More Is Different: Reconciling eV Sterile Neutrinos with Cosmological Mass Bounds

TL;DR

The paper tackles the tension between eV-scale sterile neutrinos suggested by oscillation anomalies and cosmological mass bounds. It proposes secret self-interactions in the sterile sector that generate a large matter potential to suppress early production, followed by late-time flavor equilibration with active neutrinos. By solving quantum kinetic equations, it shows that flavor equilibration can occur after BBN, leading to a reduced late-time $N_{\rm eff}$, especially when multiple sterile states are present. This framework relaxes the cosmological mass bounds and can accommodate Planck-era constraints, with $n=3$ sterile species being a minimal viable extension; it also highlights the role of a dark sector in setting initial $\delta N_{\rm eff}^{0}$. Overall, the work suggests a pathway to reconcile short-baseline neutrino anomalies with cosmological observations via a multi-sterile, self-interacting sector.

Abstract

It is generally expected that adding light sterile species would increase the effective number of neutrinos, $N_{eff}$. In this paper we discuss a scenario that $N_{eff}$ can actually decrease due to the neutrino oscillation effect if sterile neutrinos have self-interactions. We specifically focus on the eV mass range, as suggested by the neutrino anomalies. With large self-interactions, sterile neutrinos are not fully thermalized in the early Universe because of the suppressed effective mixing angle or matter effect. As the Universe cools down, flavor equilibrium between active and sterile species can be reached after big bang nucleosynthesis (BBN) epoch, but leading to a decrease of $N_{eff}$. In such a scenario, we also show that the conflict with cosmological mass bounds on the additional sterile neutrinos can be relaxed further when more light species are introduced.

Figures (4)

• Figure 1: Thermal history of active/sterile neutrinos. When the temperature is high, $\nu_s$s are not in thermal equilibrium with $\nu_a$s because of the suppression from a large matter potential. As the Universe cools down, equilibrium between active and sterile neutrinos could be reached.
• Figure 2: Evolution of $\delta N_{\textrm{eff}}$ as temperature $T_\gamma$ decreases. $\delta N^{\textrm{bbn}}_{\textrm{eff}}$ depends on the self-interaction strength $G_X$. Black curve shows the non-interacting case, $G_X=0$. The self-interaction can suppress the production of sterile neutrino at high temperature, but lead to flavor equilibrium at later time. Increasing the strength of self-interacting would delay the equilibrium time.
• Figure 3: $\delta N^{\textrm{bbn}}_{\textrm{eff}}$ vs $\delta N^{\textrm{cmb}}_{\textrm{eff}}$. (Left panel)We choose several cases for the number of sterile species, as indicated by $n$. For each case, the solid curve shows $\delta N^{\textrm{bbn}}_{\textrm{eff}}$ while the dashed one gives $\delta N^{\textrm{cmb}}_{\textrm{eff}}$. Sizable differences can arise in the low $T_{\nu_s}/T^0_{\nu_a}$ region. (Right panel)$\delta N^{\textrm{cmb}}_{\textrm{eff}}$ as function of $\delta N^{\textrm{bbn}}_{\textrm{eff}}$. The solid black line is for $\delta N^{\textrm{cmb}}_{\textrm{eff}}=\delta N^{\textrm{bbn}}_{\textrm{eff}}$ in non-interacting case, and from up to down, dashed lines correspond to $n=1,2,3,6$. Dot-dashed orange lines mark the current bounds from PlanckPlanck:2015xua.
• Figure 4: (Left panel)$m^{\textrm{eff}}_{\nu}$ vs $n$. $m^{\textrm{eff}}_{\nu}$ is a model-dependent quantity. We show how it changes as $T_{\nu_s}/T^0_{\nu_a}$ varies in four cases with different $n$. $m_{\nu_4}=1$eV is assumed to be dominant on the mass. (Right panel)$m^{\textrm{eff}}_{\nu}$ as functions of $\delta N^{\textrm{cmb}}_{\mathrm{eff}}$ and $n$. Parameter space inside region marked with arrows is still allowed.