# The Galaxy Halo Connection in Modified Gravity Cosmologies: Environment Dependence of Galaxy Luminosity function

## TL;DR

This study explores how modified gravity models like $f(R)$ and nDGP influence the galaxy-halo connection and galaxy luminosity function across different environments, revealing potential observational tests to distinguish these models from standard $\Lambda$CDM.

## Contribution

It provides the first detailed analysis of environment-dependent galaxy luminosity functions in modified gravity cosmologies, including new HOD parameters for these models.

## Key findings

- Galaxy-halo connection varies up to 40% across models.
- f(R) models show environmental galaxy density deviations of ±10%.
- Differences in galaxy luminosity functions are around 10% in voids.

## Abstract

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.