Primordial bouncing cosmology in the Deser-Woodard nonlocal gravity

The Deser-Woodard (DW) nonlocal gravity model has been proposed in order to describe the late-time acceleration of the universe without introducing dark energy. In this paper we focus, however, on the early stage of the universe and demonstrate how a primordial bounce in the vacuum spacetime can be realized in the framework of the DW nonlocal model. We reconstruct the nonlocal distortion function, which encodes all the modifications to the Einstein-Hilbert action, in order to generate bouncing solutions to solve the initial singularity problem. We show that the initial conditions can be chosen in such a way that the distortion function and its first order derivative approach zero after the bounce and the standard cosmological solution described by general relativity is recovered afterwards. We also study the evolution of anisotropies near the bounce. It turns out that the shear density defined by the anisotropy grows towards the bounce, but due to the presence of nonlocal effects, it grows in a milder manner compared with that in Einstein gravity.