Local thermal equilibrium for quantum fields on cosmological spacetimes

We investigate the consistency of local thermal equilibrium for scalar and Dirac fields on cosmological spacetimes with respect to general covariance and the Hadamard renormalization prescription for the stress-energy tensor. The renormalized stress-energy tensor fulfilling the local thermal equilibrium condition has a thermal part, a dynamical part and a purely geometrical part. The latter contains the renormalization freedom. Since the thermal part differs from the total stress-energy, one finds a temperature dependence on cosmological time which has a stronger singularity in the limit of early cosmological times than in the classical treatment of radiation.