Warm inflation in the stochastic inflation formalism

Full text: The basic assumption of stochastic inflation is the splitting, through the definition of a appropriate window function, of the quantum inflaton field in a long wavelength part (modes outside of the de Sitter horizon) and in a short wavelength (modes inside the de Sitter horizon) part. The inflationary mechanism then continuously shifts more and more modes of the bath field into the system stretching their physical wavelengths beyond the de Sitter horizon size, what generates an effective system-bath interaction. Therefore, the system field develops a stochastic dynamics driven by the bath field, that plays the role of noise source. The resulting equation of motion (EoM) is a Langevin-like equation. Applying this formalism to Warm Inflation scenario (where, alternatively to the cold inflation, we assume that the inflaton evolves in a thermal bath and through a dissipative process continuously generates radiation, thus avoiding the necessity of a reheating mechanism), we contrast the exact numerical solution of thermal power spectrum and two approximations currently used in the literature, and compare this to the quantum power spectrum at horizon crossing. Finally, we consider a more realistic model based on microscopic derivations to estimate the effects of non-Markovianity on the inflaton dynamics and on the thermal power spectrum. (author)