Constraints on Disformal Couplings from the Properties of the Cosmic
  Microwave Background Radiation
  Certain modified gravity theories predict the existence of an additional,
non-conformally coupled scalar field. A disformal coupling of the field to the
Cosmic Microwave Background (CMB) is shown to affect the evolution of the
energy density in the radiation fluid and produces a modification of the
distribution function of the CMB, which vanishes if photons and baryons couple
in the same way to the scalar. We find the constraints on the couplings to
matter and photons coming from the measurement of the CMB temperature evolution
and from current upper limits on the $\mu$--distortion of the CMB spectrum. We
also point out that the measured equation of state of photons differs from
$w_\gamma = 1/3$ in the presence of disformal couplings.
