Spherical collapse and halo mass function in the symmetron model

We study the gravitational clustering of spherically symmetric overdensities and the statistics of the resulting dark matter halos in the "symmetron model", in which a new long range force is mediated by a $Z_2$ symmetric scalar field. Depending on the initial radius of the overdensity, we identify two distinct regimes: for small initial radii the symmetron mediated force affects the spherical collapse at all redshifts; for initial radii larger than some critical size this force vanishes before collapse because of the symmetron screening mechanism. In both cases overdensities collapse earlier than in the $\Lambda$CDM and statistically tend to form more massive dark matter halos. Regarding the halo-mass function of these objects, we observe order one departures from standard $\Lambda$CDM predictions. The formalism developed here can be easily applied to other models where fifth-forces participate to the dynamics of the gravitational collapse.