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.
