Relic neutrino decoupling with flavour oscillations revisited

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, N eff . We find a value of N eff = 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 N eff can be reduced down to 3.040 or enhanced up to 3.059.

Status of Neutrino Properties and Future Prospects—Cosmological and Astrophysical Constraints

“…More precisely, it represents the density in relativistic species, other than photons, normalized to the energy density of a massless neutrino that decouples well before electron-positron annihilation (that, we remember, is not actually the case). As explained in section 2.5, the standard framework, in which photons and active neutrinos are the only relativistic degrees of freedom present, and neutrino interactions follow the SM of particle physics, predicts N eff = 3.046 after electron-positron annihilation [12,47,48].…”

“…This introduces nonthermal distortions at the subpercent level in the neutrino energy spectrum; the integrated effect is that at early times the combined energy densities of the three neutrino species are not exactly equal to 3ρ ν , with ρ ν given by the upper row of Equation (18), but instead are given by (3.046ρ ν ) [12,47]. A recent improved calculation, including the full collision integrals for both the diagonal and off-diagonal elements of the neutrino density matrix, has refined this value to (3.045ρ ν ) [48]. It is then customary to introduce an effective number of neutrino families N eff and rewrite the energy density at early times as:…”

“…In this review, we will consider N eff = 3.046 as the "standard" value of this parameter in the CDM model, and not the more precise value found in de Salas and Pastor [48], since most of the literature still makes use of the former value. This does not make any difference, however, from the practical point of view, given the sensitivity of present and next-generation instruments.…”

Do joint CMB and HST data support a scale invariant spectrum?

“…This to account for the fact that neutrinos are not completely decoupled during electron-positron annihilation, among other effects (see, e.g., Refs. [29][30][31]). 4 PArthENoPE website: http://parthenope.na.infn.it/ measurement is used as an external Gaussian prior and we refer to this joint data set as "PLC+HST".…”

Thermal axion cosmology and inflationary freedom

“…Thermal axions, while still relativistic, will increase the amount of radiation in the universe, contributing to the effective number of relativistic degrees of freedom N eff . In the standard cosmological ΛCDM model with three active neutrino species, we expect N eff = 3.046 [4,5], where the 0.046 takes into account corrections for the non-instantaneous neutrino decoupling from the primordial plasma. An extra ∆N eff = N eff − 3.046 modifies the damping tail of the Cosmic Microwave Background (CMB) temperature angular power spectrum, changing two important scales at recombination, the sound horizon and the Silk damping, as well as also the primordial abundances of the light elements predicted by Big Bang Nucleosynthesis.…”