Exact Solutions for Nonlocal Nonlinear Field Equations in Cosmology

TL;DR

This paper develops a method to find exact solutions for nonlocal scalar field equations in cosmology, applicable to various potentials, including those motivated by string theory, enhancing understanding of nonlocal models in the universe's evolution.

Contribution

The paper introduces a novel method for deriving exact solutions of nonlocal scalar field equations in non-flat cosmological metrics, covering a wide range of potentials.

Findings

Exact solutions for cubic, exponential, logarithmic, and power potentials.

Method applicable to non-flat metrics with arbitrary potentials (excluding linear and quadratic).

Inclusion of k-essence fields allows solutions satisfying all Einstein equations.

Abstract

A method for the search of exact solutions for equation of a nonlocal scalar field in a non-flat metric is considered. In the Friedmann-Robertson-Walker metric the proposed method can be used in the case of an arbitrary potential, with the exception of linear and quadratic potentials, and allows to get in quadratures solutions, which depend on two arbitrary parameters. Exact solutions have been found for an arbitrary cubic potential, which consideration is motivated by the string field theory, as well as for exponential, logarithmic and power potentials. It has been shown that one can add the k-essence field to the model to get exact solutions for all Einstein equations.