Spherical Collapse in covariant Galileon theory

In this paper we study the evolution of a spherical matter overdensity in the context of the recently introduced Galileon field theory. Our analysis considers the complete covariant Lagrangian in four dimensions. This theory is composed by a potential and a standard kinetic term, a cubic kinetic term and two additional terms that include the coupling between the Galileon and the metric, to preserve the original properties of Galileons also in curved space-times. Here we extend previous studies, which considered both the quintessence and the cubic terms, by focussing on the role of the last two terms. The background evolution we consider is driven by a tracker solution. Studying scalar perturbations in the non-linear regime, we find constraints on the parameter of the model. We will show how the new terms contribute to the collapse phase and how they modify physical parameters, such as the linearized density contrast and the virial overdensity. The results show that the Galileon modifies substantially the dynamics of the collapse, thus making it possible to observationally constrain the parameters of this theory.