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 generic 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 \mu-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 \mu-distortion
provides further information about gravity in the very early universe well
before decoupling.
