Numerical implementation of the Cubic Galileon model in PINOCCHIO
  This paper presents a perturbative treatment of non-linear clustering in the
context of the cubic Galileon modified gravity model. We numerically implement
the modified gravity version of 2nd order Lagrangian perturbation theory in the
PINOCCHIO code, as well as an extension of ellipsoidal collapse that includes
Vainshtein screening. We then use the extended code to generate realizations of
the matter density field and halo catalogs according to the PINOCCHIO
algorithm, and compute the matter power spectrum and halo mass function,
studying different approximations for the computation of collapse times. The
enhancement in the matter power spectrum with respect to the standard LambdaCDM
model gradually appears in the small scales when the redshift is z<1, with a
maximum relative difference to LambdaCDM of about 23% at k=1/Mpc and z=0. We
find that the Vainshtein screening mechanism in PINOCCHIO is less efficient
than the one in N-body simulations, due to a different definition of collapse
time. In the halo mass function, the modified gravity effect is larger in the
high mass end, similarly to what is found for other modified gravity models.
Our code is publicly available in a dedicated branch, dubbed ``G3-PINOCCHIO''.
