Perturbations In Cosmological Models Research Articles

Cosmological perturbation theory in generalized Einstein-Aether models

We investigate the evolution of cosmological perturbations in models of dark energy described by a timelike unit normalized vector field specified by a general function $\mathcal{F}(\mathcal{K})$, so-called generalized Einstein-Aether models. First we study the background dynamics of such models via a designer approach in an attempt to model this theory as dark energy. We find that only one specific form of this designer approach matches $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ at background order, and we also obtain a differential equation which $\mathcal{F}(\mathcal{K})$ must satisfy for general $w\mathrm{CDM}$ cosmologies, where CDM refers to cold dark matter. We also present the equations of state for perturbations in generalized Einstein-Aether models, which completely parametrize these models at the level of linear perturbations. A generic feature of modified gravity models is that they introduce new degrees of freedom. By fully eliminating these we are able to express the gauge invariant entropy perturbation and the scalar, vector, and tensor anisotropic stresses in terms of the perturbed fluid variables and metric perturbations only. These can then be used to study the evolution of perturbations in the scalar, vector, and tensor sectors, and we use these to evolve the Newtonian gravitational potentials.

Perturbations of ultralight vector field dark matter

We study the dynamics of cosmological perturbations in models of dark matter based on ultralight coherent vector fields. Very much as for scalar field dark matter, we find two different regimes in the evolution: for modes with {k}^2ll mathrm{mathscr{H}}ma , we have a particle-like behaviour indistinguishable from cold dark matter, whereas for modes with {k}^2gg mathrm{mathscr{H}}ma , we get a wave-like behaviour in which the sound speed is non-vanishing and of order cs2 ≃ k2/m2a2. This implies that, also in these models, structure formation could be suppressed on small scales. However, unlike the scalar case, the fact that the background evolution contains a non-vanishing homogeneous vector field implies that, in general, the evolution of the three kinds of perturbations (scalar, vector and tensor) can no longer be decoupled at the linear level. More specifically, in the particle regime, the three types of perturbations are actually decoupled, whereas in the wave regime, the three vector field perturbations generate one scalar-tensor and two vector-tensor perturbations in the metric. Also in the wave regime, we find that a non-vanishing anisotropic stress is present in the perturbed energy-momentum tensor giving rise to a gravitational slip of order (Φ − Ψ)/Φ ∼ cs2. Moreover in this regime the amplitude of the tensor to scalar ratio of the scalar-tensor modes is also h/Φ ∼ cs2. This implies that small-scale density perturbations are necessarily associated to the presence of gravity waves in this model. We compare their spectrum with the sensitivity of present and future gravity waves detectors.

Observational Constraints on Tensor Perturbations in Cosmological Models with Dynamical Dark Energy

We constrain the contribution of tensor-mode perturbations with free $n_t$ in the models with dynamical dark energy with the barotropic equation of state using Planck-2015 data on CMB anisotropy, polarization and lensing, BICEP2/Keck Array data on B-mode polarization, power spectrum of galaxies from WiggleZ and SN Ia data from the JLA compilation. We also investigate the uncertainties of reconstructed potential of the scalar field dark energy.

Scalar perturbations in cosmological models with dark energy-dark matter interaction

Scalar cosmological perturbations are investigated in the framework of a model with interacting dark energy and dark matter. In addition to these constituents, the inhomogeneous Universe is supposed to be filled with the standard noninteracting constituents corresponding to the conventional ΛCDM model. The interaction term is chosen in the form of a linear combination of dark sector energy densities with evolving coefficients. The methods of discrete cosmology are applied, and strong theoretical constraints on the parameters of the model are derived. A brief comparison with observational data is performed.

Scalar perturbations in cosmological models with quark nuggets

In this paper we consider the Universe at the late stage of its evolution and deep inside the cell of uniformity. At these scales, the Universe is filled with inhomogeneously distributed discrete structures (galaxies, groups and clusters of galaxies). Supposing that a small fraction of colored objects escaped hadronization and survived up to now in the form of quark-gluon nuggets (QNs), and also taking into account radiation, we investigate scalar perturbations of the FRW metrics due to inhomogeneities of dustlike matter as well as fluctuations of QNs and radiation. In particular, we demonstrate that the nonrelativistic gravitational potential is defined by the distribution of inhomogeneities/fluctuations of both dustlike matter and QNs. Consequently, QNs can be distributed around the baryonic inhomogeneities (e.g., galaxies) in such a way that it can solve the problem of the flatness of the rotation curves. We also show that the fluctuations of radiation are caused by both the inhomogeneities in the form of galaxies and the fluctuations of quark-gluon nuggets. Therefore, if QNs exist, the CMB anisotropy should contain also the contributions from QNs. Additionally, the spatial distribution of the radiation fluctuations is defined by the gravitational potential. All these results look physically reasonable.

High frequency limit for gravitational perturbations of cosmological models in modified gravity theories

In general relativity, it has been shown that the effective gravitational stress-energy tensor for short-wavelength metric perturbations acts just like that for a radiation fluid, and thus, in particular, cannot provide any effects that mimic dark energy. However, it is far from obvious if this property of the effective gravitational stress-energy tensor is a specific nature held only in the Einstein gravity, or holds also in other theories of gravity. In particular, when considering modified gravity theories that involve higher order derivative terms, one may expect to have some non-negligible effects arising from higher order derivatives of short-wavelength perturbations. In this paper, we argue this is not the case at least in the cosmological context. We show that when the background, or coarse-grained metric averaged over several wavelengths has FLRW symmetry, the effective gravitational stress-energy tensor for metric perturbations of a cosmological model in a simple class of f(R) gravity theories, as well as that obtained in the corresponding scalar-tensor theory, takes a similar form to that in general relativity and is in fact traceless, hence acting again like a radiation fluid.

Cosmological perturbations in SFT inspired non-local scalar field models

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.

Density perturbations in a finite scale factor singularity universe

We discuss evolution of density perturbations in cosmological models which admit finite scale factor singularities. After solving the matter perturbations equations we find that there exists a set of the parameters which admit a finite scale factor singularity in future and instantaneously recover matter density evolution history which are indistinguishable from the standard LCDM scenario.

The importance of slow-roll corrections during multi-field inflation

We re-examine the importance of slow-roll corrections during the evolution of cosmological perturbations in models of multi-field inflation. We find that in many instances the presence of light degrees of freedom leads to situations in which next to leading order slow-roll corrections become significant. Examples where we expect such corrections to be crucial include models in which modes exit the Hubble radius while the inflationary trajectory undergoes an abrupt turn in field space, or during a phase transition. We illustrate this with several examples — hybrid inflation, double quadratic inflation and double quartic inflation. Utilizing both analytic estimates and full numerical results, we find that corrections can be as large as 20%. Our results have implications for many existing models in the literature, as these corrections must be included to obtain accurate observational predictions — particularly given the level of accuracy expected from CMB experiments such as Planck.

Analysis of scalar perturbations in cosmological models with a non-local scalar field

We develop the cosmological perturbations formalism 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 in the presence of arbitrary potential and formulate the local system of equations for perturbations in the linearized model when both simple and double roots of the characteristic equation are present. We carry out the general analysis related to the curvature and entropy perturbations and consider the most specific example of perturbations when important quantities in the model become complex.

Cosmological perturbations in models of coupled dark energy

Models in which dark energy interacts with dark matter have been proposed in the literature to help explain why dark energy should only come to dominate in recent times. In this paper, we present a dynamical framework to calculate cosmological perturbations for a general quintessence potential and interaction term. Our formalism is built upon the powerful phase-space approach often used to analyze the dynamical attractors in the background. We obtain a set of coupled differential equations purely in terms of dimensionless, bounded variables and apply these equations to calculate perturbations in a number of scenarios. Interestingly, in the presence of dark-sector interactions, we find that dark energy perturbations do not redshift away at late times, but can cluster even on small scales. We also clarify the initial conditions for the perturbations in the dark sector, showing that adiabaticity is no longer conserved in the presence of dark-sector interactions, even on large scales. Some issues of instability in the perturbations are also discussed.

Aspects of nonlinear perturbations in cosmological models

Nonlinearities in the perturbations of the cosmological models may be important. This paper briefly reviews three cases in which we have studied the effects of such nonlinearities. In de Sitter spacetime, the bare necessity that the perturbations should be a part of a consistent expansion of the field equations leads to the requirement, using the so-called linearization stability arguments developed in the 1970s, that the quantum field theory of a scalar field on de Sitter spacetime should de Sitter invariant—not covariant. In other words, all states of the field should be de Sitter invariant. For the Einstein static universe these constraints lead to the conclusion that all pertubations are unstable. This follows from the requirement that all perturbations must include the homogeneous mode at equal amplitude to the other modes if the linearization stabilty constraints are to be satisfied. Finally, the concern that the effect of second-order perturbations on the long-wavelength (super-Hubble modes) perturbations could be much stronger than that of the first-order perturbations for a large range of slow-roll conditions was explored. While this result is gauge dependent, and is the result of a variety of poorly controlled approximations (in particular, in the handling of the ultraviolet divergences) it is worrying in its implications for the conclusions drawn from the various inflationary scenarios.

Density perturbations in cosmological models

An explicitly coordinate-independent method, based on previous work by Hawking, is used to study linearized density perturbations of k=0 Friedmann cosmological models.Received 19 April 1976DOI:https://doi.org/10.1103/PhysRevD.14.327©1976 American Physical Society

Density perturbations in cosmological models

Differential equations are derived, following the methods ofLifshitz (1946) andLifshitz andKhalatnikov (1963), for density perturbations in isotropic, spatially homogeneous cosmological models of arbitrary space curvature. The unperturbed models contain both matter and radiation. An explicit third-order equation is obtained for the time development of the perturbations, and it is shown that one of the solutions is not covariantly defined. The two remaining solutions are compared with existing solutions for the limiting cases of radiation-filled and dust-filled models. The results ofBonnor's (1957) Newtonian analysis are shown to be a valid limiting case of our equation when the pressurep is finite, but small compared with the densityp timesc 2. A detailed analysis is given of a model containing coupled radiation (p=pc 2/3) and dust (p=0). It is shown that density perturbations with long wavelengths are unstable (with slow growth rate) for all time. The instability exists because for a long-wavelength disturbance, the time scale governing the propagation of pressure effects (which stabilize perturbations) is longer than the time scale for which pressure falls to the point of ineffectiveness. The present value of the critical wavelength is ∼60 Mpc in models based on flat space sections in which the present background radiation temperature is 3 °K.