Revisiting primordial neutrino asymmetries, spectral distortions and cosmological constraints with full neutrino transport

The primordial neutrino asymmetry leave profound imprints on the evolution history of the universe, which can be constrained by cosmological observations, including Big Bang Nucleosynthesis (BBN), Cosmic Microwave Background (CMB), and Large-Scale Structure (LSS). We present comprehensive analysis on implications and constraints of the primordial neutrino asymmetry $\xi_\nu$, based on a precise treatment of neutrino decoupling by solving the complete (anti)neutrino quantum kinetic equations in the Closed-Time-Path formalism. The effective number of neutrinos $ N_{\rm eff}$ and (anti)neutrino spectral distortions are calculated, and we find that the non-instantaneous decoupling correction is given by $\delta N_{\rm eff} = 0.0440 + 0.0102 \, \xi_\nu^2$. Then we perform the state-of-the-art calculation for the abundance of light elements including (anti)neutrino spectral distortions, which indicate a positive asymmetry $0.032 \leq \xi_\nu \leq 0.052$ from EMPRESS data. The implications of the neutrino asymmetry for the CMB and LSS are studied in detail, and we find that the Baryon Acoustic Oscillations (BAO) are also significantly affected by $\xi_\nu$ in addition to the sum of neutrino masses. A combined analysis with EMPRESS BBN, Planck CMB and BOSS BAO data yields a tighter constraint $\xi_\nu = 0.024 \pm 0.013$, which provides constraints on UV models capable of producing large asymmetries.