Testing chameleon gravity with the Coma cluster
  We propose a novel method to test the gravitational interactions in the
outskirts of galaxy clusters. When gravity is modified, this is typically
accompanied by the introduction of an additional scalar degree of freedom,
which mediates an attractive fifth force. The presence of an extra
gravitational coupling, however, is tightly constrained by local measurements.
In chameleon modifications of gravity, local tests can be evaded by employing a
screening mechanism that suppresses the fifth force in dense environments.
While the chameleon field may be screened in the interior of the cluster, its
outer region can still be affected by the extra force, introducing a deviation
between the hydrostatic and lensing mass of the cluster. Thus, the chameleon
modification can be tested by combining the gas and lensing measurements of the
cluster. We demonstrate the operability of our method with the Coma cluster,
for which both a lensing measurement and gas observations from the X-ray
surface brightness, the X-ray temperature, and the Sunyaev-Zel'dovich effect
are available. Using the joint observational data set, we perform a Markov
chain Monte Carlo analysis of the parameter space describing the different
profiles in both the Newtonian and chameleon scenarios. We report competitive
constraints on the chameleon field amplitude and its coupling strength to
matter. In the case of f(R) gravity, corresponding to a specific choice of the
coupling, we find an upper bound on the background field amplitude of
|f_{R0}|<6*10^{-5}, which is currently the tightest constraint on cosmological
scales.
