Neutrino energy transport in weak decoupling and big bang nucleosynthesis

TL;DR

This work presents a fully self-consistent, non-perturbative treatment of neutrino energy transport during the weak-decoupling and BBN epochs by coupling a multi-energy-group Boltzmann transport for active neutrinos to a complete strong/electromagnetic/weak nuclear reaction network. It demonstrates a nonlinear feedback between evolving neutrino spectra, entropy transfer, and plasma thermodynamics, leading to measurable shifts in the radiation content and primordial abundances. The study finds that neutrino transport increases D/H by about 0.4% and raises $N_ extnormal{eff}$ to approximately $3.03$–$3.05$ depending on QED corrections, with helium and lithium impacts being smaller and within current observational uncertainties. These results emphasize the need for fully coupled, non-equilibrium modeling to reach percent-level precision in early-universe predictions and motivate future quantum kinetic analyses including neutrino flavor oscillations.

Abstract

We calculate the evolution of the early universe through the epochs of weak decoupling, weak freeze-out and big bang nucleosynthesis (BBN) by simultaneously coupling a full strong, electromagnetic, and weak nuclear reaction network with a multi-energy group Boltzmann neutrino energy transport scheme. The modular structure of our code provides the ability to dissect the relative contributions of each process responsible for evolving the dynamics of the early universe in the absence of neutrino flavor oscillations. Such an approach allows a detailed accounting of the evolution of the $ν_e$, $\barν_e$, $ν_μ$, $\barν_μ$, $ν_τ$, $\barν_τ$ energy distribution functions alongside and self-consistently with the nuclear reactions and entropy/heat generation and flow between the neutrino and photon/electron/positron/baryon plasma components. This calculation reveals nonlinear feedback in the time evolution of neutrino distribution functions and plasma thermodynamic conditions (e.g., electron-positron pair densities), with implications for: the phasing between scale factor and plasma temperature; the neutron-to-proton ratio; light-element abundance histories; and the cosmological parameter \neff. We find that our approach of following the time development of neutrino spectral distortions and concomitant entropy production and extraction from the plasma results in changes in the computed value of the BBN deuterium yield. For example, for particular implementations of quantum corrections in plasma thermodynamics, our calculations show a $0.4\%$ increase in deuterium. These changes are potentially significant in the context of anticipated improvements in observational and nuclear physics uncertainties.

Figures (12)

• Figure 1: (Color online) The relative change, as in Eq. \ref{['trans-eqn:dfandfeq']}, in the occupation probability as a function of the comoving temperature $T_\textnormal{cm}$. Three values of $\epsilon$ are evaluated at $\epsilon=3,5$ and $7$. The solid lines are for electron-flavor neutrinos, and the dashed lines are for muon-flavor neutrinos. The larger $\delta f$ correspond to larger $\epsilon$ values.
• Figure 2: (Color online) The relative change, as in Eq. \ref{['trans-eqn:dfandfeq']}, in the occupation probability as a function of $\epsilon$ for $T_\textnormal{cm}\xspace=1$ keV. The larger change is the electron-flavor neutrinos, over the muon-flavor neutrinos. The antineutrino evolution is nearly identical to the neutrino evolution for all flavors.
• Figure 3: (Color online) The difference in relative changes in the occupation probabilities of $\nu$ and $\overline{\nu}$ [Eq. \ref{['eqn:dfbar']}] as a function of comoving temperature $T_\textnormal{cm}$. Three values of $\epsilon$ are plotted at $\epsilon=3,5$ and $7$. The solid lines are for electron-flavor neutrinos, and the dashed lines are for muon-flavor neutrinos. The $\nu_{e}$ experience a larger change than the $\nu_\mu$.
• Figure 4: (Color online) The normalized change in the differential energy density [Eq. \ref{['eqn:ded']}] as a function of $\epsilon$. The electron neutrinos exhibit a larger change compared to the muon neutrinos. The antineutrino evolution is nearly identical to the neutrino evolution for all flavors.
• Figure 5: (Color online) Quantities related to energy density and temperature are plotted against the comoving temperature parameter. The blue solid curve shows the change in $N_\textnormal{eff}$ using Eq. \ref{['trans-eqn:neffevolve']}. The red dashed curve shows the relative change in the energy density of $\nu_{e}$. The green dash-dot curve shows the relative change in the energy density of $\nu_\mu$. The magenta dotted curve shows the relative change in $T_\textnormal{cm}/T$ using Eq. \ref{['trans-eqn:dtcmpl']}. At a given $T_\textnormal{cm}$, $\delta T_\textnormal{cm}/T\xspace>0$ is equivalent to a lower plasma temperature in the transport case compared to no transport.