Lepton Number and Expansion of the Universe

Abstract

We show that the non-integer effective number of neutrinos $N_{\nu }^{\mathrm{eff}}$ can be understood as an effect of lepton $L$ asymmetry in the early Universe carried by the Dirac neutrino cosmic background. We show that $N_{\nu }^{\mathrm{eff}}=3.36\pm 0.34$ (CMB only) and $N_{\nu }^{\mathrm{eff}}=3.62\pm 0.25$ (CMB and $H_0$) require a ratio between baryon number $B$ and lepton number to be $1.16\times 10^{-9}⩽B/|L|⩽1.51\times 10^{-9}$. These values are close to the baryon-to-photon ratio $0.57\times 10^{-9}⩽B/N_{\gamma }⩽0.67\times 10^{-9}$. Thus instead of the usual $|L|\ll N_{\gamma }$ and $B\simeq |L|$, we propose to use $0.4⩽|L|/N_{\gamma }⩽0.52$ and $B\ll |L|$ as another natural choice, which resolves the tension between Planck-CMB and $H_0$ and leads to a non-integer value of $N_{\nu }^{\mathrm{eff}}>3$.

Comments: 6 pages, 5 figures