Nonlocal gravity and the diffusion equation

TL;DR

This paper introduces a nonlocal gravity model inspired by string theory, using pseudodifferential operators, and finds exact cosmological solutions including bounces and singularities.

Contribution

It develops a localized nonlocal gravity model with infinite derivatives and explores its cosmological solutions, extending standard general relativity.

Findings

Existence of exponential and power-law solutions in open universe

Solutions with sudden future singularities or bounce

Spontaneous symmetry breaking in the model

Abstract

We propose a nonlocal scalar-tensor model of gravity with pseudodifferential operators inspired by the effective action of p-adic string and string field theory on flat spacetime. An infinite number of derivatives act both on the metric and scalar field sector. The system is localized via the diffusion equation approach and its cosmology is studied. We find several exact dynamical solutions, also in the presence of a barotropic fluid, which are stationary in the diffusion flow. In particular, and contrary to standard general relativity, there exist solutions with exponential and power-law scale factor also in an open universe, as well as solutions with sudden future singularities or a bounce. Also, from the point of view of quantum field theory, spontaneous symmetry breaking can be naturally realized in the class of actions we consider.