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

Abstract

We present the graviton propagator for an infinite derivative, D-dimensional, non-local 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 blackhole, generalised 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 non-singular bouncing cosmology.

Newtonian potential and geodesic completeness in infinite derivative gravity

“…We describe the relationship between a( ) and c( ) using (10), and by inserting (10) into (19) we find that…”

“…The full non-linear equations of motion were computed in [17] and the boundary terms found in [18]. The gravitational entropy for the IDG action was investigated around an (A)dS metric in [19], while the form of the (A)dS propagator was given in [20]. Constraints were put on the mass scale M of IDG, either by using data on the tensorscalar ratio and spectral tilt of the Cosmic Microwave Background [21], or by looking at the deflection of light around the Sun [22].…”

Infinite derivative gravity: non-singular cosmology & blackhole solutions

“…V µν Π αβ µν V αβ , where V 's are the conserved vertices. Here, I summarise the results for the propagator Π without the spacetime indices, which can be expressed in terms of the Fourier space, by [18,20,26] …”

“…Quantum-loop corrections will not ruin this property due to diffeomorphism invariance 8 . This analysis has been extended to arbitrary d spacetime dimensions [26], and also around dS and AdS backgrounds [21,22]. Note that the exponentially suppressed 2.…”

Generalised boundary terms for higher derivative theories of gravity

“…In such classes of theory, the gravitational entropy [49][50][51][52], of a static and axisymmetric metric receives zero contribution from the infinite derivative sector of the action, when no additional scalar propagating modes are introduced. In this case, the gravitational entropy is strictly given by the area-law arising solely from the contribution of the Einstein-Hilbert action [53,54].…”