  This paper proposes a systematic study of cosmological signatures of
modifications of gravity via the presence of a scalar field with a
multiplicative coupling to the electromagnetic Lagrangian. We show that, in
this framework, variations of the fine structure constant, violations of the
distance duality relation, evolution of the cosmic microwave background (CMB)
temperature and CMB distortions are intimately and unequivocally linked. 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 distortions using current constraints on the fine structure
constant. Alternatively, this offers interesting possibilities to test a wide
range of theories of gravity by analysing several datasets concurrently. We
discuss results obtained using current data as well as some forecasts for
future data sets such as those coming from EUCLID or the SKA.

Cosmology and Nongalactic Astrophysics;General Relativity and Quantum Cosmology