Linear Cosmological Perturbation Theory Research Articles

Fluctuation-dissipation relation in cosmic microwave background

We study the fluctuation-dissipation relation for sound waves in the cosmic microwave background (CMB), employing effective field theory (EFT) for fluctuating hydrodynamics.Treating sound waves as the linear response to thermal radiation, we establish the fluctuation-dissipation relation within a cosmological framework.While dissipation is elucidated in established linear cosmological perturbation theory, the standard Boltzmann theory overlooks the associated noise, possibly contributing to inconsistencies in Lambda Cold Dark Matter (ΛCDM) cosmology. This paper employs EFT for fluctuating hydrodynamics in cosmological perturbation theory, deriving sound wave noise.Notably, the long-time limit of the noise spectrum is independent of viscosity details, resembling a Brownian motion bounded in a harmonic potential.The net energy transfer between the sound wave system and the radiation environment reaches a balance within Hubble time, suggesting the thermal equilibrium of the sound waves themselves.The induced density power spectrum is characterized as white noise dependent on the inverse of the entropy density, which is negligibly small on the CMB scale. The energy density of the entire sound wave system scales as a -4, akin to radiation. While the numerical factor is not determined in the present calculation, the back reaction of the sound wave system to the background radiation may not be negligible, serving as a potential source for various fitting issues in ΛCDM cosmology.

Temporal evolution of cosmological density perturbations of the Bose–Einstein condensate dark matter

Dark matter is assumed to be composed of scalar boson particles that form Bose–Einstein condensate during the cosmic evolution of the Universe when the temperature of the dark matter is below the critical temperature Tcr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{cr}$$\\end{document}. At around a redshift z∼1200\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$z\\sim 1200$$\\end{document}, the normal dark matter converted to Bose–Einstein condensate dark matter through a first-order phase transition and continued to complete the condensation process for nearly 106\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10^6$$\\end{document} years, until then, both phases coexist. In this manuscript, considering Bose–Einstein condensate dark matter as a Gross–Pitaevskii–Poisson system, we study the time evolution of density contrast of Bose–Einstein condensate dark matter using cosmological linear perturbation theory following previous works on the subject. The evolution equation contains quantum pressure due to Heisenberg’s uncertainty principle and self-interaction pressure terms. We solve the temporal density contrast equation of Bose–Einstein condensate dark matter analytically for both the Thomas-Fermi limit and the non-interacting case where the expansion rule follows similarly to that of the Einstein–de Sitter Universe. In addition, we also numerically analyze the temporal nature of the evolution of density contrast of Bose–Einstein condensate dark matter for the complete equation without applying any approximation. We find that the Bose–Einstein condensate model of dark matter could modify the temporal nature of density contrast evolution due to the presence of self-interaction and quantum pressure terms, which shows significant differences with respect to the conventional standard cold dark matter, and successfully solves the small-scale problems in the context of cosmological structure formation.

Peculiar velocities in the early Universe

Large-scale peculiar motions are commonplace in our universe. Nevertheless, their origin, evolution and implications are still largely unknown. It is generally assumed that bulk motions are a relatively recent addition to the universal kinematics, triggered by the increasing inhomogeneity and anisotropy of the post-recombination epoch. In this work, we focus on the linear evolution of peculiar velocities prior to recombination, namely in the late radiation era and also during a phase of de Sitter inflation. We begin by showing/confirming that bulk motions are triggered and sustained by the non-gravitational forces developed during structure formation. Since density and therefore peculiar-velocity perturbations cannot grow in the baryonic sector before recombination, we consider drift motions in non-baryonic species, which can start growing in the late radiation era. Using relativistic linear cosmological perturbation theory, we find that peculiar motions in the low-energy dark component exhibit power-law growth, which increases further after equipartition. Turning to the very early universe, we consider the evolution of linear peculiar velocities during a phase of de Sitter inflation. We find that typical slow-roll scenarios do not source peculiar motions. Moreover, even if the latter were to be present at the onset of the de Sitter phase, the subsequent exponential expansion should quickly wash away any traces of peculiar-velocity perturbations.

Nonclassical cosmological dynamics in the low-energy limit of loop quantum scalar-tensor theory

In previous work, we showed that in loop quantum cosmology of scalar-tensor theory (STT) with the holonomy correction the background equations of motion in the Jordan frame have two branches, i.e., the ${b}_{+}$ branch and the ${b}_{\ensuremath{-}}$ branch. In the low-energy limit, the ${b}_{+}$ branch of the equations of motion reproduce the equations of motion of classical STT, while the ${b}_{\ensuremath{-}}$ branch of equations of motion do not reproduce the classical equations. In this paper, we investigate cosmological dynamics in an expanding universe whose background is described by the ${b}_{\ensuremath{-}}$ branch of equations of motion of STT, and we especially focus on the dynamics of the perturbations in the low-energy limit because it is most relevant to the current observational range. First, we show that the low-energy limit of the ${b}_{\ensuremath{-}}$ branch of equations of motion can be a stable attractor in the expansion phase of a universe. Then, we find a low-energy effective Hamiltonian on the spatially flat Friedmann-Robertson-Walker background. The background part of this Hamiltonian can yield the low-energy limit of the ${b}_{\ensuremath{-}}$ branch of equations, and this Hamiltonian consists of constraints whose constraint algebra is different from the classical case but also closed up to arbitrary order of perturbations. Remarkably, we find that this Hamiltonian can be transformed into the Hamiltonian of the Einstein frame by field redefinitions different from the classical case. Moreover, we also develop the linear cosmological perturbation theory and apply it to study the slow-roll inflation in this context. Finally, we study a specific model of STT. In this model, a contracting universe described by classical STT in the remote past can pass through the bounce and evolve into an expanding universe whose background dynamics is described by the ${b}_{\ensuremath{-}}$ branch of equations of motion. It is also shown that the slow-roll inflation can take place in this case, and the spectral indices of the slow-roll inflation agree well with the observations. The results in this paper indicate that there exists an alternative consistent theory which is different from the classical theory in the low-energy limit of loop quantum STT.

Can the homogeneity scale be used as a standard ruler?

The Universe on comoving scales larger than 100 Mpc/h is assumed to be statistically homogeneous, with the transition scale where we have $1\%$ deviation from homogeneity being known as the homogeneity scale $R_H$. The latter was recently proposed in Ntelis et al. (2018) [arXiv:1810.09362] to be a standard ruler. In this paper we perform a comparison between the baryon acoustic oscillations and the homogeneity scales $R_H$, assuming a spatially flat universe, linear cosmological perturbation theory and the cosmological constant cold dark matter $\Lambda$CDM model. By direct theoretical calculations, we demonstrate that the answer to the question of whether the homogeneity scale can be used as a standard ruler, is clearly negative due to the non-monotonicity of the homogeneity scale $R_H$ with the matter density parameter $\Omega_{m0}$ of the $\Lambda$CDM model. Furthermore, we also consider the effect of redshift space distortions and we find that they do not break the degeneracies but instead only change the value of $R_H$ by a few percent. Finally, we also confirm our findings with the help of an N-Body simulation.

A general theory of linear cosmological perturbations: stability conditions, the quasistatic limit and dynamics

We analyse cosmological perturbations around a homogeneous and isotropic background for scalar-tensor, vector-tensor and bimetric theories of gravity. Building on previous results, we propose a unified view of the effective parameters of all these theories. Based on this structure, we explore the viable space of parameters for each family of models by imposing the absence of ghosts and gradient instabilities. We then focus on the quasistatic regime and confirm that all these theories can be approximated by the phenomenological two-parameter model described by an effective Newton's constant and the gravitational slip. Within the quasistatic regime we pinpoint signatures which can distinguish between the broad classes of models (scalar-tensor, vector-tensor or bimetric). Finally, we present the equations of motion for our unified approach in such a way that they can be implemented in Einstein-Boltzmann solvers.

Perturbation theory for cosmologies with nonlinear structure

The next generation of cosmological surveys will operate over unprecedented scales, and will therefore provide exciting new opportunities for testing general relativity. The standard method for modelling the structures that these surveys will observe is to use cosmological perturbation theory for linear structures on horizon-sized scales, and Newtonian gravity for non-linear structures on much smaller scales. We propose a two-parameter formalism that generalizes this approach, thereby allowing interactions between large and small scales to be studied in a self-consistent and well-defined way. This uses both post-Newtonian gravity and cosmological perturbation theory, and can be used to model realistic cosmological scenarios including matter, radiation and a cosmological constant. We find that the resulting field equations can be written as a hierarchical set of perturbation equations. At leading-order, these equations allow us to recover a standard set of Friedmann equations, as well as a Newton-Poisson equation for the inhomogeneous part of the Newtonian energy density in an expanding background. For the perturbations in the large-scale cosmology, however, we find that the field equations are sourced by both non-linear and mode-mixing terms, due to the existence of small-scale structures. These extra terms should be expected to give rise to new gravitational effects, through the mixing of gravitational modes on small and large scales - effects that are beyond the scope of standard linear cosmological perturbation theory. We expect our formalism to be useful for accurately modelling gravitational physics in universes that contain non-linear structures, and for investigating the effects of non-linear gravity in the era of ultra-large-scale surveys.

Revealing the nonadiabatic nature of dark energy perturbations from galaxy clustering data

We study structure formation using relativistic cosmological linear perturbation theory in the presence of intrinsic and relative (with respect to matter) non-adiabatic dark energy perturbations. For different dark energy models we assess the impact of non-adiabaticity on the matter growth promoting a comparison with growth rate data. The dark energy models studied lead to peculiar signatures of the (non)adiabatic nature of dark energy perturbations in the evolution of the $f \sigma_{8}(z)$ observable. We show that non-adiabatic DE models become close to be degenerated with respect to the $\Lambda$CDM model at first order in linear perturbations. This would avoid the identification of the non-adiabatic nature of dark energy using current available data. Therefore, such evidence indicates that new probes are necessary to reveal the non-adiabatic features in the dark energy sector.

Matrix formalism of excursion set theory: A new approach to statistics of dark matter halo counting

Excursion set theory (EST) is an analytical framework to study the large-scale structure of the Universe. EST introduces a procedure to calculate the number density of structures by relating the cosmological linear perturbation theory to the nonlinear structures in late time. In this work, we introduce a novel approach to reformulate the EST in matrix formalism. We propose that the matrix representation of EST will facilitate the calculations in this framework. The method is to discretize the two-dimensional plane of variance and density contrast of EST, where the trajectories for each point in the Universe lived there. The probability of having a density contrast in a chosen variance is represented by a probability ket. Naturally, the concept of the transition matrix pops up to define the trajectories. We also define the probability transition rate which is used to obtain the first up-crossing of trajectories and the number count of the structures. In this work we show that the discretization let us study the non-Markov processes by forcing them to look like a Wiener process. Also we discuss that the zero drift processes with Gaussian and also non-Gaussian initial conditions can be studied by this formalism. The continuous limit of the formalism is discussed, and the known Fokker-Planck dispersion equation is recovered. Finally we show that the probability of the most massive progenitors can be extracted in this framework.

Linear density perturbations in multifield coupled quintessence

We study the behaviour of linear perturbations in multifield coupled quintessence models. Using gauge invariant linear cosmological perturbation theory we provide the full set of governing equations for this class of models, and solve the system numerically. We apply the numerical code to generate growth functions for various examples, and compare these both to the standard $\Lambda$CDM model and to current and future observational bounds. Finally, we examine the applicability of the "small scale approximation", often used to calculate growth functions in quintessence models, in light of upcoming experiments such as SKA and Euclid. We find the deviation of the full equation results for large k modes from the approximation exceeds the experimental uncertainty for these future surveys. The numerical code, PYESSENCE, written in Python will be publicly available.

Double power series method for approximating cosmological perturbations

We introduce a double power series method for finding approximate analytical solutions for systems of differential equations commonly found in cosmological perturbation theory. The method was set out, in a non-cosmological context, by Feshchenko, Shkil' and Nikolenko (FSN) in 1966, and is applicable to cases where perturbations are on sub-horizon scales. The FSN method is essentially an extension of the well known Wentzel-Kramers-Brillouin (WKB) method for finding approximate analytical solutions for ordinary differential equations. The FSN method we use is applicable well beyond perturbation theory to solve systems of ordinary differential equations, linear in the derivatives, that also depend on a small parameter, which here we take to be related to the inverse wave-number. We use the FSN method to find new approximate oscillating solutions in linear order cosmological perturbation theory for a flat radiation-matter universe. Together with this model's well known growing and decaying M\'esz\'aros solutions, these oscillating modes provide a complete set of sub-horizon approximations for the metric potential, radiation and matter perturbations. Comparison with numerical solutions of the perturbation equations shows that our approximations can be made accurate to within a typical error of 1%, or better. We also set out a heuristic method for error estimation. A Mathematica notebook which implements the double power series method is made available online.

A general theory of linear cosmological perturbations: bimetric theories

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.

A general theory of linear cosmological perturbations: scalar-tensor and vector-tensor theories

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 (à la Einstein-Aether gravity), where the theory only propagates one scalar DoF. As a result, we identify the complete forms of the quadratic actions for perturbations, and the number of free parameters that need to be defined, to cosmologically characterize these two broad classes of theories.

Nonlinear stability of cosmological solutions in massive gravity

We investigate nonlinear stability of two classes of cosmological solutions in massive gravity: isotropic Friedmann-Lemaître-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.

COSMOLOGICAL POST-NEWTONIAN APPROXIMATION COMPARED WITH PERTURBATION THEORY

We compare the cosmological first-order post-Newtonian (1PN) approximation with the relativistic cosmological linear perturbation theory in a zero-pressure medium with the cosmological constant. We compare equations and solutions in several different gauge conditions available in both methods. In the PN method we have perturbation equations for density, velocity and gravitational potential independently of the gauge condition to 1PN order. However, correspondences with these 1PN equations are available only in certain gauge conditions in the perturbation theory. Equations of perturbed velocity and the perturbed gravitational potential in the zero-shear gauge exactly coincide with the Newtonian equations which remain valid even to 1PN order (the same is true for perturbed velocity in the comoving gauge), and equations of perturbed density in the zero-shear gauge and the uniform-expansion gauge coincide to 1PN order. We identify other correspondences available in different gauge conditions of the perturbation theory.

Towards a nonsingular bouncing cosmology

We present a nonsingular bouncing cosmology using single scalar field matter with non-trivial potential and non-standard kinetic term. The potential sources a dynamical attractor solution with Ekpyrotic contraction which washes out small amplitude anisotropies. At high energy densities the field evolves into a ghost condensate, leading to a nonsingular bounce. Following the bounce there is a smooth transition to standard expanding radiation and matter dominated phases. Using linear cosmological perturbation theory we track each Fourier mode of the curvature fluctuation throughout the entire cosmic evolution. Using standard matching conditions for nonsingular bouncing cosmologies we verify that the spectral index does not change during the bounce. We show there is a controlled period of exponential growth of the fluctuation amplitude for the perturbations (but not for gravitational waves) around the bounce point which does not invalidate the perturbative treatment. This growth induces a natural suppression mechanism for the tensor to scalar ratio of fluctuations. Moreover, we study the generation of the primordial power spectrum of curvature fluctuations for various types of initial conditions. For the pure vacuum initial condition, on scales which exit the Hubble radius in the phase of Ekpyrotic contraction, the spectrum is deeply blue. For thermal particle initial condition, one possibility for generating a scale-invariant spectrum makes use of a special value of the background equation of state during the contracting Ekpyrotic phase. If the Ekpyrotic phase is preceded by a period of matter-dominated contraction, the primordial power spectrum is nearly scale-invariant on large scales (scales which exit the Hubble radius in the matter-dominated phase) but acquires a large blue tilt on small scales. Thus, our model provides a realization of the “matter bounce” scenario which is free of the anisotropy problem.

RELATIVE INFORMATION ENTROPY AND WEYL TENSOR

Due to cosmic structures in the Universe, the inhomogeneities influence the evolution of the background Universe. To characterize this influence, we extend the Kullback-Leibler relative entropy in information theory to cosmology. We study the relation between the relative entropy and the averaging problem in the perturbed Universe, and explore the temporal evolution in linear cosmological perturbation theory and beyond. The possible relationship of the relative entropy and the Weyl tensor is also discussed briefly.

우주구조 선형건드림 이론

Cosmological linear perturbation theory has fundamental importance in securing the current cosmological paradigm by connecting theories with observations. Here we present an explanation of the method used in relativistic cosmological perturbation theory and show the derivation of basic perturbation equations.

Evolution of cosmological perturbations in a renormalization-group-driven inflationary scenario

A gauge-invariant, linear cosmological perturbation theory of an almost homogeneous and isotropic universe with dynamically evolving Newton constant G and cosmological constant $\Lambda$ is presented. The equations governing the evolution of the comoving fractional spatial gradients of the matter density, G and $\Lambda$ are thus obtained. Explicit solutions are discussed in cosmologies, featuring an accelerated expansion, where both G and $\Lambda$ vary according to renormalization group equations in the vicinity of an ultraviolet fixed point. Finally, a similar analysis is carried out in the late universe regime described by the part of the renormalization group trajectory close to the gaussian fixed point.

The impact of primordial supersonic flows on early structure formation, reionization and the lowest-mass dwarf galaxies

Abstract Tseliakhovich and Hirata recently discovered that higher order corrections to the cosmological linear-perturbation theory lead to supersonic coherent baryonic flows just after recombination (i.e. z ≈ 1020), with rms velocities of ∼30 km s−1 relative to the underlying dark matter distribution, on comoving scales of ≲3 Mpc h−1. To study the impact of these coherent flows, we performed high-resolution N-body plus smoothed particle hydrodynamic simulations in boxes of 5.0 and 0.7 Mpc h−1, for bulk-flow velocities of 0 (as reference), 30 and 60 km s−1. The simulations follow the evolution of cosmic structures by taking into account detailed, primordial, non-equilibrium gas chemistry (i.e. H, He, H2, HD, HeH, etc.), cooling, star formation and feedback effects from stellar evolution. We find that these bulk flows suppress star formation in low-mass haloes (i.e. Mvir≲ 108 M⊙ until z ∼ 13), lower the abundance of the first objects by ∼1–20 per cent and as a consequence delay cosmic star formation history by ∼2 × 107 yr. The gas fractions in individual objects can change by up to a factor of 2 at very early times. Coherent bulk flow therefore has implications for (i) the star formation in the lowest-mass haloes (e.g. dSphs); (ii) the start of reionization by suppressing it in some patches of the Universe; and (iii) the heating (i.e. spin temperature) of neutral hydrogen. We speculate that the patchy nature of reionization and heating on several Mpc scales could lead to enhanced differences in the H i spin temperature, giving rise to stronger variations in the H i brightness temperatures during the late dark ages.