Monomial warm inflation revisited

We revisit the idea that the inflaton may have dissipated part of its energy into a thermal bath during inflation, considering monomial inflationary potentials and three different forms of dissipation rate. Using a numerical Fokker-Planck approach to describe the stochastic dynamics of inflationary fluctuations, we confront this scenario with current bounds on the spectrum of curvature fluctuations and primordial gravitational waves. We also obtain purely analytical approximations that improve over previously used ones in the small dissipation regime for the amplitude of the spectrum and its tilt. We show that only our numerical Fokker-Planck method is accurate, fast and precise enough to test these models against current data. We advocate its use in future studies of warm inflation. We also apply the stochastic inflation formalism to this scenario, finding that the resulting spectrum is the same as the one obtained with standard perturbation theory. We discuss the origin and convenience of using a commonly implemented large thermal correction to the primordial spectrum and the implications of such a term for a specific scenario. Improved bounds on the scalar spectral index will further constrain warm inflation in the near future.