Thermalisation of the Higgs sector at the end of heating

Determine whether the Standard-Model Higgs field, non-minimally coupled to curvature and acting as a reheaton during a kination epoch, achieves a thermal spectrum by the end of the post-inflationary heating stage.

Background

The paper studies a scenario in which the Standard-Model Higgs field, with a large non-minimal coupling to curvature, undergoes tachyonic amplification during a kination phase and can potentially reheat the Universe. While the authors can associate a radiation temperature to the heated plasma using the Higgs energy density, they explicitly note uncertainty regarding whether the Higgs sector actually attains a thermal spectrum by the end of the heating stage.

This question is important for cosmological implications such as Big Bang Nucleosynthesis bounds and the detailed evolution of the post-inflationary plasma, since true thermalisation (as opposed to a mere radiation-like equation of state) affects particle distributions and subsequent dynamics.