Structure formation in the new Deser-Woodard nonlocal gravity model

TL;DR

This paper investigates structure formation in the Deser-Woodard nonlocal gravity model, demonstrating its compatibility with observational data and analyzing its screening mechanism and distinctive growth rate features.

Contribution

It introduces a reconstructed nonlocal distortion function for the DW-2019 model and analyzes its implications for structure growth and screening effects.

Findings

The nonlocal distortion function is fixed as an exponential form close to previous proposals.

The model's growth rate curve fits observational data and shows a unique feature at redshift 0.39.

The DW-2019 model exhibits strong nonlocal effects influencing matter perturbations.

Abstract

We consider the structure formation in the nonlocal gravity model proposed recently by Deser and Woodard (DW-2019 model), which can not only reproduce the $\Lambda$CDM cosmology without fine-tuning puzzle but also may provide a screening mechanism for free. By using the direct numerical method of the reconstructing technique, the nonlocal distortion function $f(Y)$ is fixed as $f(Y)\simeq\boldsymbol{e}^{2.153(Y-16.97)}$ which has a small deviation with the fitted function proposed by Deser and Woodard. Based on the numerical results, we plotted the curve of the growth rate $f\sigma_8(z)$ under the DW-2019 model, which shows this model is not ruled out by the $f\sigma_8$ data from the Redshift-space distortions measurements. The evolving curve of the growth rate has a distinct plummet at $z\simeq0.39$, which is a great difference with the DW model. The possible reason is that the DW-2019 model provides the strong nonlocal effect, which behaves as the anisotropic effect to influence the matter perturbation in the low-redshift range. Finally the qualitative analysis of the screening mechanism is discussed by considering the spacial dependence of the nonlocal modification in the small-scale range.