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

Abstract

In this work, we extend previous analyses of the structure formation in the f(□−1R) model of nonlocal gravity proposed by Deser and Woodard (DW), which reproduces the background expansion of ΛCDM 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 ΛCDM. In fact, the DW model presents a suppressed growth of matter perturbations with respect to ΛCDM and a slightly lower value of σ8, as favored by observations. We also produce analytical approximations of the two modified gravity functions, i.e. the anisotropic stress η and the relative change of Newton's constant Y, and of fσ8(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.