Shear viscous effects on the primordial power spectrum from warm inflation

Abstract

We compute the primordial curvature spectrum generated during warminflation, including shear viscous effects. The primordial spectrum isdominated by the thermal fluctuations of the radiation bath, sourcedby the dissipative term of the inflaton field. The dissipativecoefficient Υ, computed from first principles in theclose-to-equilibrium approximation, depends in general on thetemperature T, and this dependence renders the system of the linearfluctuations coupled. Whenever the dissipative coefficient is larger than theHubble expansion rate H, there is a growing mode in the fluctuationsbefore horizon crossing. However, dissipation intrinsically meansdepartures from equilibrium, and therefore the presence of a shearviscous pressure in the radiation fluid. This in turn acts as an extrafriction term for the radiation fluctuations that tends to damp the growth of the perturbations. Independently of the T functionaldependence of the dissipation and the shear viscosity, we find thatwhen the shear viscous coefficient ζs is larger than 3ρr/H at horizon crossing, ρr being the radiation energydensity, the shear damping effect wins and there is no growing mode inthe spectrum.