Abstract
We study the decoupling process of neutrinos in the early universe in the presence of three-flavour oscillations. The evolution of the neutrino spectra is found by solving the corresponding momentum-dependent kinetic equations for the neutrino density matrix, including for the first time the proper collision integrals for both diagonal and off-diagonal elements. This improved calculation modifies the evolution of the off-diagonal elements of the neutrino density matrix and changes the deviation from equilibrium of the frozen neutrino spectra. However, it does not vary the contribution of neutrinos to the cosmological energy density in the form of radiation, usually expressed in terms of the effective number of neutrinos, Neff. We find a value of Neff = 3.045, in agreement with previous theoretical calculations and consistent with the latest analysis of Planck data. This result does not depend on the ordering of neutrino masses. We also consider the effect of non-standard neutrino-electron interactions (NSI), predicted in many theoretical models where neutrinos acquire mass. For two sets of NSI parameters allowed by present data, we find that Neff can be reduced down to 3.040 or enhanced up to 3.059.
Highlights
We study the decoupling process of neutrinos in the early universe in the presence of three-flavour oscillations
We have calculated the evolution of the momentum spectra of neutrinos and found their final contribution to the cosmological energy density in the form of radiation, given by the effective number of neutrinos, Neff
This problem requires the numerical solution of the corresponding momentum-dependent kinetic equations for the neutrino density matrix, that we have performed including the full collision terms for neutrino-electron processes
Summary
We study the decoupling process of neutrinos in the early universe in the presence of three-flavour oscillations. We find a value of Neff = 3.045, in agreement with previous theoretical calculations and consistent with the latest analysis of Planck data This result does not depend on the ordering of neutrino masses. The process of neutrino decoupling in the early universe takes place at a temperature of the order of MeV, when weak interactions are no longer effective to keep neutrinos in thermal contact with electrons, positrons, and, indirectly, with photons. It has been shown in previous works In order to take into account the effects of both interactions and oscillations, we consider the evolution of the neutrino density matrix p, ee eμ eτ fνe a1 + ia b1 + ib
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