Minimal warm inflation with complete medium response
  If a homogeneous field evolves within a medium, with the latter gradually
picking up a temperature, then the friction felt by the field depends on how
its evolution rate compares with medium time scales. We suggest a framework
which permits to incorporate the contributions from all medium time scales. As
an example, we illustrate how warm axion inflation can be described by
inputting the retarded pseudoscalar correlator of a thermal Yang-Mills plasma.
Adopting a semi-realistic model for the latter, and starting the evolution at
almost vanishing temperature, we show how the system heats up and then enters
the "weak" or "strong" regime of warm inflation. Previous approximate
treatments are scrutinized.
