A general framework to test gravity using galaxy clusters I: Modelling
  the dynamical mass of haloes in $ f(R) $ gravity
  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 $ \Lambda $CDM 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, $
f_R(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.
