A Simple Guide to Warm Inflation Model Building

Inflaton couplings during warm inflation result in the 
production of a thermal bath. Thermal friction and fluctuations can 
dominate the standard de Sitter analogues, resulting in a modified 
slow-roll scenario with a new source of density fluctuations. Due to 
issues with back-reaction, it is advantageous to consider inflaton 
couplings with the thermal bath that are pseudo-scalar in nature, e.g., 
derivative interactions or topological $F tilde F$ couplings. We 
demonstrate that every single existing model of warm inflation utilizing 
pseudo-scalar couplings needs to be corrected to properly account for 
all of the chemical potentials that the thermal bath acquires in 
response to the inflaton coupling. These chemical potentials are for 
non-conserved charges, and are non-zero only because of the applied 
inflaton couplings.  The model-dependent chemical potentials modify the 
fluctuation-dissipation theorem, making the relationship between the 
thermal friction and thermal fluctuations model-dependent. In extreme 
cases, these chemical potentials can cause the friction term to vanish 
while thermal fluctuations remain non-zero. In the context of a simple 
example, we demonstrate how to calculate the chemical potentials, 
thermal friction, and thermal fluctuations using both the Boltzmann 
equations and by calculating thermal expectation values, showing 
explicitly that the two approaches give the same result.