N-body Simulations of $\gamma$ Gravity

We have investigated structure formation in the $\gamma$ gravity $f(R)$ model with {\it N}-body simulations. The $\gamma$ gravity model is a proposal which, unlike other viable $f(R)$ models, not only changes the gravitational dynamics, but can in principle also have signatures at the background level that are different from those obtained in $\Lambda$CDM (Cosmological constant, Cold Dark Matter). The aim of this paper is to study the nonlinear regime of the model in the case where, at late times, the background differs from $\Lambda$CDM. We quantify the signatures produced on the power spectrum, the halo mass function, and the density and velocity profiles. To appreciate the features of the model, we have compared it to $\Lambda$CDM and the Hu-Sawicki $f(R)$ models. For the considered set of parameters we find that the screening mechanism is ineffective, which gives rise to deviations in the halo mass function that disagree with observations. This does not rule out the model per se, but requires choices of parameters such that $|f_{R0}|$ is much smaller, which would imply that its cosmic expansion history cannot be distinguished from $\Lambda$CDM at the background level.