Loosely coupled particles in warm inflation

Cosmological perturbations in warm inflation are conventionally described by an EFT. It consists of the inflaton field coupled to a radiation fluid and applies to energy scales of order Hubble $H$ and inflaton decay width $\gamma$, but well below temperature $T$. This EFT lacks a proper treatment of inflatons produced with energy $\sim T$. While the direct contribution of these ``UV inflatons'' to the super-horizon curvature perturbations is subdominant because of the cosmological redshift, for $\gamma \sim H$, their indirect contribution is potentially important -- by their effect on the equation of state, by being exchanged as long-lived intermediate states, and by sourcing gravitational waves with their sizable anisotropic stress. To include these effects, we add to the EFT the Boltzmann distribution of the gas of UV inflatons and compute some of the corrections.