive or negative slopes. The former conditional distribution is likely to be more robust in constraining the cosmological parameters as the underlying dynamics is less evolved in such regions. A fiducial dark energy experiment is implemented on such counts derived from Lambda-CDM simulations.
Perturbations and quantum relaxation
Kandhadai, Adithya
2016-01-01
We investigate whether small perturbations can cause relaxation to quantum equilibrium over very long timescales. We consider in particular a two-dimensional harmonic oscillator, which can serve as a model of a field mode on expanding space. We assume an initial wave function with small perturbations to the ground state. We present evidence that the trajectories are highly confined so as to preclude relaxation to equilibrium even over very long timescales. Cosmological implications are briefly discussed.
Directory of Open Access Journals (Sweden)
Sirada Pinjai
2013-01-01
Full Text Available This paper is concerned with the problem of robust exponential stability for linear parameter-dependent (LPD neutral systems with mixed time-varying delays and nonlinear perturbations. Based on a new parameter-dependent Lyapunov-Krasovskii functional, Leibniz-Newton formula, decomposition technique of coefficient matrix, free-weighting matrices, Cauchy’s inequality, modified version of Jensen’s inequality, model transformation, and linear matrix inequality technique, new delay-dependent robust exponential stability criteria are established in terms of linear matrix inequalities (LMIs. Numerical examples are given to show the effectiveness and less conservativeness of the proposed methods.
Liu, Pin-Lin
2015-07-01
This paper studies the problem of the stability analysis of interval time-varying delay systems with nonlinear perturbations. Based on the Lyapunov-Krasovskii functional (LKF), a sufficient delay-range-dependent criterion for asymptotic stability is derived in terms of linear matrix inequality (LMI) and integral inequality approach (IIA) and delayed decomposition approach (DDA). Further, the delay range is divided into two equal segments for stability analysis. Both theoretical and numerical comparisons have been provided to show the effectiveness and efficiency of the present method. Two well-known examples are given to show less conservatism of our obtained results and the effectiveness of the proposed method.
Directory of Open Access Journals (Sweden)
Chi-Chang Wang
2013-09-01
Full Text Available This paper seeks to use the proposed residual correction method in coordination with the monotone iterative technique to obtain upper and lower approximate solutions of singularly perturbed non-linear boundary value problems. First, the monotonicity of a non-linear differential equation is reinforced using the monotone iterative technique, then the cubic-spline method is applied to discretize and convert the differential equation into the mathematical programming problems of an inequation, and finally based on the residual correction concept, complex constraint solution problems are transformed into simpler questions of equational iteration. As verified by the four examples given in this paper, the method proposed hereof can be utilized to fast obtain the upper and lower solutions of questions of this kind, and to easily identify the error range between mean approximate solutions and exact solutions.
Cervantes-Cota, Jorge L
2014-01-01
We review the role of fluids in cosmology by first introducing them in General Relativity and then applied to a FRW Universe's model. We describe how relativistic and non-relativistic components evolve in the background dynamics. We also introduce scalar fields to show that they are able to yield an inflationary dynamics at very early times (inflation) and late times (quintessence). Then, we proceed to study the thermodynamical properties of the fluids and, lastly, its perturbed kinematics. We make emphasis in the constrictions of parameters by recent cosmological probes.
Li, Chonghong
2012-01-01
We study cosmological perturbation spectra using the dynamical equations of gauge invariant perturbations with a generalized blue/red-shift term. Combined with the power-law index of cosmological background, {\
The Effective Field Theory of nonsingular cosmology
Cai, Yong; Li, Hai-Guang; Qiu, Taotao; Piao, Yun-Song
2016-01-01
In this paper, we explore the nonsingular cosmology within the framework of the Effective Field Theory(EFT) of cosmological perturbations. Due to the recently proved no-go theorem, any nonsingular cosmological models based on the cubic Galileon suffer from pathologies. We show how the EFT could help us clarify the origin of the no-go theorem, and offer us solutions to break the no-go. Particularly, we point out that the gradient instability can be removed by using some spatial derivative operators in EFT. Based on the EFT description, we obtain a realistic healthy nonsingular cosmological model, and show the perturbation spectrum can be consistent with the observations.
Lacivita, Valentina; Rérat, Michel; Kirtman, Bernard; Ferrero, Mauro; Orlando, Roberto; Dovesi, Roberto
2009-11-01
The high-frequency dielectric ɛ and the first nonlinear electric susceptibility χ(2) tensors of crystalline potassium dihydrogen phosphate (KH2PO4) are calculated by using the coupled perturbed Hartree-Fock and Kohn-Sham methods as implemented in the CRYSTAL code. The effect of basis sets of increasing size on ɛ and χ(2) is explored. Five different levels of theory, namely, local-density approximation, generalized gradient approximation (PBE), hybrids (B3LYP and PBE0), and HF are compared using the experimental and theoretical structures corresponding not only to the tetragonal geometry I4d2 at room temperature but also to the orthorhombic phase Fdd2 at low temperature. Comparison between the two phases and their optical behavior is made. The calculated results for the tetragonal phase are in good agreement with the experimental data.
Path integral for inflationary perturbations
Prokopec, T.; Rigopoulos, G.
2010-01-01
The quantum theory of cosmological perturbations in single-field inflation is formulated in terms of a path integral. Starting from a canonical formulation, we show how the free propagators can be obtained from the well-known gauge-invariant quadratic action for scalar and tensor perturbations, and
Giblin, John T; Mertens, James B; Starkman, Glenn D
2016-06-24
While the use of numerical general relativity for modeling astrophysical phenomena and compact objects is commonplace, the application to cosmological scenarios is only just beginning. Here, we examine the expansion of a spacetime using the Baumgarte-Shapiro-Shibata-Nakamura formalism of numerical relativity in synchronous gauge. This work represents the first numerical cosmological study that is fully relativistic, nonlinear, and without symmetry. The universe that emerges exhibits an average Friedmann-Lemaître-Robertson-Walker (FLRW) behavior; however, this universe also exhibits locally inhomogeneous expansion beyond that expected in linear perturbation theory around a FLRW background.
Directory of Open Access Journals (Sweden)
M.H. Tiwana
2017-04-01
Full Text Available This work investigates the fractional non linear reaction diffusion (FNRD system of Lotka-Volterra type. The system of equations together with the boundary conditions are solved by Homotopy perturbation transform method (HPTM. The series solutions are obtained for the two cases (homogeneous and non-homogeneous of FNRD system. The effect of fractional parameter on the mass concentration of two species are shown and discussed with the help of 3D graphs.
Investigating inhomogeneous Szekeres models and their applications to precision cosmology
Peel, Austin Chandler
Exact solutions of Einstein's field equations that can describe the evolution of complex structures in the universe provide complementary frameworks to standard perturbation theory in which to analyze cosmological and astrophysical phenomena. The flexibility and generality of the inhomogeneous and anisotropic Szekeres metric make it the best known exact solution to explore nonlinearities in the universe. We study applications of Szekeres models to precision cosmology, focusing on the influence of inhomogeneities in two primary contexts---the growth rate of cosmic structures and biases in distance determinations to remote sources. We first define and derive evolution equations for a Szekeres density contrast, which quantifies exact deviations from a smooth background cosmology. Solving these equations and comparing to the usual perturbative approach, we find that for models with the same matter content, the Szekeres growth rate is larger through the matter-dominated cosmic era. Including a cosmological constant, we consider exact global perturbations, as well as the evolution of a single extended structure surrounded by an almost homogeneous background. For the former, we use growth data to obtain a best fit Szekeres model and find that it can fit the data as well as the standard Lambda-Cold Dark Matter (LCDM) cosmological model but with different cosmological parameters. Next, to study effects of inhomogeneities on distance measures, we build an exact relativistic Swiss-cheese model of the universe, where a large number of non-symmetric and randomly placed Szekeres structures are embedded within a LCDM background. Solving the full relativistic propagation equations, light beams are traced through the model, where they traverse the inhomogeneous structures in a way that mimics the paths of real light beams in the universe. For beams crossing a single structure, their magnification or demagnification reflects primarily the net density encountered along the path
The Cosmological Memory Effect
Tolish, Alexander; Wald, Robert M.
2016-01-01
The "memory effect" is the permanent change in the relative separation of test particles resulting from the passage of gravitational radiation. We investigate the memory effect for a general, spatially flat FLRW cosmology by considering the radiation associated with emission events involving particle-like sources. We find that if the resulting perturbation is decomposed into scalar, vector, and tensor parts, only the tensor part contributes to memory. Furthermore, the tensor contribution to m...
String Scale Cosmological Constant
Chalmers, Gordon
2006-01-01
The cosmological constant is an unexplained until now phenomena of nature that requires an explanation through string effects. The apparent discrepancy between theory and experiment is enourmous and has already been explained several times by the author including mechanisms. In this work the string theory theory of abolished string modes is documented and given perturbatively to all loop orders. The holographic underpinning is also exposed. The matching with the data of the LIGO and D0 experi...
Initial Conditions for Accurate N-Body Simulations of Massive Neutrino Cosmologies
Zennaro, Matteo; Villaescusa-Navarro, Francisco; Carbone, Carmelita; Sefusatti, Emiliano; Guzzo, Luigi
2016-01-01
The set-up of the initial conditions in cosmological N-body simulations is usually implemented by rescaling the desired low-redshift linear power spectrum to the required starting redshift consistently with the Newtonian evolution of the simulation. The implementation of this practical solution requires more care in the context of massive neutrino cosmologies, mainly because of the non-trivial scale-dependence of the linear growth that characterises these models. In this work we consider a simple two-fluid, Newtonian approximation for cold dark matter and massive neutrinos perturbations that can reproduce the cold matter linear evolution predicted by Boltzmann codes such as CAMB or CLASS with a 0.1% accuracy or below for all redshift relevant to nonlinear structure formation. We use this description, in the first place, to quantify the systematic errors induced by several approximations often assumed in numerical simulations, including the typical set-up of the initial conditions for massive neutrino cosmolog...
Non-linear dark matter collapse under diffusion
Velten, Hermano E S
2014-01-01
Diffusion is one of the physical processes allowed for describing the large scale dark matter dynamics. At the same time, it can be seen as a possible mechanism behind the interacting cosmologies. We study the non-linear spherical "top-hat" collapse of dark matter which undergoes velocity diffusion into a solvent dark energy field. We show constraints on the maximum magnitude allowed for the dark matter diffusion. Our results reinforce previous analysis concerning the linear perturbation theory.
Thermal Tachyacoustic Cosmology
Agarwal, Abhineet
2014-01-01
An intriguing possibility that can address pathologies in both early universe cosmology (i.e. the horizon problem) and quantum gravity (i.e. non-renormalizability), is that particles at very high energies and/or temperatures could propagate arbitrarily fast. A concrete realization of this possibility for the early universe is the Tachyacoustic (or Speedy Sound) cosmology, which could also produce a scale-invariant spectrum for scalar cosmological perturbations. Here, we study Thermal Tachyacoustic Cosmology (TTC), i.e. this scenario with thermal initial conditions. We find that a phase transition in the early universe, around the scale of Grand Unified Theories (GUT scale; $T\\sim 10^{15}$ GeV), during which the speed of sound drops by $25$ orders of magnitude within a Hubble time, can fit current CMB observations. We further discuss how production of primordial black holes constrains the cosmological acoustic history, while coupling TTC to Horava-Lifshitz gravity leads to a lower limit on the amplitude of ten...
Thermal tachyacoustic cosmology
Agarwal, Abhineet; Afshordi, Niayesh
2014-08-01
An intriguing possibility that can address pathologies in both early Universe cosmology (i.e. the horizon problem) and quantum gravity (i.e. nonrenormalizability), is that particles at very high energies and/or temperatures could propagate arbitrarily fast. A concrete realization of this possibility for the early Universe is the tachyacoustic (or speedy sound) cosmology, which could also produce a scale-invariant spectrum for scalar cosmological perturbations. Here, we study thermal tachyacoustic cosmology (TTC), i.e. this scenario with thermal initial conditions. We find that a phase transition in the early Universe, around the scale of the grand unified theory (GUT scale; T ˜1015 GeV), during which the speed of sound drops by 25 orders of magnitude within a Hubble time, can fit current CMB observations. We further discuss how production of primordial black holes constrains the cosmological acoustic history, while coupling TTC to Horava-Lifshitz gravity leads to a lower limit on the amplitude of tensor modes (r≳10-3), that are detectable by CMBpol (and might have already been seen by the BICEP-Keck Collaboration).
Cosmological dynamics of extended chameleons
Tamanini, Nicola
2016-01-01
We investigate the cosmological dynamics of the recently proposed extended chameleon models at both background and linear perturbation levels. Dynamical systems techniques are employed to fully characterize the evolution of the universe at the largest distances, while structure formation is analysed at sub-horizon scales within the quasi-static approximation. The late time dynamical transition from dark matter to dark energy domination can be well described by almost all extended chameleon models considered, with no deviations from $\\Lambda$CDM results at both background and perturbation levels. The results obtained in this work confirm the cosmological viability of extended chameleons as alternative dark energy models.
Metzler, Holger; Müller, Markus; Sierra, Carlos A.
2017-04-01
Carbon fluxes in the ocean-atmosphere-biosphere system are governed by nonlinear processes, which are usually modeled by a system of ordinary differential equations. It is very difficult to analyze such nonlinear models and to predict their future behavior, particularly their internal age structure: How old is the carbon in different pools (ages) and how old is the carbon that leaves the system (transit times)? How is this age structure modified by the addition of fossil fuel emissions? To answer these questions, we developed a new mathematical approach that allows us to compute and visualize the age structure of models of well mixed pools even if they are nonlinear and nonautonomous. We do not only consider mean ages and mean transit times, but entire distributions. Consequently, we can consider important statistics such as the median, quantiles, or the variance. We applied this mathematical approach to a nonlinear global carbon model consisting of three pools (atmosphere, surface ocean, and terrestrial biosphere) and driven by four emission scenarios (RCP3-PD, RCP4.5, RCP6, RCP8.5). Results showed that the addition of fossil fuels modifies the age structure of C in the atmosphere by drastically increasing its proportion of young carbon. We found little differences among predicted mean ages for the four emission scenarios, but changes in the overall distributions were large with effects on median, quantiles and variance. In the short-term, fossil-fuel emissions have an important effect on the amount of carbon that is exchanged among Earth's main C reservoirs. In the long-term, most added C will eventually end up in the deep ocean, but the time required to return to pre-industrial C age distributions is largely dependent on emission scenarios.
Tartaglia, Angelo
2015-01-01
Starting from some relevant facts concerning the behaviour of the universe over large scale and time span, the analogy between the geometric approach of General Relativ- ity and the classical description of an elastic strained material continuum is discussed. Extending the elastic deformation approach to four dimensions it is shown that the accelerated expansion of the universe is recovered. The strain field of space-time repro- duces properties similar to the ones ascribed to the dark energy currently called in to explain the accelerated expansion. The strain field in the primordial universe behaves as radiation, but asymptotically it reproduces the cosmological constant. Subjecting the theory to a number of cosmological tests confirms the soundness of the approach and gives an optimal value for the one parameter of the model, i.e. the bulk modulus of the space-time continuum. Finally various aspects of the Strained State Cosmology (SSC) are discussed and contrasted with some non-linear massive gravity theor...
Bond, Alan M; Duffy, Noel W; Elton, Darrell M; Fleming, Barry D
2009-11-01
Under most experimental conditions, a distinctly nonlinear background current is encountered in all forms of voltammetry which arises from the potential dependence of the capacitance. The nonlinear background current has been successfully modeled under large amplitude sinusoidal ac voltammetric conditions with a fourth order polynomial. The model was applied to a dummy cell containing a nonideal ceramic capacitor and commonly used electrodes. The nonlinearity in behavior of the background capacitance is particularly significant when considering the discrimination between the Faradaic and background contributions in the higher order harmonics resolved in ac voltammetry by Fourier transform-inverse Fourier transform approaches and in the simulation of the background current and hence double-layer capacitance as a function of potential. Typically, measurable background current under large amplitude conditions is detectable in the dc and fundamental to fourth harmonic components in large amplitude ac voltammetry. For analytical purposes, this background current can be corrected on a per harmonic basis without the need for any model. Background correction has been successfully applied to the first four harmonics for the oxidation of ferrocenemonocarboxylic acid over the concentration range of 5-500 microM in aqueous 0.5 M NaCl solution.
Chen, Hao; Zhong, Shouming; Li, Min; Liu, Xingwen; Adu-Gyamfi, Fehrs
2016-07-01
In this paper, a novel delay partitioning method is proposed by introducing the theory of geometric progression for the stability analysis of T-S fuzzy systems with interval time-varying delays and nonlinear perturbations. Based on the common ratio α, the delay interval is unequally separated into multiple subintervals. A newly modified Lyapunov-Krasovskii functional (LKF) is established which includes triple-integral terms and augmented factors with respect to the length of every related proportional subintervals. In addition, a recently developed free-matrix-based integral inequality is employed to avoid the overabundance of the enlargement when dealing with the derivative of the LKF. This innovative development can dramatically enhance the efficiency of obtaining the maximum upper bound of the time delay. Finally, much less conservative stability criteria are presented. Numerical examples are conducted to demonstrate the significant improvements of this proposed approach.
Wu, Xiaomao; Schelly, Z. A.; Vastano, John A.
1994-07-01
Results of studies of the limited Explodator model in a continuous-flow stirred tank reactor (CSTR) under square wave perturbation of the flow rate are reported. The perturbation is applied in such a way that the system is alternately attracted to two different periodic attractors in the parameter region close the Hopf bifurcation point. The system is shown to display a variety of entrainment bands, birhythmicity, quasiperiodicity, resonance-like phenomenon, period doubling and intermittency routes to chaos, and a complicated window structure of the chaotic region. In addition, a novel phenomenon, “intermittent alternative laminar oscillations”, was observed in a chaotic regime sandwiched between two entrainment bands. Transient chaos occurs in one of the entrainment bands, which intimates chaos in the adjacent regime. Positive Lyapunov exponents were found to be associated with the chaotic behavior. The folding and stretching property of the chaotic attractors was analyzed through stroboscopic representations. The deterministic nature of the chaotic behavior was confirmed by the quadratic-like curve formed in the one-dimensional map.
Non-Gaussianity of Large-Scale CMB Anisotropies beyond Perturbation Theory
Bartolo, N; Riotto, Antonio
2005-01-01
We compute the fully non-linear Cosmic Microwave Background (CMB) anisotropies on scales larger than the horizon at last-scattering in terms of only the curvature perturbation, providing a generalization of the linear Sachs-Wolfe effect at any order in perturbation theory. We show how to compute the $n$-point connected correlation functions of the large-scale CMB anisotropies for generic primordial seeds provided by standard slow-roll inflation as well as the curvaton and other scenarios for the generation of cosmological perturbations. As an application of our formalism, we compute the three- and four-point connected correlation functions whose detection in future CMB experiments might be used to assess the level of primordial non-Gaussianity, giving the theoretical predictions for the parameters of quadratic and cubic non-linearities f_NL and g_NL.
Directory of Open Access Journals (Sweden)
P. P. Hallan
2008-01-01
Full Text Available The effect of perturbations in Coriolis and cetrifugal forces on the nonlinear stability of the equilibrium point of the Robe's (1977 restricted circular three-body problem has been studied when the density parameter K is zero. By applying Kolmogorov-Arnold-Moser (KAM theory, it has been found that the equilibrium point is stable for all mass ratios μ in the range of linear stability 8/9+(2/3((43/25ϵ1−(10/3ϵ<μ<1, where ϵ and ϵ1 are, respectively, the perturbations in Coriolis and centrifugal forces, except for five mass ratios μ1=0.93711086−1.12983217ϵ+1.50202694ϵ1, μ2 = 0.9672922−0.5542091ϵ+ 1.2443968ϵ1, μ3=0.9459503−0.70458206ϵ+ 1.28436549ϵ1, μ4=0.9660792−0.30152273ϵ + 1.11684064ϵ1, μ5=0.893981−2.37971679ϵ + 1.22385421ϵ1, where the theory is not applicable.
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Belendez, A. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es; Pascual, C.; Gallego, S.; Ortuno, M.; Neipp, C. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2007-11-26
A modified He's homotopy perturbation method (HHPM) is used to calculate the periodic solutions of a conservative nonlinear oscillator for which the elastic force term is proportional to x{sup 1/3}. The He's homotopy perturbation method is modified by truncating the infinite series corresponding to the first-order approximate solution before introducing this solution in the second-order linear differential equation, and so on. We find this modified HHPM works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. Only one iteration leads to high accuracy of the solutions with a maximal relative error for the approximate frequency of less than 0.6% for small and large values of oscillation amplitude, while this relative error is 0.17% for the second iteration and as low as 0.024% when the third approximation is considered. Comparison of the result obtained using this method with those obtained by different harmonic balance methods reveals that the former is very effective and convenient.
Jones, Bernard J. T.
2017-04-01
Preface; Notation and conventions; Part I. 100 Years of Cosmology: 1. Emerging cosmology; 2. The cosmic expansion; 3. The cosmic microwave background; 4. Recent cosmology; Part II. Newtonian Cosmology: 5. Newtonian cosmology; 6. Dark energy cosmological models; 7. The early universe; 8. The inhomogeneous universe; 9. The inflationary universe; Part III. Relativistic Cosmology: 10. Minkowski space; 11. The energy momentum tensor; 12. General relativity; 13. Space-time geometry and calculus; 14. The Einstein field equations; 15. Solutions of the Einstein equations; 16. The Robertson–Walker solution; 17. Congruences, curvature and Raychaudhuri; 18. Observing and measuring the universe; Part IV. The Physics of Matter and Radiation: 19. Physics of the CMB radiation; 20. Recombination of the primeval plasma; 21. CMB polarisation; 22. CMB anisotropy; Part V. Precision Tools for Precision Cosmology: 23. Likelihood; 24. Frequentist hypothesis testing; 25. Statistical inference: Bayesian; 26. CMB data processing; 27. Parametrising the universe; 28. Precision cosmology; 29. Epilogue; Appendix A. SI, CGS and Planck units; Appendix B. Magnitudes and distances; Appendix C. Representing vectors and tensors; Appendix D. The electromagnetic field; Appendix E. Statistical distributions; Appendix F. Functions on a sphere; Appendix G. Acknowledgements; References; Index.
Ultracompact Minihalos as Probes of Inflationary Cosmology
Aslanyan, Grigor; Price, Layne C.; Adams, Jenni; Bringmann, Torsten; Clark, Hamish A.; Easther, Richard; Lewis, Geraint F.; Scott, Pat
2016-09-01
Cosmological inflation generates primordial density perturbations on all scales, including those far too small to contribute to the cosmic microwave background. At these scales, isolated ultracompact minihalos of dark matter can form well before standard structure formation, if the perturbations have sufficient amplitude. Minihalos affect pulsar timing data and are potentially bright sources of gamma rays. The resulting constraints significantly extend the observable window of inflation in the presence of cold dark matter, coupling two of the key problems in modern cosmology.
Time-sliced perturbation theory for large scale structure I: general formalism
Blas, Diego; Garny, Mathias; Ivanov, Mikhail M.; Sibiryakov, Sergey
2016-07-01
We present a new analytic approach to describe large scale structure formation in the mildly non-linear regime. The central object of the method is the time-dependent probability distribution function generating correlators of the cosmological observables at a given moment of time. Expanding the distribution function around the Gaussian weight we formulate a perturbative technique to calculate non-linear corrections to cosmological correlators, similar to the diagrammatic expansion in a three-dimensional Euclidean quantum field theory, with time playing the role of an external parameter. For the physically relevant case of cold dark matter in an Einstein-de Sitter universe, the time evolution of the distribution function can be found exactly and is encapsulated by a time-dependent coupling constant controlling the perturbative expansion. We show that all building blocks of the expansion are free from spurious infrared enhanced contributions that plague the standard cosmological perturbation theory. This paves the way towards the systematic resummation of infrared effects in large scale structure formation. We also argue that the approach proposed here provides a natural framework to account for the influence of short-scale dynamics on larger scales along the lines of effective field theory.
Differentiating G-inflation from string gas cosmology using the effective field theory approach
He, Minxi; Liu, Junyu; Lu, Shiyun; Zhou, Siyi; Cai, Yi-Fu; Wang, Yi; Brandenberger, Robert
2016-12-01
A characteristic signature of String Gas Cosmology is primordial power spectra for scalar and tensor modes which are almost scale-invariant but with a red tilt for scalar modes but a blue tilt for tensor modes. This feature, however, can also be realized in the so-called G-inflation model, in which Horndeski operators are introduced which leads to a blue tensor tilt by softly breaking the Null Energy Condition. In this article we search for potential observational differences between these two cosmologies by performing detailed perturbation analyses based on the Effective Field Theory approach. Our results show that, although both two models produce blue tilted tensor perturbations, they behave differently in three aspects. Firstly, String Gas Cosmology predicts a specific consistency relation between the index of the scalar modes ns and that of tensor ones nt, which is hard to be reproduced by G-inflation. Secondly, String Gas Cosmology typically predicts non-Gaussianities which are highly suppressed on observable scales, while G-inflation gives rise to observationally large non-Gaussianities because the kinetic terms in the action become important during inflation. However, after finely tuning the model parameters of G-inflation it is possible to obtain a blue tensor spectrum and negligible non-Gaussianities with a degeneracy between the two models. This degeneracy can be broken by a third observable, namely the scale dependence of the nonlinearity parameter, which vanishes for G-inflation but has a blue tilt in the case of String Gas Cosmology. Therefore, we conclude that String Gas Cosmology is in principle observationally distinguishable from the single field inflationary cosmology, even allowing for modifications such as G-inflation.
Perturbations in electromagnetic dark energy
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Jiménez, Jose Beltrán; Maroto, Antonio L. [Departamento de Física Teórica, Universidad Complutense de Madrid, 28040 Madrid (Spain); Koivisto, Tomi S. [Institute for Theoretical Physics, University of Heidelberg, 69120 Heidelberg (Germany); Mota, David F., E-mail: jobeltra@fis.ucm.es, E-mail: T.Koivisto@thphys.uni-heidelberg.de, E-mail: maroto@fis.ucm.es, E-mail: d.f.mota@astro.uio.no [Institute of Theoretical Astrophysics, University of Oslo, 0315 Oslo (Norway)
2009-10-01
It has been recently proposed that the presence of a temporal electromagnetic field on cosmological scales could explain the phase of accelerated expansion that the universe is currently undergoing. The field contributes as a cosmological constant and therefore, the homogeneous cosmology produced by such a model is exactly the same as that of ΛCDM. However, unlike a cosmological constant term, electromagnetic fields can acquire perturbations which in principle could affect CMB anisotropies and structure formation. In this work, we study the evolution of inhomogeneous scalar perturbations in this model. We show that provided the initial electromagnetic fluctuations generated during inflation are small, the model is perfectly compatible with both CMB and large scale structure observations at the same level of accuracy as ΛCDM.
Effective perfect fluids in cosmology
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Ballesteros, Guillermo [Museo Storico della Fisica e Centro Studi e Ricerche Enrico Fermi, Piazza del Viminale 1, I-00184 Rome (Italy); Bellazzini, Brando, E-mail: guillermo.ballesteros@unige.ch, E-mail: brando.bellazzini@pd.infn.it [Dipartimento di Fisica, Università di Padova and INFN, Sezione di Padova, Via Marzolo 8, I-35131 Padova (Italy)
2013-04-01
We describe the cosmological dynamics of perfect fluids within the framework of effective field theories. The effective action is a derivative expansion whose terms are selected by the symmetry requirements on the relevant long-distance degrees of freedom, which are identified with comoving coordinates. The perfect fluid is defined by requiring invariance of the action under internal volume-preserving diffeomorphisms and general covariance. At lowest order in derivatives, the dynamics is encoded in a single function of the entropy density that characterizes the properties of the fluid, such as the equation of state and the speed of sound. This framework allows a neat simultaneous description of fluid and metric perturbations. Longitudinal fluid perturbations are closely related to the adiabatic modes, while the transverse modes mix with vector metric perturbations as a consequence of vorticity conservation. This formalism features a large flexibility which can be of practical use for higher order perturbation theory and cosmological parameter estimation.
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The impact of sulfate aerosol, ClOx and NOx perturbations for two different magnitudes of CH4 sources on lower stratospheric ozone is studied by using a heterogeneous chemical system that consists of 19 species belonging to 5 chemical families (oxygen, hydrogen, nitrogen, chlorine and carbon). The results show that the present modeled photochemical system can present several different solutions, for instance,periodic states and multi-equilibrium states appearing in turn under certain parameter domains, through chlorine chemistry and nitrogen chemistry together with sulfate aerosol as well as the increasing magnitude of CH4 sources. The existence of catastrophic transitions could produce a dramatic reduction in the ozone concentration with the increase of external sources.
Perturbative treatment of the non-linear q-Schr\\"odinger and q-Klein-Gordon equations
Zamora, D J; Plastino, A; Ferri, G L
2016-01-01
Interesting nonlinear generalization of both Schr\\"odinger's and Klein-Gordon's equations have been recently advanced by Tsallis, Rego-Monteiro, and Tsallis (NRT) in [Phys. Rev. Lett. {\\bf 106}, 140601 (2011)]. There is much current activity going on in this area. The non-linearity is governed by a real parameter $q$. It is a fact that the ensuing non linear q-Schr\\"odinger and q-Klein-Gordon equations are natural manifestations of very high energy phenomena, as verified by LHC-experiments. This happens for $q-$values close to unity [Nucl. Phys. A {\\bf 955}, 16 (2016), Nucl. Phys. A {\\bf 948}, 19 (2016)]. It is also well known that q-exponential behavior is found in quite different settings. An explanation for such phenomenon was given in [Physica A {\\bf 388}, 601 (2009)] with reference to empirical scenarios in which data are collected via set-ups that effect a normalization plus data's pre-processing. Precisely, the ensuing normalized output was there shown to be q-exponentially distributed if the input dat...
Sanders, RH; Papantonopoulos, E
2005-01-01
I discuss the classical cosmological tests, i.e., angular size-redshift, flux-redshift, and galaxy number counts, in the light of the cosmology prescribed by the interpretation of the CMB anisotropies. The discussion is somewhat of a primer for physicists, with emphasis upon the possible systematic
Exploring Bouncing Cosmologies with Cosmological Surveys
Cai, Yi-Fu
2014-01-01
In light of the recent observational data coming from the sky we have two significant directions in the field of theoretical cosmology recently. First, we are now able to make use of present observations, such as the Planck and BICEP2 data, to examine theoretical predictions from the standard inflationary $\\Lambda$CDM which were made decades of years ago. Second, we can search for new cosmological signatures as a way to explore physics beyond the standard cosmic paradigm. In particular, a subset of early universe models admit a nonsingular bouncing solution that attempts to address the issue of the big bang singularity. These models have achieved a series of considerable developments in recent years, in particular in their perturbative frameworks, which made brand-new predictions of cosmological signatures that could be visible in current and forthcoming observations. In this article we present two representative paradigms of very early universe physics. The first is the so-called new matter (or matter-ekpyro...
Cosmology With Extra Dimensions
Martín, J
2005-01-01
We review several properties of models that include extra dimensions, focusing on aspects related to cosmology and particle physics phenomenology. The properties of effective four dimensional inflationary geometry are studied in two distinct frameworks: (i) in Kaluza- Klein (KK) compactifications and (ii) in braneworld scenarios. From numerical simulations we find that inflationary braneworlds are unstable if the scale of inflation is too large in comparison with the stabilization scale of the interbrane distance. The analysis of perturbations confirms the existence of a tachyon associated with the volume modulus of the extra dimensions both in braneworlds and KK compactifications. With the numerical program BRANECODE non- perturbative properties of braneworlds are studied. We fully understand the non-perturbative consequences of this instability. Generic attractors are (i) an increase of the interbrane distance and the formation of a naked singularity, (ii) the brane colli...
Parameterized post-Newtonian cosmology
Sanghai, Viraj A. A.; Clifton, Timothy
2017-03-01
Einstein’s theory of gravity has been extensively tested on solar system scales, and for isolated astrophysical systems, using the perturbative framework known as the parameterized post-Newtonian (PPN) formalism. This framework is designed for use in the weak-field and slow-motion limit of gravity, and can be used to constrain a large class of metric theories of gravity with data collected from the aforementioned systems. Given the potential of future surveys to probe cosmological scales to high precision, it is a topic of much contemporary interest to construct a similar framework to link Einstein’s theory of gravity and its alternatives to observations on cosmological scales. Our approach to this problem is to adapt and extend the existing PPN formalism for use in cosmology. We derive a set of equations that use the same parameters to consistently model both weak fields and cosmology. This allows us to parameterize a large class of modified theories of gravity and dark energy models on cosmological scales, using just four functions of time. These four functions can be directly linked to the background expansion of the universe, first-order cosmological perturbations, and the weak-field limit of the theory. They also reduce to the standard PPN parameters on solar system scales. We illustrate how dark energy models and scalar-tensor and vector-tensor theories of gravity fit into this framework, which we refer to as ‘parameterized post-Newtonian cosmology’ (PPNC).
Brandenberger, R H; Brandenberger, Robert H.; Magueijo, Joao
1999-01-01
We review a few off-the-beaten-track ideas in cosmology. They solve a variety of fundamental problems; also they are fun. We start with a description of non-singular dilaton cosmology. In these scenarios gravity is modified so that the Universe does not have a singular birth. We then present a variety of ideas mixing string theory and cosmology. These solve the cosmological problems usually solved by inflation, and furthermore shed light upon the issue of the number of dimensions of our Universe. We finally review several aspects of the varying speed of light theory. We show how the horizon, flatness, and cosmological constant problems may be solved in this scenario. We finally present a possible experimental test for a realization of this theory: a test in which the Supernovae results are to be combined with recent evidence for redshift dependence in the fine structure constant.