Spherical collapse in Galileon gravity: fifth force solutions, halo mass function and halo bias

We study spherical collapse in the Quartic and Quintic Covariant Galileon gravity models within the framework of the excursion set formalism. We derive the nonlinear spherically symmetric equations in the quasi-static and weak-field limits, focusing on model parameters that fit current CMB, SNIa and BAO data. We demonstrate that the equations of the Quintic model do not admit physical solutions of the fifth force in high density regions, which prevents the study of structure formation in this model. For the Quartic model, we show that the effective gravitational strength deviates from unity at late times ($z \lesssim 1$), becoming larger if the density is low, but smaller if the density is high. This shows that the Vainshtein mechanism at high densities is not enough to screen all of the modifications of gravity. This makes halos that collapse at $z \lesssim 1$ feel an overall weaker gravity, which suppresses halo formation. However, the matter density in the Quartic model is higher than in standard $\Lambda$CDM, which boosts structure formation and dominates over the effect of the weaker gravity. In the Quartic model there is a significant overabundance of high-mass halos relative to $\Lambda$CDM. Dark matter halos are also less biased than in $\Lambda$CDM, with the difference increasing appreciably with halo mass. However, our results suggest that the bias may not be small enough to fully reconcile the predicted matter power spectrum with LRG clustering data.