$\mathrm{U}{(1)}_{B-L}$ symmetry restoration and effective neutrino species

Abstract

The $\mathrm{U}{(1)}_{B-L}$ symmetry could be restored during inflation, since the BICEP2 results suggest a GUT-scale inflation with the Hubble parameter, $H_{\inf }\simeq {10}^{14}\text{GeV}$, close to the $\mathrm{U}{(1)}_{B-L}$ breaking scale. We consider a scenario in which the $B-L$ Higgs field dominates the Universe after inflation, and mainly decays into the $\mathrm{U}{(1)}_{B-L}$ gauge bosons, whose subsequent decays reheat the Universe. Interestingly, if one of the right-handed neutrinos is extremely light and behaves as dark radiation or hot dark matter, its abundance is determined by the $B-L$ charge assignment and the relativistic degree of freedom in plasma. We find that $\mathrm{\Delta }{N}_{\mathrm{eff}}$ takes discrete values between 0.188 and 0.220 in the standard model plus three right-handed neutrinos, depending on whether the decay into heavier right-handed neutrinos is kinematically accessible or not. In the fiveness $\mathrm{U}{(1)}_{\mathbf{5}}$ case, we find that $\mathrm{\Delta }{N}_{\mathrm{eff}}$ takes discrete values between 0.313 and 0.423. The tension between BICEP2 and Planck can be partially relaxed by dark radiation.