1212.6943 (Jeremiah Birrell et al.)

Massive Free-Streaming Neutrinos and Rise of $N_ν$ at Recombination    [PDF]

Jeremiah Birrell, Cheng-Tao Yang, Pisin Chen, Johann Rafelski

We present the Einstein-Vlasov solution for the momentum distribution of the relic free-streaming neutrinos. We show that it is possible to explain the rise in the effective number of neutrinos $N_\nu$ from those present at the end of the big bang nucleosynthesis (BBN) $N_\nu(T_{BBN})=3.71^{+0.47}_{-0.45}$ towards $N_\nu(T_{r})=4.34^{+.086}_{-0.88}$ noted at time of electron-ion recombination (r). This increase is due to the interplay of the neutrino mass and the non-equilibrium form of the neutrino distribution after the freeze-out. One implication of our scenario is that the mass of the heaviest neutrino should be near the recombination temperature, $T_r=0.253$ eV. If instead of the Einstein-Vlasov solution, a thermal equilibrium distribution is inadvertently invoked, one would expect a decrease in $N_\nu$ at recombination.

View original: http://arxiv.org/abs/1212.6943