# Did the Universe Reheat After Recombination?

A key assumption of the standard cosmological model is that the temperature of the cosmic microwave background (CMB) radiation scales with cosmological redshift $z$ as $T_{\rm CMB}(z) \propto (1+z)$ at all times after recombination at $z_\star \simeq 1090$. However, this assumption has only been precisely tested at $z \lesssim 3$. Here, we consider cosmological models with post-recombination reheating (PRR), in which the CMB monopole temperature abruptly increases due to energy injection after last scattering. Such a scenario can potentially resolve tensions between inferences of the current cosmic expansion rate (the Hubble constant, $H_0$). We consider an explicit model in which a metastable sub-component of dark matter (DM) decays to Standard Model photons, whose spectral energy distribution is assumed to be close to that of the CMB blackbody. A fit to Planck CMB anisotropy, COBE/FIRAS CMB monopole, and SH0ES distance-ladder measurements yields $H_0 = 71.2 \pm 1.1$ km/s/Mpc, matter fluctuation amplitude $S_8 = 0.774 \pm 0.018$, and CMB temperature increase $\delta T_{\rm CMB} = 0.109^{+0.033}_{-0.044}$ K, which is sourced by DM decay at $z \gtrsim 10$. However, matter density constraints from baryon acoustic oscillation and supernovae data highly constrain this scenario, with a joint fit to all datasets yielding $H_0 = 68.69 \pm 0.35$ km/s/Mpc, $S_8 = 0.8035 \pm 0.0081$, and $\delta T_{\rm CMB} < 0.0342$ K (95% CL upper limit). These bounds can be weakened if additional dark relativistic species are present in the early universe, yielding higher $H_0$. We conclude that current data disfavor models with significant PRR solely through its impact on background and linear-theory observables, completely independent of CMB spectral distortion constraints. However, a small amount of such energy injection could play a role in restoring cosmological concordance.

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