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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 $μ$--distortion of the CMB spectrum. We also point out that the measured equation of state of photons differs from $w_γ= 1/3$ in the presence of disformal couplings.