Metric theories of gravity are studied, beginning with a general action that is quadratic in curvature and allows arbitrary inverse powers of the d'Alembertian operator, resulting in infrared non-local extensions of general relativity. The field equations are derived in full generality and their consistency is checked by verifying the Bianchi identities. The weak-field limit is computed and a straightforward algorithm is presented to infer the post-Newtonian corrections directly from the action. This is then applied to various infrared gravity models including non-local Rf (R/ ) dark energy and non-local massive gravity models. Generically, the Newtonian potentials are not identical and deviate from the 1/r behaviour at large distances. However, the former does not occur in a specific class of theories that does not introduce additional degrees of freedom in flat spacetime. A new non-local model within this class is proposed, defined by the exponential of the inverse d'Alembertian. This model exhibits novel features, such as the weakening of the gravity in the infrared, suggesting de-gravitation of the cosmological constant.

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.

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In this paper we wish to find the corresponding Gibbons-Hawking-York term for the most general quadratic in curvature gravity by using Coframe slicing within the Arnowitt-Deser-Misner (ADM) decomposition of spacetime in four dimensions. In order to make sure that the higher derivative gravity is ghost and tachyon free at a perturbative level, one requires infinite covariant derivatives, which yields a generalised covariant infinite derivative theory of gravity. We will be exploring the boundary term for such a covariant infinite derivative theory of gravity.

We study the correlators of two circular Wilson loops of different radii at strong coupling. In our setup one Wilson loop is located inside the other. We use holography to calculate the connected two-point function. Both an AdS background and a confining background are considered. As the computation for the confining case cannot be carried out analytically we solve the problem numerically. In the AdS case our results agree with similar holographic calculations. In the case of a confining background we find an asymptotic area law, in agreement with the result of the lattice strong coupling expansion. We also elaborate on the subtle issue of the interplay between connected and disconnected string worldsheets.