Searching for deviations from the General Relativity Theory with gas
  mass fraction of galaxy clusters and complementary probes
  Nowadays, thanks to the improved precision of cosmological data, it has been
possible to search for deviation from the general relativity theory with tests
on large cosmic scales. Particularly, there is a class of modified gravity
theories that breaks the Einstein equivalence principle (EEP) in the
electromagnetic sector, generating variations of the fine structure constant,
violations of the cosmic distance duality relation and the evolution law of the
cosmic microwave background (CMB) radiation. In recent papers, this class of
theories has been tested with angular diameter distances from galaxy clusters,
type Ia supernovae and CMB temperature.
  In this work we propose a new test by considering the most recent X-ray
surface brightness observations of galaxy clusters jointly with type Ia
supernovae and CMB temperature. {The crucial point here is that we take into
account the dependence of the X-ray gas mass fraction of galaxy clusters on
possible variations of the fine structure constant and violations of the cosmic
distance duality relation.} Our basic result is that this new approach is
competitive with the previous one and it also does not show significant
deviations from the general relativity.
