We propose a new framework for testing gravity using cluster observations, which aims to provide an unbiased constraint on modified gravity models from Sunyaev Zel'dovich (SZ) and X-ray cluster counts and the cluster gas fraction, among other possible observables. Focusing on a popular f(R) model of gravity, we propose a novel procedure to recalibrate mass scaling relations from ΛCDM to f(R) gravity for SZ and X-ray cluster observables. We find that the complicated modified gravity effects can be simply modelled as a dependence on a combination of the background scalar field and redshift, fR(z)/(1+z), regardless of the f(R) model parameter. By employing a large suite of N-body simulations, we demonstrate that a theoretically derived tanh fitting formula is in excellent agreement with the dynamical mass enhancement of dark matter haloes for a large range of background field parameters and redshifts. Our framework is sufficiently flexible to allow for tests of other models and inclusion of further observables. The one-parameter description of the dynamical mass enhancement can have important implications on the theoretical modelling of observables and on practical tests of gravity.
@article{arxiv.1802.02165,
title = {A general framework to test gravity using galaxy clusters I: Modelling the dynamical mass of haloes in $ f(R) $ gravity},
author = {Myles A. Mitchell and Jian-hua He and Christian Arnold and Baojiu Li},
journal= {arXiv preprint arXiv:1802.02165},
year = {2018}
}