Cosmologically Safe eV-Scale Sterile Neutrinos and Improved Dark Matter Structure

We show that sterile neutrinos with masses $\gtrsim 1\mathrm{eV}$, as motivated by several short baseline oscillation anomalies, can be consistent with cosmological constraints if they are charged under a hidden sector force mediated by a light boson. In this case, sterile neutrinos experience a large thermal potential that suppresses mixing between active and sterile neutrinos in the early Universe, even if vacuum mixing angles are large. Thus, the abundance of sterile neutrinos in the Universe remains very small, and their impact on big bang nucleosynthesis, cosmic microwave background, and large-scale structure formation is negligible. It is conceivable that the new gauge force also couples to dark matter, possibly ameliorating some of the small-scale structure problems associated with cold dark matter.

Figure 1

Comparison of the effective matter potential $V_{\text{eff}}$ for sterile neutrinos (black curves) to the active-sterile oscillation frequency $\mathrm{\Delta }{m}^2/(2E)$ (green line) at $E\simeq T_{\gamma }$ and $\mathrm{\Delta }{m}^2=1{\mathrm{eV}}^2$. As long as $|V_{\text{eff}}|\gg \mathrm{\Delta }{m}^2/(2E)$, oscillations are suppressed. Different black curves show $|V_{\text{eff}}|$ for different values of the gauge boson mass $M$, with solid lines corresponding to $V_{\text{eff}}>0$ and dashed lines indicating $V_{\text{eff}}<0$. Thin (thick) lines show exact numerical (approximate analytical) results. The hidden sector fine-structure constant is taken as ${\alpha }_{\chi }\equiv e_{\chi }^2/(4\pi )=10^{-2}/(4\pi )$. Red lines show the contribution to $V_{\text{eff}}$ from an asymmetric DM particle with $m_{\chi }=1\mathrm{GeV}$. The QCD phase transition and active neutrino decoupling epochs are annotated. The small kinks in the curves are due to changes in $g_{*}$, the effective number of degrees of freedom in the Universe.

Figure 2

Constraints on DM self-interactions from the requirements that the self-interaction in galaxy clusters is small, i.e., $⟨{\sigma }_T⟩/m_{\chi }\lesssim 1{\mathrm{cm}}^2/\mathrm{g}$, and that production of 1 eV sterile neutrinos is suppressed, i.e., ${\sin }^{2}2{\theta }_m\lesssim 10^{-3}$ at $T_{\gamma }=1\mathrm{MeV}$. We also show the favored parameter region for mitigating the cusp versus core and too big to fail problems, i.e., $⟨{\sigma }_T⟩/m_{\chi }=0.1–1{\mathrm{cm}}^2/\mathrm{g}$ in dwarf galaxies, and solve the missing satellites problem ($M_{\text{cut}}=10^{9–10}{M}_{\text{Sun}}$). The kink in the ${\sigma }_T$ contours is from an approximate treatment of the regime between the Born and classical limits.