# Convolution Lagrangian perturbation theory for biased tracers beyond general relativity

## TL;DR

This paper evaluates and extends Lagrangian Perturbation Theory methods to accurately predict the clustering statistics of biased tracers in modified gravity models, incorporating environmental effects and screening mechanisms.

## Contribution

It introduces a convolution Lagrangian perturbation theory approach that effectively models biased tracers in scalar-tensor modified gravity theories beyond general relativity.

## Key findings

- CLPT and SPT provide accurate predictions for correlation functions and power spectra.
- The methods characterize BAO, power-law, and small-scale regimes effectively.
- Analytic bias parameters can incorporate environmental sensitivity in modified gravity.

## Abstract

We compare analytic predictions for real and Fourier space two-point statistics for biased tracers from a variety of Lagrangian Perturbation Theory approaches against those from state of the art N-body simulations in $f(R)$ Hu-Sawicki and the nDGP braneworld modified gravity theories. We show that the novel physics of gravitational collapse in scalar tensor theories with the chameleon or the Vainshtein screening mechanism can be effectively factored in with bias parameters analytically predicted using the Peak-Background Split formalism when updated to include the environmental sensitivity of modified gravity theories as well as changes to the halo mass function. We demonstrate that Convolution Lagrangian Perturbation Theory (CLPT) and Standard Perturbation Theory (SPT) approaches provide accurate analytic methods to predict the correlation function and power spectra, respectively, for biased tracers in modified gravity models and are able to characterize both the BAO, power-law and small scale regimes needed for upcoming galaxy surveys such as DESI, Euclid, LSST and WFIRST.