Nonlinear structure formation in Nonlocal Gravity

TL;DR

This study investigates the nonlinear growth of cosmic structures in a specific nonlocal gravity model, revealing slight differences from standard cosmology that may be detectable with future observations.

Contribution

It provides the first detailed N-body simulation analysis of nonlinear structure formation in a nonlocal gravity model with a specific inverse-squared d'Alembertian operator.

Findings

Massive haloes are more abundant and concentrated in the nonlocal model.

The Sheth-Tormen formalism accurately predicts halo mass function and bias.

Nonlinear matter power spectrum shows a modest enhancement compared to $ m ext{Lambda CDM}$.

Abstract

We study the nonlinear growth of structure in nonlocal gravity models with the aid of N-body simulation and the spherical collapse and halo models. We focus on a model in which the inverse-squared of the d'Alembertian operator acts on the Ricci scalar in the action. For fixed cosmological parameters, this model differs from $\Lambda{\rm CDM}$ by having a lower late-time expansion rate and an enhanced and time-dependent gravitational strength ($\sim 6\%$ larger today). Compared to $\Lambda{\rm CDM}$ today, in the nonlocal model, massive haloes are slightly more abundant (by $\sim 10\%$ at $M \sim 10^{14} M_{\odot}/h$) and concentrated ($\approx 8\%$ enhancement over a range of mass scales), but their linear bias remains almost unchanged. We find that the Sheth-Tormen formalism describes the mass function and halo bias very well, with little need for recalibration of free parameters. The fitting of the halo concentrations is however essential to ensure the good performance of the halo model on small scales. For $k \gtrsim 1 h/{\rm Mpc}$, the amplitude of the nonlinear matter and velocity divergence power spectra exhibits a modest enhancement of $\sim 12\%$ to $15\%$, compared to $\Lambda{\rm CDM}$ today. This suggests that this model might only be distinguishable from $\Lambda{\rm CDM}$ by future observational missions. We point out that the absence of a screening mechanism may lead to tensions with Solar System tests due to local time variations of the gravitational strength, although this is subject to assumptions about the local time evolution of background averaged quantities.