A relativistic calculation of super-Hubble suppression of inflation with thermal dissipation

We investigated the evolution of the primordial density perturbations produced by inflation with thermal dissipation. A full relativistic analysis on the evolution of initial perturbations from the warm inflation era to a radiation-dominated universe has been developed. The emphasis is on tracking the ratio between the adiabatic and the isocurvature mode of the initial perturbations. This result is employed to calculate a testable factor: the super-Hubble suppression of the power spectrum of the primordial perturbations. We show that based on the warm inflation scenario, the super-Hubble suppression factor, $s$, for an inflation with thermal dissipation is at least 0.5. This prediction does not depend on the details of the model parameters. If $s$ is larger than 0.5, it implies that the friction parameter $\Gamma$ is larger than the Hubble expansion parameter $H$ during the inflation era.