Aspects of Ultraviolet Non-local Gravity

The objective of this thesis is to introduce ultraviolet (UV) non-local gravity and dis- cuss some new results in it. Motivated from approaches to quantum gravity like string theory, this is a higher derivative modification of General Relativity (GR) which aims to provide a softer description of gravity at short distances, while simultaneously keeping at bay the typical illnesses that accompany higher derivative theories. The derivatives appearing in the action are of infinite order, making the theory ‘non-local’. Moreover, it is ‘UV’ because the derivatives modify gravity at high energies, while recovering GR at low energies. We discuss how such theories 1) possess linearized solutions with non- divergent gravitational potentials and curvatures, 2) admit non-maximally symmetric backgrounds which are stable (free from ghosts/tachyons) under perturbations, 3) ad- mit non-singular, isotropic and homogeneous bouncing cosmological solutions with sta- ble perturbations and 4) admit non-singular, anisotropic and homogeneous bouncing cosmological solutions where, unlike in GR, there is no unstable growth of spacetime anisotropies during the contraction phase of the universe, and isotropy and homogeneity is recovered at late times during the expanding phase.