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

Mitchell, Myles A and Arnold, Christian and Li, Baojiu (2021) 'A general framework to test gravity using galaxy clusters – V. A self-consistent pipeline for unbiased constraints of f(R) gravity.', Monthly Notices of the Royal Astronomical Society, 508 (3). pp. 4157-4174.


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 fR0, performs very well for both Lambda cold dark matter (ΛCDM) 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.

Item Type:Article
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Publisher statement:© The Author(s) 2021. Published by Oxford University Press on behalf of Royal Astronomical Society. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
Date accepted:15 September 2021
Date deposited:01 November 2021
Date of first online publication:22 October 2021
Date first made open access:01 November 2021

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