Aindriú Conroy

Nonlocal gravity in D dimensions: Propagators, entropy, and a bouncing cosmology

We present the graviton propagator for an infinite derivative, D-dimensional, nonlocal action, up to quadratic order in curvature around a Minkowski background, and discuss the conditions required for this class of gravity theory to be ghost-free. We then study the gravitational entropy for de-Sitter and anti-de Sitter backgrounds, before comparing with a recently derived result for a Schwarzschild black hole, generalized to arbitrary D dimensions, whereby the entropy is given simply by the area law. A novel approach of decomposing the entropy into its (r,t) and spherical components is adopted in order to illustrate the differences more clearly. We conclude with a discussion of de-Sitter entropy in the framework of a nonsingular bouncing cosmology.

Geodesic completeness and homogeneity condition for cosmic inflation

There are two disjointed problems in cosmology within General Relativity (GR), which can be addressed simultaneously by studying the nature of geodesics around

Wald Entropy for Ghost-Free, Infinite Derivative Theories of Gravity

t\rightarrow 0

Defocusing of Null Rays in Infinite Derivative Gravity

, where

Newtonian Potential and Geodesic Completeness in Infinite Derivative Gravity

t

Criteria for resolving the cosmological singularity in Infinite Derivative Gravity around expanding backgrounds

is the physical time. One is related to the past geodesic completeness of the inflationary trajectory due to the presence of a cosmological singularity, and the other one is related to the homogeneity condition required to inflate a local space-time patch of the universe. We will show that both the problems have a common origin, arising from how the causal structure of null and timelike geodesics are structured within GR. In particular, we will show how a non-local extension of GR can address both problems, while satisfying the null energy condition for the matter sources.

Generalized ghost-free quadratic curvature gravity

In this Letter, we demonstrate that the Wald entropy for any spherically symmetric black hole within an infinite derivative theory of gravity that is quadratic in curvature is determined solely by the area law. Thus, the infrared behavior of gravity is captured by the Einstein-Hilbert term, provided that the massless graviton remains the only propagating degree of freedom in the spacetime.

Generalized quadratic curvature, non-local infrared modifications of gravity and Newtonian potentials

Einsteins General theory of relativity permits spacetime singularities, where null geodesic congruences focus in the presence of matter, which satisfies an appropriate energy condition. In this paper, we provide a minimal defocusing condition for null congruences without assuming any Ansatz-dependent background solution. The two important criteria are: (1) an additional scalar degree of freedom, besides the massless graviton must be introduced into the spacetime; and (2) an infinite derivative theory of gravity is required in order to avoid tachyons or ghosts in the graviton propagator. In this regard, our analysis strengthens earlier arguments for constructing non-singular bouncing cosmologies within an infinite derivative theory of gravity, without assuming any Ansatz to solve the full equations of motion.

Corrigendum: Generalized ghost-free quadratic curvature gravity (2014 Class. Quantum Grav. 31 015022)

Recent study has shown that a nonsingular oscillating potential—a feature of infinite derivative gravity theories—matches current experimental data better than the standard General Relativity potential. In this work, we show that this nonsingular oscillating potential can be given by a wider class of theories which allows the defocusing of null rays and therefore geodesic completeness. We consolidate the conditions whereby null geodesic congruences may be made past complete, via the Raychaudhuri equation, with the requirement of a nonsingular Newtonian potential in an infinite derivative gravity theory. In doing so, we examine a class of Newtonian potentials characterized by an additional degree of freedom in the scalar propagator, which returns the familiar potential of General Relativity at large distances.

Criteria for resolving the cosmological singularity in Infinite Derivative Gravity

Einsteins General theory of relativity permits space-time singularities, where null congruences \emph{focus} in the presence of matter, which satisfies an appropriate energy condition. In this paper, we argue that such a singularity may be avoided if two important criteria are satisfied: (1) An additional scalar degree of freedom, besides the massless graviton, must be introduced to the spacetime; and (2) An infinite-derivative extension is required in order to avoid tachyons or ghosts from the graviton propagator.