Some cosmological consequences of a breaking of the Einstein equivalence
  principle
  In this communication, we consider a wide class of extensions to General
Relativity that break explicitly the Einstein Equivalence Principle by
introducing a multiplicative coupling between a scalar field and the
electromagnetic Lagrangian. In these theories, we show that 4 cosmological
observables are intimately related to each other: a temporal variation of the
fine structure constant, a violation of the distance-duality relation, the
evolution of the cosmic microwave background (CMB) temperature and CMB spectral
distortions. This enables one to put very stringent constraints on possible
violations of the distance-duality relation, on the evolution of the CMB
temperature and on admissible CMB spectral distortions using current
constraints on the fine structure constant. Alternatively, this offers
interesting possibilities to test a wide range of theories of gravity by
analyzing several data sets concurrently.
