U(1)${}_{B-L}$ Symmetry Restoration and Effective Neutrino Species

Abstract

The U(1)${}_{B-L}$ symmetry could be restored during inflation, since the BICEP2 results suggest a GUT-scale inflation with the Hubble parameter, $H_{\inf }\simeq 10^{14}$ GeV, close to the 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 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 $\hat{I}”N_{\mathrm{eff}}$ 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 are kinematically accessible or not. In the fiveness U(1)${}_5$ case, we find that $\hat{I}”N_{\mathrm{eff}}$ takes discrete values between $0.313$ and $0.423$. The tension between BICEP2 and {\it Planck} can be partially relaxed by dark radiation.

14 pages, v2: corrected small errors in calculations, conclusions unchanged