U(1)B−LU(1)B−L symmetry restoration and effective neutrino species

The U(1)B−LU(1)B−L symmetry could be restored during inflation, since the BICEP2 results suggest a GUT-scale inflation with the Hubble parameter, Hinf≃1014 GeVHinf≃1014 GeV, close to the U(1)B−LU(1)B−L breaking scale. We consider a scenario in which the B−LB−L Higgs field dominates the Universe after inflation, and mainly decays into the U(1)B−LU(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−LB−L charge assignment and the relativistic degree of freedom in plasma. We find that ΔNeffΔNeff 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 U(1)5U(1)5 case, we find that ΔNeffΔNeff takes discrete values between 0.313 and 0.423. The tension between BICEP2 and Planck can be partially relaxed by dark radiation.