- qc / 9 60 70 77 v 1 3 1 Ju l 1 99 6 ETH - TH / 96 - 24 Cosmological Perturbations of Ultrarelativistic Plasmas

Scalar cosmological perturbations of a weakly self-interacting plasma mixed with a perfect radiation fluid are investigated. Effects of this plasma are considered through order λ3/2 of perturbative thermal-field-theory in the radiation dominated universe. The breakdown of thermal perturbation theory at vastly subhorizon scales is circumvented by a Padé approximant solution. Compared to collisionless plasmas the phase speed and subhorizon damping of the plasma density perturbations are changed. An example for a self-interacting thermal field is provided by the neutrinos with effective 4-fermion interactions. The evolution of cosmological perturbations depends on the matter content of the universe. In the radiation dominated epoch photons, electrons, and baryons are coupled strongly, hence an effective description as a perfect radiation fluid is possible. The energy density of the perfect fluid is related to its pressure by the equation of state ρ = 3p. The cosmological perturbations [1] are determined by the linearized Einstein equations together with the perturbed equation of state δρ = c2sδp, where cs is the sound speed of the perfect radiation fluid; the anisotropic pressure vanishes. Neutrinos interact weakly, therefore they decouple from the strongly interacting matter at a temperature ∼ 1 MeV and propagate freely thereafter. This almost collisionless gas of neutrinos may be described by the linearized Einstein-Vlasov equations [2] or by a thermal-field-theoretic approach [3]. In the latter the perturbed energymomentum tensor is calculated from the response of the ultrarelativistic plasma on a metric perturbation δ( √ −gT )(x) = ∫ y δΓ δgμν(x)δgαβ(y) δgαβ(y) , (1) where Γ is the effective action of (thermal) matter. The Hubble rate H ∼ T /mPlanck is much smaller than the temperature T , thus momenta k of cosmological interest are much smaller than T as well. The second variation of the effective action, the gravitational