No warm inflation from a vanilla axion

At finite temperature, the coupling of an axion to non-Abelian gauge fields causes dissipation due to sphaleron heating. This mechanism has been considered as ideal for realizing warm inflation, since it can lead to large thermal friction while preserving the flatness of the potential. We show, however, that requiring standard properties of an axion—in particular, a discrete shift symmetry—excludes the strong regime of warm slow-roll inflation, in which thermal friction dominates. The present argument, which does not rely on any phenomenological input, leaves room for the weak regime of warm axion inflation, but in this case a super-Planckian decay constant represents a well-known issue. Finally, we discuss nonminimal and axionlike models as a way out.