U_{(1)B -L} symmetry restoration and effective neutrino species

The U_{(1)B -L} symmetry could be restored during inflation, since the BICEP2 results suggest a GUT-scale inflation with the Hubble parameter, _Hinf ≃¹⁰¹⁴GeV, 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 δ_Neff 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₎₅ case, we find that δ_Neff takes discrete values between 0.313 and 0.423. The tension between BICEP2 and Planck can be partially relaxed by dark radiation.