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Abstract Taking axion inflation as an example, we estimate the maximal temperature (T max) that can be reached in the post-inflationary universe, as a function of the confinement scale of a non-Abelian dark sector (ΛIR). Below a certain threshold ΛIR < Λ0 ∼ 2 × 10 −8 m pl, the system heats up to T max ∼ Λ0 > T c, and a first-order thermal phase transition takes place. On the other hand, if ΛIR > Λ0, then T max ∼ ΛIR < T c: very high temperatures can be reached, but there is no phase transition. If the inflaton thermalizes during heating-up (which we find to be unlikely), or if the plasma includes light degrees of freedom, then heat capacity and entropy density are larger, and T max is lowered towards Λ0. The heating-up dynamics generates a gravitational wave background. Its contribution to N eff at GHz frequencies, the presence of a monotonic ∼ f 0 3 $$ {f}_0^3 $$ shape at (10 −4 – 102) Hz frequencies, and the frequency domain of peaked features that may originate via first-order phase transitions, are discussed. |
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