Impact on the power spectrum of Screening in Modified Gravity Scenarios

We study the effects of screened modified gravity of the $f(R)$, dilaton and symmetron types on structure formation, from the quasi-linear to the non-linear regime, using semi-analytical methods. For such models, where the range of the new scalar field is typically within the Mpc range and below in the cosmological context, non-linear techniques are required to understand the deviations of the power spectrum of the matter density contrast compared to the $\Lambda$-CDM template. This is nowadays commonly tackled using extensive N-body simulations. Here we present new results combining exact perturbation theory at the one loop level (and a partial resummation of the perturbative series) with a halo model. The former allows one to extend the linear perturbative analysis up to $k\lesssim 0.15{\rm h Mpc}^{-1}$ at the perturbative level while the latter leads to a reasonable, up to a few percent, agreement with numerical simulations for $k\lesssim 3{\rm h Mpc}^{-1}$ for large curvature $f(R)$ models, and $k\lesssim 1{\rm h Mpc}^{-1}$ for dilatons and symmetrons, at $z=0$. We also discuss how the behaviors of the perturbative expansions and of the spherical collapse differ for $f(R)$, dilaton, and symmetron models.