A precision calculation of the effective number of cosmological neutrinos
G. Mangano, G. Miele, S. Pastor, M. Peloso
TL;DR
The paper tackles a precision calculation of the cosmological effective number of neutrinos, $N_\nu^{\rm eff}$, by solving the Boltzmann equations for incomplete neutrino decoupling during $e^{\pm}$ annihilation and incorporating finite-temperature QED corrections to the electromagnetic plasma. The main result is $N_\nu^{\rm eff}=3.0395$ for three massless active neutrinos, in excellent agreement with the CMBFAST benchmark $3.04$, with the non-additive interplay between the two effects reducing the total correction by about 10%. The authors also develop a framework to assess extra relativistic relics via $\Delta N_\nu^{\rm eff}$ and to quantify the impact of finite neutrino masses on $N_\nu^{\rm eff}$, providing mass-dependent corrections. These results refine the input for high-precision CMB analyses and for constraining new relativistic species in the early Universe.
Abstract
The neutrino energy density of the Universe can be conveniently parametrized in terms of the so-called effective number of neutrinos, N_nu^eff. This parameter enters in several cosmological observables. In particular it is an important input in those numerical codes, like CMBFAST, which are used to study the Cosmic Microwave Background anisotropy spectrum. By studying the neutrino decoupling with Boltzmann equations, one can show that this quantity differs from the number of massless neutrino species for an additional contribution due to a partial heating of neutrinos during the electron-positron annihilations, leading to non thermal features in their final distributions. In this paper we review the different results obtained in the literature and perform a new analysis which takes into account, in a fully consistent way, the QED corrections at finite temperature to the photon and e^+- plasma equation of state. The value found for three massless active neutrinos is N_nu^eff=3.0395, in perfect agreement with the recommended value used in CMBFAST, N_nu^eff=3.04. We also discuss the case of additional relativistic relics and massive active neutrinos.