We outline the construction of metastable de Sitter vacua of type IIB string theory. Our starting point is highly warped IIB compactifications with nontrivial NS and RR three-form fluxes. By incorporating known corrections to the superpotential from Euclidean D-brane instantons or gaugino condensation, one can make models with all moduli fixed, yielding a supersymmetric AdS vacuum. Inclusion of a small number of $\overline{\mathrm{D}3}$-branes in the resulting warped geometry allows one to uplift the AdS minimum and make it a metastable de Sitter ground state. The lifetime of our metastable de Sitter vacua is much greater than the cosmological time scale of ${10}^{10}\mathrm{yr}.$ We also prove, under certain conditions, that the lifetime of dS space in string theory will always be shorter than the recurrence time.

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De Sitter vacua in string theory

Modified gravity theories have received increased attention lately due to combined motivation coming from high-energy physics, cosmology, and astrophysics. Among numerous alternatives to Einstein's theory of gravity, theories that include higher-order curvature invariants, and specifically the particular class of $f(R)$ theories, have a long history. In the last five years there has been a new stimulus for their study, leading to a number of interesting results. Here $f(R)$ theories of gravity are reviewed in an attempt to comprehensively present their most important aspects and cover the largest possible portion of the relevant literature. All known formalisms are presented---metric, Palatini, and metric affine---and the following topics are discussed: motivation; actions, field equations, and theoretical aspects; equivalence with other theories; cosmological aspects and constraints; viability criteria; and astrophysical applications.

f ( R ) theories of gravity

Modified Gravity and Cosmology

Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models

Over the past decade, f(R) theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various applications of f(R) theories to cosmology and gravity - such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds. We present a number of ways to distinguish those theories from General Relativity observationally and experimentally. We also discuss the extension to other modified gravity theories such as Brans-Dicke theory and Gauss-Bonnet gravity, and address models that can satisfy both cosmological and local gravity constraints.

f(R) theories

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 de Sitter space 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 Poincar? recurrence time. This is supported by recent results of Kachru, Kallosh, Linde and Trivedi.

https://iopscience.iop.org/article/10.1088/1126-6708/2003/07/056/pdf

The trouble with de Sitter space

We show that within the class of $f(R)$ gravity theories, Friedmann-Lema\^{\i}tre-Robertson-Walker 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.

Power-law cosmic expansion in f ( R ) gravity 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) = Rn 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 a future bounce, a phenomenon which is absent in general relativity.

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

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{sub s}{sup 2}>({radical}(5)-1/6){approx_equal}0.21. This result is remarkably similar to the general relativity case, where it was found that the Einstein static model is stable for c{sub s}{sup 2}>(1/5)

Existence of Einstein static universes and their stability in fourth-order theories of gravity

Recently, spatially inhomogeneous cosmological models have been proposed as an alternative to the ΛCDM model, with the aim of reproducing the late time dynamics of the Universe without introducing a cosmological constant or dark energy. This paper investigates the possibility of distinguishing such models from the standard ΛCDM using background or large scale structure data. It also illustrates and emphasizes the necessity of testing the Copernican principle in order to confront the tests of general relativity with the large scale structure.

http://iopscience.iop.org/article/10.1088/1475-7516/2010/06/017/pdf

Naureen Goheer

Papers

The trouble with de Sitter space

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

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

Existence of Einstein static universes and their stability in fourth-order theories of gravity

How close can an Inhomogeneous Universe mimic the Concordance Model