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

We show that within the class of f(R) gravity theories, FLRW power-law perfect fluid solutions only exist for R^n gravity. This significantly restricts the set of exact cosmological solutions which have similar properties to what is found in standard General Relativity.Comment: 4 pages, 2 figure

1+1 Dimensional Compactifications of String Theory

We argue that stable, maximally symmetric compactifications of string theory to 1+1 dimensions are in conflict with holography. In particular, the finite horizon entropies of the Rindler wedge in 1+1 dimensional Minkowski and anti de Sitter space, and of the de Sitter horizon in any dimension, are inconsistent with the symmetries of these spaces. The argument parallels one made recently by the same authors, in which we demonstrated the incompatibility of the finiteness of the entropy and the symmetries of de Sitter space in any dimension. If the horizon entropy is either infinite or zero the conflict is resolved.Comment: 11 pages, 2 figures v2: added discussion of AdS_2 and comment

The Existence of Einstein Static Universes and their Stability in Fourth order Theories of Gravity

We investigate whether or not an Einstein Static universe is a solution to the cosmological equations in $f(R)$ gravity. It is found that only one class of $f(R)$ theories admits an Einstein Static model, and that this class is neutrally stable with respect to vector and tensor perturbations for all equations of state on all scales. Scalar perturbations are only stable on all scales if the matter fluid equation of state satisfies $c_s^2>\frac{\sqrt{5}-1}{6}\approx 0.21$. This result is remarkably similar to the GR case, where it was found that the Einstein Static model is stable for $c_s^2>{1/5}$.Comment: Minor changes, To appear in PR

Large-scale perturbations on the brane and the isotropy of the cosmological singularity

We present the complete set of propagation and constraint equations for the kinematic and non-local first order quantities which describe general linear inhomogeneous and anisotropic perturbations of a flat FRW braneworld with vanishing cosmological constant and decompose them in the standard way into their scalar, vector and tensor contributions. A detailed analysis of the perturbation dynamics is performed using dimensionless variables that are specially tailored for the different regimes of interest; namely, the low energy GR regime, the high energy regime and the dark energy regime. Tables are presented for the evolution of all the physical quantities, making it easy to do a detailed comparison of the past asymptotic behaviour of the perturbations of these models. We find results that exactly match those obtained in the analysis of the spatially inhomogeneous $G_{2}$ braneworld cosmologies presented recently; i.e., that isotropization towards the ${\cal F}_b$ model occurs for $\gamma > 4/3$.Comment: 13 pages, revtex

Are braneworlds born isotropic?

It has recently been suggested that an isotropic singularity may be a generic feature of brane cosmologies, even in the inhomogeneous case. Using the covariant and gauge-invariant approach we present a detailed analysis of linear perturbations of the isotropic model ${\cal F}_b$ which is a past attractor in the phase space of homogeneous Bianchi models on the brane. We find that for matter with an equation of state parameter $\gamma > 1$, the dimensionless variables representing generic anisotropic and inhomogeneous perturbations decay as $t\to 0$, showing that the model ${\cal F}_b$ is asymptotically stable in the past. We conclude that brane universes are born with isotropy naturally built-in, contrary to standard cosmology. The observed large-scale homogeneity and isotropy of the universe can therefore be explained as a consequence of the initial conditions if the brane-world paradigm represents a description of the very early universe.Comment: Changed to match published versio

Dynamics of f(R)-cosmologies containing Einstein static models

We study the dynamics of homogeneous isotropic FRW cosmologies with positive spatial curvature in $f(R)$-gravity, paying special attention to the existence of Einstein static models and only study forms of $f(R)=R^n$ for which these static models have been shown to exist. We construct a compact state space and identify past and future attractors of the system and recover a previously discovered future attractor corresponding to an expanding accelerating model. We also discuss the existence of universes which have both a past and future bounce, a phenomenon which is absent in General Relativity.Comment: 14 pages, 6 figure

Braneworld Dynamics of Inflationary Cosmologies with Exponential Potentials

In this work we consider Randall-Sundrum braneworld type scenarios, in which the spacetime is described by a five-dimensional manifold with matter fields confined in a domain wall or three-brane. We present the results of a systematic analysis, using dynamical systems techniques, of the qualitative behaviour of Friedmann-Lemaitre-Robertson-Walker type models, whose matter is described by a scalar field with an exponential potential. We construct the state spaces for these models and discuss how their structure changes with respect to the general-relativistic case, in particular, what new critical points appear and their nature and the occurrence of bifurcation.Comment: 15 pages, 9 figures, RevTex 4. Submitted to Physical Review

The Trouble with de Sitter Space

In this paper we assume the de Sitter Space version of Black Hole Complementarity which states that a single causal patch of de Sitter space is described as an isolated finite temperature cavity bounded by a horizon which allows no loss of information. We discuss the how the symmetries of de Sitter space should be implemented. Then we prove a no go theorem for implementing the symmetries if the entropy is finite. Thus we must either give up the finiteness of the de Sitter entropy or the exact symmetry of the classical space. Each has interesting implications for the very long time behavior. We argue that the lifetime of a de Sitter phase can not exceed the Poincare recurrence time. This is supported by recent results of Kachru, Kallosh, Linde and Trivedi.Comment: 15 pages, 1 figure. v2: added fifth section with comments on long time stability of de Sitter space, in which we argue that the lifetime can not exceed the Poincare recurrence time. v3: corrected a minor error in the appendi

Compactifying the state space for alternative theories of gravity

In this paper we address important issues surrounding the choice of variables when performing a dynamical systems analysis of alternative theories of gravity. We discuss the advantages and disadvantages of compactifying the state space, and illustrate this using two examples. We first show how to define a compact state space for the class of LRS Bianchi type I models in $R^n$-gravity and compare to a non--compact expansion--normalised approach. In the second example we consider the flat Friedmann matter subspace of the previous example, and compare the compact analysis to studies where non-compact non--expansion--normalised variables were used. In both examples we comment on the existence of bouncing or recollapsing orbits as well as the existence of static models.Comment: 18 pages, revised to match published versio