The spectrum of tensor perturbations in warm inflation

We compute the spectrum of tensor perturbations in warm inflation. We find that the spectrum, besides the standard component $\propto H^2\mathrm{/}{M}_P^2$ associated to the amplification of the tensor vacuum fluctuations, acquires a component $\propto {\mathrm{\ell }}_{\mathrm{m}\mathrm{f}\mathrm{p}}{T}^5\mathrm{/}{M}_P^4$, where ${\mathrm{\ell }}_{\mathrm{m}\mathrm{f}\mathrm{p}}$ and $T$ are respectively the mean free path and the temperature of the thermal degrees of freedom. The new contribution is due to the direct production of gravitational waves by the thermal bath, and can exceed the standard one in a viable region of parameter space. This contribution is dominated by thermal fluctuations at scales longer than ${\mathrm{\ell }}_{\mathrm{m}\mathrm{f}\mathrm{p}}$.