Peter K. S. Dunsby

Cosmological perturbations and the physical meaning of gauge invariant variables

This paper concerns gauge-invariant perturbations of Robertson-Walker spacetimes, with the aim of (1) giving a complete set of perturbation equations and (2) comparing the coordinate-based method of Bardeen with the covariant approach of Ellis & Bruni. To this end, we first consider covariantly defined quantities which are gauge-invariant in a perturbed Robertson-Walker universe; for these variables we derive a complete set of covariant linearized equations as they follow from the Bianchi and Ricci identities, and we show various possible ways of obtaining a second-order linear equation for the density perturbation variables

Evolution of density perturbations in f(R) gravity

We give a rigorous and mathematically well defined presentation of the covariant and gauge invariant theory of scalar perturbations of a Friedmann-Lema\^{\i}tre-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

Cosmological dynamics of Rn gravity

{R}^{n}

Some remarks on the dynamical systems approach to fourth order gravity

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

Power-law cosmic expansion in f(R) gravity models

n

On the LCDM Universe in f(R) gravity

there is always a growing mode for the density contrast, even if the universe undergoes an accelerated expansion. Such behavior 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 of fourth order gravity models.

Cosmological dynamics of scalar-tensor gravity

A detailed analysis of dynamics of cosmological models based on Rn gravity is presented. We show that the cosmological equations can be written as a first-order autonomous system and analysed using the standard techniques of dynamical system theory. In the absence of perfect fluid matter, we find exact solutions whose behaviour and stability are analysed in terms of the values of the parameter n. When matter is introduced, the nature of the (non-minimal) coupling between matter and higher order gravity induces restrictions on the allowed values of n. Selecting such intervals of values and following the same procedure used in the vacuum case, we present exact solutions and analyse their stability for a generic value of the parameter n. From this analysis emerges the result that for a large set of initial conditions an accelerated expansion is an attractor for the evolution of the Rn cosmology. When matter is considered a transient almost-Friedman phase can also be present before the transition to accelerated expansion.

Cosmological dynamics of R**n gravity

Building on earlier work, we discuss a general framework for exploring the cosmological dynamics of Higher Order Theories of Gravity. We show that once the theory of gravity has been specified, the cosmological equations can be written as a first-order autonomous system and we give several examples which illustrate the utility of our method. We also discuss a number of results which have appeared recently in the literature.

How close can an inhomogeneous universe mimic the concordance model

We show that within the class of f(R) gravity theories, Friedmann-Lemaitre-Robertson-Walker power-law perfect fluid solutions only exist for R{sup n} gravity. This significantly restricts the set of exact cosmological solutions which have similar properties to what is found in standard general relativity.

Coexistence of matter dominated and accelerating solutions in f ( G ) gravity

Several different explicit reconstructions of f(R) gravity are obtained from the background Friedmann-Laimatre-Robertson-Walker expansion history. It is shown that the only theory whose Lagrangian is a simple function of the Ricci scalar R, that admits an exact {Lambda}CDM expansion history, is standard general relativity with a positive cosmological constant and the only way to obtain this behavior of the scale factor for more general functions of R is to add additional degrees of freedom to the matter sector.