K-mouflage Cosmology: Formation of Large-Scale Structures

We study structure formation in K-mouflage cosmology whose main feature is the absence of screening effect on quasilinear scales. We show that the growth of structure at the linear level is affected by both a new time dependent Newton constant and a friction term which depend on the background evolution. These combine with the modified background evolution to change the growth rate by up to ten percent since $z\sim 2$. At the one loop level, we find that the nonlinearities of the K-mouflage models are mostly due to the matter dynamics and that the scalar perturbations can be treated at tree level. We also study the spherical collapse in K-mouflage models and show that the critical density contrast deviates from its $\mathrm{\Lambda }$-CDM value and that, as a result, the halo mass function is modified for large masses by an order one factor. Finally we consider the deviation of the matter spectrum from $\mathrm{\Lambda }$-CDM on nonlinear scales where a halo model is utilized. We find that the discrepancy peaks around $1h{\mathrm{M}\mathrm{p}\mathrm{c}}^{-1}$ with a relative difference which can reach fifty percent. Importantly, these features are still true at larger redshifts, contrary to models of the chameleon-$f(R)$ and Galileon types.