Nonlinear structure formation in nonlocal gravity

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 ACDM by having a lower late-time expansion rate and an enhanced and time-dependent gravitational strength (similar to 6% larger today). Compared to ACDM today, in the nonlocal model, massive haloes are slightly more abundant (by similar to 10% at M similar to 10(14) M-circle dot/h) and concentrated (approximate to 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 greater than or similar to 1h/Mpc, the amplitude of the nonlinear matter and velocity divergence power spectra exhibits a modest enhancement of similar to 12% to 15%, compared to ACDM today. This suggests that this model might only be distinguishable from ACDM 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.