Nonequilibrium Corrections to the Spectra of Massless Neutrinos in the Early Universe

TL;DR

This work investigates nonequilibrium corrections to the spectra of massless neutrinos in the early universe by solving the covariant Boltzmann equation with a reduced two-dimensional collision integral. The authors compute the coupled evolutions of $f_{\nu_e}(x,y)$, $f_{\nu_\mu}(x,y)$ and the photon temperature $T_\gamma(x)$, using both full distribution functions and deviations from equilibrium, and enforce energy conservation via $3H^2 m_{Pl}^2 = 8\pi \rho$. They find relative neutrino energy-density corrections of about $0.9\%$ for $\nu_e$ and $0.4\%$ for $\nu_\mu,\nu_\tau$, and a corresponding impact on Big Bang Nucleosynthesis with $\Delta Y_{^4He} \approx 1.4\times10^{-4}$; spectral distortions are momentum-dependent and larger at high $y$, with notable differences between FD and MB statistics. The results refine the understanding of radiation energy density and light-element yields in the early universe, with implications for precise cosmological constraints.

Abstract

Distortion of the equilibrium spectra of cosmic neutrinos due to interaction with hotter electrons and positrons in the primeval cosmic plasma is considered. The set of integro-differential kinetic equations for neutrinos is accurately numerically solved. The relative corrections to neutrino energy densities are approximately 0.9% for $ν_e$ and 0.4% for $ν_μ$ and $ν_τ$. This effect results in $1.4 \cdot 10^{-4}$ increase in the primordial $^4 He$ abundance.