Effects of weak self-interactions in a relativistic plasma on cosmological perturbations

The exact solutions for linear cosmological perturbations which have been obtained for collisionless relativistic matter within thermal field theory are extended to a self-interacting case. The two-loop contributions of scalar λ${\mathrm{\phi }}^4$ theory to the thermal graviton self-energy are evaluated, which give the O(λ) corrections in the perturbation equations. The changes are found to be perturbative on scales comparable to or larger than the Hubble horizon, but the determination of the large-time damping behavior of subhorizon perturbations requires a resummation of thermally induced masses.