Nonlinear Scales in Luminal Horndeski -- I. Halo mass function and power spectrum boost in models with Vainshtein screening

Abstract: We investigate nonlinear structure formation in Horndeski gravity with a luminal gravitational wave speed ($c_T = 1$) using the spherical collapse model incorporating Vainshtein screening. We compute the critical and virial overdensities and use these to evaluate the halo mass function within several commonly employed formalisms. Building on the reaction method, we develop a flexible and accurate framework for computing the nonlinear matter power spectrum across a broad class of viable modified gravity models within luminal Horndeski theories. The framework interfaces seamlessly with EFTCAMB and is applicable to both covariant Horndeski models and effective field theory descriptions of dark energy, allowing for a range of background cosmologies. This approach enables systematic exploration of a wide space of theories and cosmological parameters, with the goal of informing future analyses of upcoming large-scale structure surveys.