Reconstruction Procedure in Nonlocal Cosmological Models

TL;DR

This paper develops a reconstruction method for a nonlocal gravity model involving a function of the inverse d'Alembertian of Ricci scalar, deriving explicit power-law and de Sitter solutions without introducing new parameters.

Contribution

It introduces a reconstruction procedure for nonlocal gravity models with $f(ox^{-1} R)$, providing explicit solutions including power-law and de Sitter cases.

Findings

Derived explicit power-law solutions for various n values.

Identified the form of f as sums of exponential functions for generic solutions.

Solved in detail the case with both de Sitter and power-law solutions.

Abstract

A nonlocal gravity model is considered which does not assume the existence of a new dimensional parameter in the action and includes a function $f(\Box^{-1} R)$, with $\Box$ the d'Alembertian operator. Using a reconstruction procedure for the local scalar-tensor formulation of this model, a function f is obtained for which the model exhibits power-law solutions with the Hubble parameter $H=n/t$, for any value of the constant n. For generic n - namely except for a few special values which are characterized and also specifically studied - the corresponding function f is a sum of exponential functions. Corresponding power-law solutions are found explicitly. Also the case is solved in all detail of a function f such that the model contains both de Sitter and power-law solutions.