Thermalization of large energy release in the early Universe

TL;DR

This paper investigates how large energy releases in the early Universe affect cosmic microwave background spectral distortions, revealing that thermalization is less efficient for big distortions, which tightens existing constraints on primordial black holes, small-scale curvature, and decaying particles.

Contribution

It provides a detailed analysis of the evolution of spectral distortions after large energy injections at high redshifts, improving the modeling of thermalization processes and relativistic corrections.

Findings

Thermalization efficiency decreases for large distortions.

Spectral distortion constraints on primordial black holes are tightened.

Limits on small-scale curvature and decaying particles are improved.

Abstract

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.