arXiv2024
Very different processes characterize the decoupling of neutrinos to form the cosmic neutrino background (C$ν$B) and the much later decoupling of photons from thermal equilibrium to form the cosmic microwave background (CMB). The C$ν$B emerges from the fuzzy, energy-dependent neutrinosphere and encodes the physics operating in the early universe in the temperature range $T\sim 10\,{\rm MeV}$ to $T\sim10\,{\rm keV}$. This is the epoch where beyond Standard Model (BSM) physics may be influential in setting the light element abundances and the necessarily distorted fossil neutrino energy spectra. Here we use techniques honed in extensive CMB studies to analyze the C$ν$B as calculated in detailed neutrino energy transport and nuclear reaction simulations. Our moment method, relative entropy, and differential visibility approach can leverage future high precision CMB and primordial abundance measurements to provide new insights into the C$ν$B and any BSM physics it encodes. We demonstrate that the evolution of the energy spectrum of the C$ν$B throughout the weak decoupling epoch is accurately captured in the Standard Model by only three parameters per species, a non-trivial conclusion given the deviation from thermal equilibrium. Furthermore, we can interpret each of the three parameters as physical characteristics of a non-equilibrium system. The success of our compact description within the Standard Model motivates its use also in BSM scenarios. We demonstrate how observations of primordial light element abundances can be used to place constraints on the C$ν$B energy spectrum, deriving response functions that can be applied for general C$ν$B spectral distortions. Combined with the description of those deviations that we develop here, our methods provide a convenient and powerful framework to constrain the impact of BSM physics on the C$ν$B.