Non equilibrium spectra of degenerate relic neutrinos

TL;DR

This work computes the exact kinetic evolution of relic neutrinos with a large lepton asymmetry by solving the Boltzmann equations for neutrino distributions using an orthonormal-polynomial expansion, revealing momentum-dependent spectral distortions that persist until complete decoupling. It extends prior non-degenerate analyses to degenerate neutrinos, deriving final photon-to-neutrino temperature relations and fitting the distorted spectra $f_{\nu_\alpha}^D(y)$ for $0 \leq \xi_{\nu_e} \leq 0.5$ and $0 \leq \xi_{\nu_x} \leq 1$. Numerically, the distortions are larger for antineutrinos at positive asymmetries and smaller for neutrinos, with negligible net impact on $^4$He production in BBN due to cancellations, while a small increase in the relic neutrino energy density $\Delta N_\nu$ has potential implications for CMB anisotropies and Planck-era constraints. The results validate the non-degenerate limit and provide quantitative tools (spectral fits) to incorporate degenerate neutrinos into early-universe phenomenology and parameter estimation.

Abstract

We calculate the exact kinetic evolution of cosmic neutrinos until complete decoupling, in the case when a large neutrino asymmetry exists. While not excluded by present observations, this large asymmetry can have relevant cosmological consequences and in particular may be helpful in reconciling Primordial Nucleosynthesis with a high baryon density as suggested by the most recent observations of the Cosmic Microwave Background Radiation. By solving numerically the Boltzmann kinetic equations for the neutrino distribution functions, we find the momentum-dependent corrections to the equilibrium spectra and briefly discuss their phenomenological implications.

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