$N_{\rm eff}$ in low-scale seesaw models versus the lightest neutrino mass

TL;DR

This paper analyzes how sterile neutrinos in low-scale seesaw models affect the effective number of neutrino species, $N_{\rm eff}$, and explores cosmological constraints on their masses and thermalization.

Contribution

It provides a comprehensive analysis of sterile state thermalization in low-scale seesaw models and links it to cosmological and neutrinoless double beta decay constraints.

Findings

At least two heavy sterile states always thermalize in the early universe.

The third sterile state may not thermalize if the lightest neutrino mass is below 10^{-3} eV.

Cosmological constraints restrict heavy sterile states to the 1 eV - 100 MeV range.

Abstract

We evaluate the contribution to $N_{\rm eff}$ of the extra sterile states in low-scale Type I seesaw models (with three extra sterile states). We explore the full parameter space and find that at least two of the heavy states always reach thermalisation in the Early Universe, while the third one might not thermalise provided the lightest neutrino mass is below ${\mathcal O}(10^{-3}$eV). Constraints from cosmology therefore severely restrict the spectra of heavy states in the range 1eV- 100 MeV. The implications for neutrinoless double beta decay are also discussed.