Additional Light Sterile Neutrinos and Cosmology

TL;DR

The paper investigates whether two light sterile neutrinos (a ${ m 3+2}$ scenario) can be reconciled with cosmological data while accommodating terrestrial hints of sterile neutrinos. It develops both analytic and numerical treatments of partial thermalization and mass effects, evaluating the contributions to ${N_{ m eff}}$ at BBN and at the CMB epoch (matter-radiation equality). The results show that partial thermalization and sub-relativistic masses can reduce the sterile contribution but do not suffice to satisfy all constraints at the 95% CL; specifically, ${N^{ m BBN}_{ m eff}}$ can remain too large and ${N^{z_{ m eq}}_{ m eff}}$ remains inconsistent with combined bounds when taking into account the implied neutrino mass sum. The study highlights the tension between SBL indications for sterile neutrinos and cosmological limits, and discusses potential new physics avenues such as lepton asymmetries or extra massless degrees of freedom that would need to be carefully balanced against other cosmological observables.

Abstract

Tantalizing cosmological and terrestrial evidence suggests the number of light neutrinos may be greater than 3, motivating a careful re-examination of cosmological bounds on extra light species. Big Bang Nucleosynthesis constrains the number of relativistic neutrino species present during nucleosynthesis, $N_{eff}^{BBN}$, while measurements of the CMB angular power spectrum constrain the effective energy density in relativistic neutrinos at the time of matter-radiation equality, $N_{eff}^{CMB}$. There are a number of scenarios where new sterile neutrino species may have different contributions to $ΔN_{eff}^{BBN}$ and $ΔN_{eff}^{CMB}$, for masses that may be relevant to reconciling cosmological constraints with various terrestrial claims of neutrino oscillations. We consider a scenario with two sterile neutrinos and explore whether partial thermalization of the sterile states can ease the tension between cosmological constraints on $N_{eff}^{BBN}$ and terrestrial data. We then investigate the effect of a non-zero neutrino mass on their contribution to the radiation abundance, finding reductions in $ΔN_{eff}^{CMB}$ of more than 5% for neutrinos with masses above 0.5 eV. While the effects we investigate here could play a role, we nevertheless find that two additional light sterile neutrinos species cannot fit all the data at the 95% confidence level.

Figures (3)

• Figure 1: Sterile neutrino density evolution as a fraction of the thermal density $\rho_{\rm eq}$, for the masses and mixing angles listed in Table \ref{['parameters']}. Dashed lines are for $\nu_{s}$, solid lines are for $\nu_{r}$.
• Figure 2: Contribution of one thermalized massive sterile neutrino to ${N_{\rm eff}}$ at the time of matter-radiation equality. If the sterile neutrino has an approximately Fermi-Dirac distribution, this is equivalent to $\Delta N_{\rm eff}^{z_{\rm eq}} / \Delta N_{\rm eff}^{\rm BBN}$, i.e. if the sterile neutrino is not fully thermalized and $\Delta N_{\rm eff}^{\rm BBN} < 1$, then $\Delta N_{\rm eff}^{z_{\rm eq}}$ will be reduced accordingly.
• Figure 3: Contribution of one massive sterile neutrino to ${N_{\rm eff}}$ as a function of the equivalent temperature of a massless neutrino, $T_\nu$. At matter-radiation equality, $T_\nu = 0.55$ eV Hinshaw:2012fq.