Implications of finite chemical potential for cosmological relic neutrinos*

The chemical potential for cosmological relic neutrinos is usually assumed to be zero, even though a tight bound exists only for electron-type neutrinos via Big Bang Nucleosynthesis (BBN), and large chemical potentials for muon-type and tau-type neutrinos are still allowed. We show that the Cosmic Microwave Background (CMB) and galaxy pairwise velocity data prefer a finite and large neutrino chemical potential, which would significantly alleviate both the Hubble and S8 tensions. The effect of a finite neutrino chemical potential on large-scale structures is opposite to that of neutrino mass, so care must be taken if the latter is measured in cosmological observation. We suggest ways to break this parameter degeneracy.