  It is shown how quantum field theory at finite temperature can be used to set
up self-consistent and gauge invariant equations for cosmological perturbations
sustained by an ultrarelativistic plasma. While in the collisionless case, the
results are equivalent to those obtained from the Einstein-Vlasov equations,
weak self-interactions in the plasma turn out to require the full machinery of
perturbative thermal field theories such as resummation of hard thermal loops.
Nevertheless it is still possible to use the same methods that yielded exact
solutions in the collisionless case.
