Neutrino-Dark Sector Equilibration and Primordial Element Abundances

TL;DR

This work investigates how a dark sector that equilibrates with SM neutrinos near the MeV era affects Big Bang Nucleosynthesis and light-element abundances. It develops a quantitative framework for energy transfer between neutrinos and a dark sector via a Boltzmann equation for the transfer fraction $q$, derives the equilibration temperature $T_{\rm eq}$ and the associated $N_{ m eff}$ dynamics, and implements these in the BBN codes PRIMAT and PArthENoPE to compute $Y_{\rm P}$ and D/H under varied electron-flavor content $f_e$ and baryon density $\omega_b$. The study separates cooling effects (incomplete neutrino decoupling and $\nu_e$-driven $p\leftrightarrow n$ rates) from step-like increases in $N_{ m eff}$ due to dark-sector thresholds, finding strong cooling limits down to $T_{\rm eq} \sim 100$ keV when electron neutrinos participate substantially, while electron-neutrino–poor scenarios yield no strong limits below ~2 MeV; step-based limits depend sensitively on $\omega_b$, being very strong at low $\omega_b$ but weak or mildly preferred at higher $\omega_b$. These results, combined with upcoming CMB constraints on $N_{ m eff}$ and $\omega_b$, will sharpen our understanding of sub-MeV dark radiation and neutrino-dark-sector interactions during the early universe, and may inform resolutions to deviations in deuterium abundances.

Abstract

After neutrinos decouple from the photon bath, they can populate a thermal dark sector. If this occurs at a temperature above ~100 keV, this can have measurable impacts on light element abundances. We calculate light element abundances in this scenario, studying the impact from rapid cooling of the Standard Model neutrinos, and from an increase in the number of relativistic degrees of freedom $N_{\rm{eff}}$, which can occur in the presence of a mass threshold. We incorporate these changes in the publicly available BBN code PRIMAT, using the reaction networks from PRIMAT and from the BBN code PArthENoPE, to calculate Y$_{\rm{P}}$ and D/H. We provide limits from the two different reaction networks as well as with expanded errors to include both results. If electron neutrinos significantly participate in the cooling, we find limits down to temperatures as low as 100 keV. If electron neutrinos are weakly participating (for instance if only the mass eigenstate $ν_3$ equilibrates), cooling places no limits. However, if the dark sector undergoes a "step" in $N_{\rm{eff}}$, there can be additional, $ω_b$-dependent constraints. These limits can vary from strong (for low values of $ω_b$) to a mild preference for new physics (for high values of $ω_b$). Future analyses including upcoming CMB data should improve these limits.

Figures (17)

• Figure 1: Evolution of the dark radiation and interacting (thermalizing) neutrinos versus background neutrino temperature. $q(T)$ and $1-q(T)$ describe the energy densities of the equilibrating fluids, with $q(T) = \rho_d/(N_{\rm{int}}\rho_{\nu 0})$ and $1-q(T)=\rho_{\nu}^{\rm{int}}/(N_{\rm{int}}\rho_{\nu 0})$.
• Figure 2: Change in $N_{\rm eff}$ after neutrino cooling at $T=T_{{\rm eq}}$ as a function of $q_{\rm eq}$. Recall $q_{\rm eq}=1$ corresponds to complete cooling of the equilibrating neutrinos and $q_{\rm eq}=0$ is the SM.
• Figure 3: Changes in abundances due to neutrino cooling. The reaction network used to calculate these abundances encompasses the predictions of PRIMAT Pitrou_2018 and PArthENoPE Consiglio_2018; see Section \ref{['sec:limits']}. To be compared with the experimental values $\textrm{Y}_{\textrm{P}}=0.245 \pm 0.003$Workman_2022 and $10^5\textrm{D/H}=2.527\pm 0.030$Cooke_2018.
• Figure 4: The regions allowed at $1\sigma$ (red) and $2\sigma$ (yellow) in the cooling scenario, calculated in the "combined" network, for different values of $f_e$. $\omega_b^*$ is the central value of $\omega_b$ assumed to calculate $\chi^2$, and $\chi^2_m$ is the minimum $\chi^2$ attained by the model in this region of parameter space. $f_e$ is fixed, while $\omega_b$ is profiled over (see Appendix \ref{['app:full_results']}), with $\sigma_{\omega_b^*}=0.00022$.
• Figure 5: The regions allowed at $1\sigma$ (red) and $2\sigma$ (yellow) in the step scenario, calculated in the "combined" network, for different values of $\omega_b^*$. See Figure \ref{['fig:cooling_both']} caption for definitions of $\omega_b^*$ and $\chi^2_m$.