Maximal temperature of strongly-coupled dark sectors

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 (${\Lambda }_{\mathrm{IR}}^{}$). Below a certain threshold ${\Lambda }_{\mathrm{IR}}^{}<{\Lambda }_0^{}\sim 2\times 10_{}^{-8}{m}_{\mathrm{pl}}^{}$, the system heats up to $T_{\max }^{}\sim {\Lambda }_0^{}>T_{\mathrm{c}}^{}$, and a first-order thermal phase transition takes place. On the other hand, if ${\Lambda }_{\mathrm{IR}}^{}>{\Lambda }_0^{}$, then $T_{\max }^{}\sim {\Lambda }_{\mathrm{IR}}^{}<T_{\mathrm{c}}^{}$: 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 ${\Lambda }_0^{}$. The heating-up dynamics generates a gravitational wave background. Its contribution to $N_{\mathrm{eff}}^{}$ at GHz frequencies, the presence of a monotonic $\sim f_0^3$ shape at $(10_{}^{-4}-10_{}^2)$Hz frequencies, and the frequency domain of peaked features that may originate via first-order phase transitions, are discussed.

21 pages. v2: clarifications added

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