Evolution of a homogeneous universe with a posthydrodynamic stress-energy tensor for the ultrarelativistic medium

A covariant expression is derived for the posthydrodynamic approximation to the stress-energy tensor of a continuous ultrarelativistic medium. Exact solutions to the Einstein equations with such a tensor are obtained for isotropic Friedmann cosmological models and for an anisotropic model of Bianchi type I. Far from the cosmological singularity, the solutions are asymptotically isotropic and Friedmann, but close to the singularity the universe will evolve very differently from the standard Friedmann and Kasner models: the singularity itself becomes isotropic, the temperature of the medium remains finite there, and the spacetime metric evolves by different laws