Modified Gravity and the Radiation Dominated Epoch

In this paper we consider scalar-tensor theories, allowing for both conformal and disformal couplings to a fluid with a general equation of state. We derive the effective coupling for both background cosmology and for perturbations in that fluid. As an application we consider the scalar degree of freedom to be coupled to baryons and study the dynamics of the tightly coupled photon-baryon fluid in the early Universe. We derive an expression for the effective speed of sound, which differs from its value in General Relativity. We apply our findings to the μ-distortion of the cosmic microwave background radiation, which depends on the effective sound-speed of the photon-baryon fluid, and show that the predictions differ from General Relativity. Thus, the μ-distortion provides further information about gravity in the very early Universe well before decoupling