Dynamics of Nonlocal Cosmology

TL;DR

This paper investigates nonlocal modifications to gravity using inverse d'Alembertian functions of the Ricci scalar, showing they can cause late-time cosmic acceleration and singularities, with potential regularization methods.

Contribution

It introduces a method to reconstruct nonlocal gravity models that produce specific cosmological expansions and analyzes their dynamics and singularities.

Findings

Nonlocal models can drive late-time acceleration without affecting early universe.

Simple nonlocal terms can lead to future singularities.

Regularization of the d'Alembertian can potentially avoid singularities.

Abstract

Nonlocal quantum corrections to gravity have been recently proposed as a possible solution to the cosmological fine tuning problems. We study the dynamics of a class of nonlocal actions defined by a function of the inverse d'Alembertian of the Ricci scalar. Power-law and expnential functions are considered in detail, but we also show a method to reconstruct a nonlocal correction that generates a given background expansion. We find that even the simplest terms can, while involving only Planck scale constants, drive the late time acceleration without changing early cosmology. This leads to a sudden future singularity, which however may be avoided by regularizing the d'Alembertian. We also consider the Einstein frame versions of these models.