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Quantum Field Theory at Finite Temperature and Cosmological Perturbations

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.