We give a rigorous and mathematically well defined presentation of the Covariant and Gauge Invariant theory of scalar perturbations of a Friedmann-Lemaitre-Robertson-Walker universe for Fourth Order Gravity, where the matter is described by a perfect fluid with a barotropic equation of state. The general perturbations equations are applied to a simple background solution of R^n gravity. We obtain exact solutions of the perturbations equations for scales much bigger than the Hubble radius. These solutions have a number of interesting features. In particular, we find that for all values of n there is always a growing mode for the density contrast, even if the universe undergoes an accelerated expansion. Such a behaviour does not occur in standard General Relativity, where as soon as Dark Energy dominates, the density contrast experiences an unrelenting decay. This peculiarity is sufficiently novel to warrant further investigation on fourth order gravity models.
As massive gravity and its extensions offer physically well-defined gravitational theories with a nonzero graviton mass, we present a new extension of the de Rham-Gabadadze-Tolley (dRGT)massive gravity, which is tachyonic massive gravity theory. We firstly introduce the new extension of the dRGT massive gravity, constructed by adding a tachyonic term. We then find the cosmological background equations, and present the analysis of self-accelerating solutions. We examine the tensor perturbations to calculate the dispersion relation of gravitational waves (GWs). In a special case, we consider a c…
We present a well-posed constraint-preserving scheme for evolving first-order metric perturbations on an arbitrary background with arbitrary source. We use this scheme to evolve the leading-order metric perturbation in order-reduced dynamical Chern-Simons gravity (dCS) on a Kerr background. In particular we test the stability of stationary dCS data on a Kerr background with stationary first-order dCS scalar field source. We find that the leading-order metric perturbation numerically exhibits linear growth, but that the level of this growth converges to zero with numerical resolution. This anal…
We present the cosmological analysis of the Gauss-Bonnet quasi-dilaton massive gravity theory. This offers a gravitational theory with a non-zero graviton mass. We calculate the complete set of background equations of motion. Also, we obtain the self-accelerating background solutions and we present the constraints on parameters to indicate the correct sign of parameters. In addition, we analyse tensor perturbations and calculate the mass of graviton and find the dispersion relation of gravitational waves for two cases. Finally, we investigate the propagation of gravitational perturbation in th…
We discuss the linear perturbation equations with the synchronous gauge in a minimal scenario of the bimetric massive gravity theory. We find that the matter density perturbation and matter power spectrum are suppressed. We also examine the ghost and stability problems and show that the allowed deviation of this gravitational theory from the cosmological constant is constrained to be smaller than $\mathcal{O}(10^{-2})$ by the large scale structure observational data.
Cosmological perturbations are considered in $f(T)$ and in scalar-torsion $f(φ)T$ teleparallel models of gravity. Full sets of linear perturbation equations are accurately derived and analysed at the relevant limits. Interesting features of generalisations to other teleparallel models, spatially curved backgrounds, and rotated tetrads are pointed out.
Teleparallel gravity offers a new avenue in which to construct gravitational models beyond general relativity. While teleparallel gravity can be framed in a way to be dynamically equivalent to general relativity, its modifications are mostly not equivalent to the traditional route to modified gravity. $f(T,B)$ gravity is one such gravitational theory where the second and fourth order contributions to the field equations are decoupled. In this work, we explore the all important cosmological perturbations of this new framework of gravity. We derive the gravitational propagation equation, its vec…
We discuss linear perturbations of the most general class of teleparallel spacetimes with cosmological symmetry, and perform a decomposition of these perturbations into irreducible components. We then study their behavior under gauge transformations, i.e., infinitesimal diffeomorphisms of the background spacetime, and derive a full set of gauge-invariant perturbation variables. Comparing our results with perturbations around the diagonal tetrad corresponding to a spatially flat teleparallel background cosmology, we see the appearance of new terms which depend on the particular choice of a cosm…
The study of cosmological perturbation theory in $f(T)$ gravity is a topic of great interest in teleparallel gravity since this is one of the simplest generalizations of the theory that modifies the teleparallel equivalent of general relativity. In this work, we explore the possibility of a non-flat FLRW background solution and perform perturbations for positively as well as negatively curved spatial geometries, together with a comparison to the flat case. We determine the generalized behaviour of the perturbative modes for this non-flat FLRW setting for arbitrary $f(T)$ models, when the most …
We derive an effective dynamics for scalar cosmological perturbations from quantum gravity, in the framework of group field theory (GFT) condensate cosmology. The emergent spacetime picture is obtained from the mean field hydrodynamic regime of the fundamental theory, and physical observables are defined using a relational strategy applied at the same level of approximation, in terms of suitable collective states of the GFT field. The dynamical equations we obtain for volume and matter perturbations lead to the same solutions as those of classical general relativity in the long-wavelength, sup…
We study the scalar perturbation on the background of a Kerr black hole in the dynamical Chern-Simons modified gravity with a quadratic coupling between the scalar field and Chern-Simons term. In particular, the late-time tails of scalar perturbations are investigated numerically in time domain by using the hyperboloidal foliation method. It is found that the Kerr black hole becomes unstable under linear perturbations in a certain region of the parameter space, which depends on the harmonic azimuthal index $m$ of the perturbation's mode. This may indicate that some Kerr black holes in this the…
We study the linear perturbations about a nonrotating black hole solution of Horndeski's theory, using a systematic approach that extracts the asymptotic behaviour of perturbations (at spatial infinity and near the horizon) directly from the first-order radial differential system governing these perturbations instead of finding Schrödinger-like equations for their dynamics. We illustrate this method in the case of a specific black hole solution. The knowledge of the asymptotic behaviours of the perturbations paves the way for a numerical computation of the quasinormal modes. Finally, the asymp…
The parity violating gravity models based on the symmetric teleparallel gravity have been considered in the literature, but their applications in cosmology and especially the modifications to cosmological perturbations have not been fully explored. In this paper we consider such a simple model which modifies general relativity by a parity non-conserved coupling, within the framework of the symmetric teleparallel gravity. We study in detail its cosmological applications and focus on its cosmological perturbation theory. Besides the already known parity violation in the tensor perturbations, we …
We apply the full theory of Loop Quantum Gravity (LQG) to cosmology and present a top-down derivation of gauge-invariant cosmological perturbation theory from quantum gravity. The derivation employs the reduced phase space formulation of LQG and the new discrete path integral formulation defined in arXiv:1910.03763. We demonstrate that in the semiclassical approximation and continuum limit, the result coincides with the existing formulation of gauge-invariant cosmological perturbation theory in e.g. arXiv:0711.0117. Time evolution of cosmological perturbations is computed numerically from the …
Cosmological Perturbation Theory to second order for curvature, density, and gravity waves on FRW background; and the WMAP results of inhomogeneity and clustering in the early universe
