A general framework to test gravity using galaxy clusters V: A self-consistent pipeline for unbiased constraints of $f(R)$ gravity

TL;DR

This paper introduces a robust MCMC pipeline for unbiasedly constraining $f(R)$ gravity using galaxy cluster counts, accounting for complex effects on halo properties and scaling relations, and demonstrates its effectiveness with mock data.

Contribution

The paper develops a self-consistent, adaptable pipeline that accurately constrains $f(R)$ gravity parameters from galaxy cluster data, improving upon previous methods by detailed modeling and calibration.

Findings

Pipeline performs well for $ ext{f(R)}$ and $ ext{ΛCDM}$ cosmologies.

Incomplete scaling relation modeling causes biased constraints.

Degeneracies can be mitigated with tighter priors and better parameter knowledge.

Abstract

We present a Markov chain Monte Carlo pipeline that can be used for robust and unbiased constraints of $f(R)$ gravity using galaxy cluster number counts. This pipeline makes use of a detailed modelling of the halo mass function in $f(R)$ gravity, which is based on the spherical collapse model and calibrated by simulations, and fully accounts for the effects of the fifth force on the dynamical mass, the halo concentration and the observable-mass scaling relations. Using a set of mock cluster catalogues observed through the thermal Sunyaev-Zel'dovich effect, we demonstrate that this pipeline, which constrains the present-day background scalar field $f_{R0}$, performs very well for both $\Lambda$CDM and $f(R)$ fiducial cosmologies. We find that using an incomplete treatment of the scaling relation, which could deviate from the usual power-law behaviour in $f(R)$ gravity, can lead to imprecise and biased constraints. We also find that various degeneracies between the modified gravity, cosmological and scaling relation parameters can significantly affect the constraints, and show how this can be rectified by using tighter priors and better knowledge of the cosmological and scaling relation parameters. Our pipeline can be easily extended to other modified gravity models, to test gravity on large scales using galaxy cluster catalogues from ongoing and upcoming surveys.