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 M _ { Pl } .
Warm inflation thus eludes the Lyth bound set on the tensor-to-scalar ratio by the field excursion .