Structure formation in the Deser-Woodard nonlocal gravity model: a reappraisal

TL;DR

This paper reanalyzes the Deser-Woodard nonlocal gravity model, showing it can fit structure formation data better than Lambda-CDM and predicting a slightly lower sigma_8, with analytical approximations provided.

Contribution

It demonstrates that the localized form of the DW model is not ruled out by RSD data and offers analytical tools for its predictions.

Findings

The DW model fits RSD data better than Lambda-CDM.

The model predicts a lower sigma_8 consistent with lensing.

Analytical approximations of modified gravity functions and fσ8(z) are provided.

Abstract

In this work, we extend previous analyses of the structure formation in the $f(\Box^{-1}R)$ model of nonlocal gravity proposed by Deser and Woodard (DW), which reproduces the background expansion of $\Lambda$CDM with no need of a cosmological constant nor of any dimensional constant beside Newton's one. A previous analysis based on redshift-space distortions (RSD) data concluded that the model was ruled out. In this work we revisit the issue and find that, when recast in a localized model, the DW model is not ruled out and actually gives a better fit to RSD data than $\Lambda$CDM. At the same time, the model predicts a slightly lower value of $\sigma_{8}$ than $\Lambda$CDM, in agreement with recent estimates based on lensing. We also produce analytical approximations of the two modified gravity functions and of $f\sigma_{8}(z)$ as a function of redshift. Finally, we also show how much the fit depends on initial conditions when these are generalized with respect to a standard matter-dominated era.