Thermalization of large energy release in the early Universe
  Spectral distortions of the cosmic microwave background (CMB) provide a
unique tool for learning about the early phases of cosmic history, reaching
deep into the primordial Universe. At redshifts $z<10^6$, thermalization
processes become inefficient and existing limits from COBE/FIRAS imply that no
more than $\Delta \rho/\rho<6\times 10^{-5}$ (95% c.l.) of energy could have
been injected into the CMB. However, at higher redshifts, when thermalization
is efficient, the constraint weakens and $\Delta \rho/\rho \simeq 0.01-0.1$
could in principle have occurred. Existing computations for the evolution of
distortions commonly assume $\Delta \rho/\rho \ll 1$ and thus become inaccurate
in this case. Similarly, relativistic temperature corrections become relevant
for large energy release, but have previously not been modeled as carefully.
Here we study the evolution of distortions and the thermalization process after
single large energy release at $z>10^5$. We show that for large distortions the
thermalization efficiency is significantly reduced and that the distortion
visibility is sizeable to much earlier times. This tightens spectral
distortions constraints on low-mass primordial black holes with masses $M_{\rm
PBH} < 6\times 10^{11}$ g. Similarly, distortion limits on the amplitude of the
small-scale curvature power spectrum at wavenumbers $k>10^4\,{\rm Mpc}^{-1}$
and short-lived decaying particles with lifetimes $t_X< 10^7$ s are tightened,
however, these still require a more detailed time-dependent treatment. We also
briefly discuss the constraints from measurements of the effective number of
relativistic degrees of freedom and light element abundances and how these
complement spectral distortion limits.
