Reconstructing the Distortion Function for Nonlocal Cosmology

TL;DR

This paper develops a method to reconstruct the distortion function in nonlocal gravity models to match any desired cosmic expansion history, demonstrated by fitting the LambdaCDM model with a hyperbolic tangent function.

Contribution

It introduces a novel technique for selecting the distortion function in nonlocal gravity to reproduce arbitrary cosmological expansion histories.

Findings

Successfully fits LambdaCDM expansion history with a hyperbolic tangent function

Provides a numerical method for reconstructing the distortion function

Demonstrates the approach's effectiveness in nonlocal cosmology models

Abstract

We consider the cosmology of modified gravity models in which Newton's constant is distorted by a function of the inverse d'Alembertian acting on the Ricci scalar. We derive a technique for choosing the distortion function so as to fit an arbitrary expansion history. This technique is applied numerically to the case of LambdaCDM cosmology, and the result agrees well with a simple hyperbolic tangent.