CMB spectral distortions from continuous large energy release

Accurate computations of spectral distortions of the cosmic microwave background (CMB) are required for constraining energy release scenarios at redshifts $z\gtrsim 10^3$. The existing literature focuses on distortions that are small perturbations to the background blackbody spectrum. At high redshifts ($z\gtrsim 10^6$), this assumption can be violated, and the CMB spectrum can be significantly distorted at least during part of its cosmic evolution. In this paper, we carry out accurate thermalization computations, evolving the distorted CMB spectrum in a general, fully non-linear way, consistently accounting for the time-dependence of the injection process, modifications to the Hubble expansion rate and relativistic Compton scattering. Specifically, we study single energy injection and decaying particle scenarios, discussing constraints on these cases. We solve the thermalization problem using two independent numerical approaches that are now available in {\tt CosmoTherm} as dedicated setups for computing CMB spectral distortions in the large distortion regime. New non-linear effects at low frequencies are furthermore highlighted, showing that these warrant a more rigorous study. This work eliminates one of the long-standing simplifications in CMB spectral distortion computations, which also opens the way to more rigorous treatments of distortions induced by high-energy particle cascade, soft photon injection and in the vicinity of primordial black holes.