The Galaxy Halo Connection in Modified Gravity Cosmologies: Environment
  Dependence of Galaxy Luminosity function
  We investigate the dependence of the galaxy-halo connection and galaxy
density field in modified gravity models using the $N-$body simulations for
$f(R)$ and nDGP models at $z=0$. Because of the screening mechanisms employed
by these models, chameleon and Vainshtein, halos are clustered differently in
the non-linear regime of structure formation. We quantify their deviations in
the galaxy density field from the standard $\Lambda$CDM model under different
environments. We populate galaxies in halos via the (Sub)Halo Abundance
Matching. Our main results are: 1) The galaxy-halo connection {\it strongly}
depends on the gravity model; a maximum variation of $\sim40\%$ is observed
between Halo Occupational Distribution (HOD) parameters; 2) $f(R)$ gravity
models predict an excess of galaxies in low density environments of $\sim10\%$
but predict a deficit of $\sim10\%$ at high density environments for $|f_{R0}|
= 10^{-4}$ and $10^{-6}$ while $|f_{R0}| = 10^{-5}$ predicts more high density
structures; nDGP models are consistent with $\Lambda$CDM; 3) Different gravity
models predict different dependences of the galaxy luminosity function (GLF)
with the environment, especially in void-like regions we find differences
around $\sim10\%$ for the $f(R)$ models while nDPG models remain closer to
$\Lambda$CDM for low-luminosity galaxies but there is a deficit of $\sim11\%$
for high-luminosity galaxies in all environments. We conclude that the
dependence of the GLF with environment might provide a test to distinguish
between gravity models and their screening mechanisms from the $\Lambda$CDM. We
provide HOD parameters for the gravity models analyzed in this paper.
