Observational constraints on monomial warm inflation

Warm inflation is, as of today, one of the best motivated mechanisms for explaining an early inflationary period. In this paper, we derive and analyze the current bounds on warm inflation with a monomial potential $U\propto \phi^p$, using the constraints from the PLANCK mission. In particular, we discuss the parameter space of the tensor-to-scalar ratio $r$ and the potential coupling $\lambda$ of the monomial warm inflation in terms of the number of e-folds. We obtain that the theoretical tensor-to-scalar ratio $r\sim 10^{-8}$ is much smaller than the current observational constrain $r \lesssim 0.12$, despite a relatively large value of the field excursion $\Delta \phi \sim 0.1\MP$. Warm inflation thus eludes the Lyth bound set on the tensor-to-scalar ratio by the field excursion.