Less structure on $8$ Mpc scales from decaying sterile neutrino dark matter

TL;DR

This work tackles the $S_8$ tension by proposing a dark-sector model with two interacting sterile neutrinos $N_1,N_2$ and a scalar mediator $\phi$, where $N_1$ (the dominant DM component) is produced in the early Universe and later decays to three $N_2$ when $m_1\ge 3m_2$. The decay products are all massive, yielding a non-relativistic warm component that suppresses structure on scales around $8\,\text{Mpc}$, captured by a three-body energy-release parameter $q=(m_1-3m_2)/m_1$ and lifetime $\tau\sim 10^{18}-10^{19}$ s. Production is enhanced relative to the Dodelson–Widrow mechanism by self-interactions mediated by $\phi$, allowing smaller mixing angles $\sin\theta$ to achieve the observed relic density; a mild hierarchy in the Yukawas $y_{11},y_{22},y_{12}$ ensures a sufficient $N_1$ abundance that survives conversion to $N_2$. Constraints from X-ray searches and Ly$\alpha$ forest data are incorporated, yielding a viable parameter window with $m_1\sim 10-100\,\text{keV}$ and $q$ in the range $3.3\times10^{-4}-3.7\times10^{-2}$, thus providing a concrete dark-sector realization of late-time structure modification that is consistent with existing observational bounds.

Abstract

Late decays of dark matter to a lighter, warm dark matter component are a known way to reduce the amplitude of the matter power spectrum on scales of $8$ Mpc. However, only very few particle physics models have been put forward that exhibit the required properties and allow to relate them to other observables. In this work, we investigate a model based on two interacting sterile neutrinos and a scalar singlet. The heavier of the neutrinos is produced in the early Universe by the interplay of oscillations and the new interactions in the dark sector and constitutes the dominant component of dark matter. If the Yukawa matrix that describes the interactions of the steriles with the scalar is not diagonal, the heavier state can decay to three light sterile neutrinos. In contrast to the usual scenario, this leads to an all massive final state without radiation-like particles. We identify the part of the parameter space where these decays can lead to a reduction of S$_8$ at a level that matches observations. We then confront this region with the requirements of reproducing the observed relic density, as well as existing constraints from X-ray searches and Lyman-$α$ forest data.

Figures (6)

• Figure 1: Lowest-order contributions to the sterile neutrinos' self-energy. Thick lines represent thermal propagators.
• Figure 2: Representative diagrams for the sterile neutrino processes relevant for DM production.
• Figure 3: Evolution of the fraction of $N_1$ particles as a function of the ratio $y_{22}/y_{11}$ for an illustrative mass ratio $m_\phi/m_1 = 10$. The blue solid line corresponds to $y_{11} = 10^{-3}$, while the orange solid line corresponds to $y_{11} = 5 \times 10^{-4}$. The dashed black lines indicate the fractions corresponding to $N_1$ accounting for the entire dark-matter relic abundance and for 10% of it.
• Figure 4: Representative Feynman diagram for the decay of the heavier sterile $N_1$ into three $N_2$.
• Figure 5: Parameter space in the $m_1 - \sin^2(2\theta)$ plane for a fixed mediator mass ratio $m_\phi = 10 m_1$. The black dotted contours indicate the values of $y_{11}$ for which, in the absence of the other Yukawa couplings, the relic abundance of $N_1$ matches the observed value. The allowed parameter space is limited by X-ray constraints (gray) and Lyman-$\alpha$ bounds (light purple), see text for details. Between the solid color lines (blue and yellow) the lifetime of $N_1$ is of the order of $10^{18}\,\text{s}$ and $3.3 \times 10^{-4}\leq q\leq 3.7 \times 10^{-2}$ as preferred to solve the S$_8$ tension.