Modelling the matter bispectrum at small scales in modified gravity

TL;DR

This paper evaluates various theoretical models for the matter bispectrum in modified gravity theories, comparing them to N-body simulations, and finds that current models lack sufficient accuracy for upcoming high-precision surveys, with halo-model corrections performing best.

Contribution

It provides a comprehensive comparison of bispectrum modelling schemes in modified gravity, highlighting their limitations and identifying the most accurate approach among existing methods.

Findings

Current models fail to meet the accuracy needed for Stage IV surveys.

Halo-model corrected fitting formulas perform best among tested schemes.

Scale-dependent growth in modified gravity complicates bispectrum modelling.

Abstract

Future large-scale structure surveys will measure three-point statistics with high statistical significance. This will offer significant improvements on our understanding of gravity, provided we can model these statistics accurately. We assess the performance of several schemes for theoretical modelling of the matter bispectrum, including halo-model based approaches and fitting formulae. We compare the model predictions against N-body simulations, considering scales up to $k_{\rm max} = 4 h/{\rm Mpc}$, well into non-linear regime of structure formation. Focusing on the equilateral configuration, we conduct this analysis for three theories of gravity: general relativity, $f(R)$ gravity, and the DGP braneworld model. Additionally, we compute the lensing convergence bispectrum for these models. We find that all current modelling prescriptions in modified gravity, in particular for theories with scale-dependent linear growth, fail to attain the accuracy required by the precision of the Stage IV surveys such as \emph{Euclid}. Among these models, we find that a halo-model corrected fitting formula achieves the best overall performance.