Sterile Neutrinos with Secret Interactions - Lasting Friendship with Cosmology

TL;DR

This work reexamines eV-scale sterile neutrinos with secret $U(1)_s$ interactions mediated by a MeV-scale gauge boson $A'$, focusing on their production and impact on cosmology. By tracking the early-Universe evolution, including collisionless and collisional production and three recoupling histories, the authors identify two parameter regions where BBN, CMB, and LSS constraints are simultaneously satisfied. They show that collisional dynamics can suppress late-time production and free-streaming, relaxing structure-formation bounds, while still allowing consistent $N_{\text{eff}}$ values across epochs. The study also notes a potential connection between large $A'$ coupling and dark-matter halo structure, and emphasizes the need for momentum-dependent quantum kinetic equation solutions and dedicated nonlinear simulations to firm up the viability of secret-interacting sterile neutrinos.

Abstract

Sterile neutrinos with mass ~1 eV and order 10% mixing with active neutrinos have been proposed as a solution to anomalies in neutrino oscillation data, but are tightly constrained by cosmological limits. It was recently shown that these constraints are avoided if sterile neutrinos couple to a new MeV-scale gauge boson A'. However, even this scenario is restricted by structure formation constraints when A'-mediated collisional processes lead to efficient active-to-sterile neutrino conversion after neutrinos have decoupled. In view of this, we reevaluate in this paper the viability of sterile neutrinos with such "secret" interactions. We carefully dissect their evolution in the early Universe, including the various production channels and the expected modifications to large scale structure formation. We argue that there are two regions in parameter space - one at very small A' coupling, one at relatively large A' coupling - where all constraints from big bang nucleosynthesis (BBN), cosmic microwave background (CMB), and large scale structure (LSS) data are satisfied. Interestingly, the large A' coupling region is precisely the region that was previously shown to have potentially important consequences for the small scale structure of dark matter halos if the A' boson couples also to the dark matter in the Universe.

Figures (5)

• Figure 1: Possible cosmological histories of the active neutrinos $\nu_a$, the sterile neutrinos $\nu_s$, and the sterile sector gauge bosons $A'$ below the electroweak (EW) scale. Various possibilities, labeled as A1, A2 and B1, B2, B3, are determined by the values of the $A'$ mass $M$ and the $U(1)_s$ fine structure constant $\alpha_s$ and lead to testable predictions for $N_\text{eff}$ at both the BBN and CMB epochs. See text for details.
• Figure 2: Evolution of the collisional $\nu_a\rightarrow \nu_s$ production rate $\Gamma_s$, normalized by the Hubble rate $H$, versus the photon temperature $T_\gamma$, for different representative choices of the secret gauge boson mass $M$ and the secret fine structure constant $\alpha_s$. When $\Gamma_s/H > 1$, collisional production of $\nu_s$ from the thermal bath of $\nu_a$ is effective. The solid black curve shows a case where this never happens. The shoulder around $T_\gamma \sim M$ is where the $A'$ decay away. The dotted blue and dashed red curves correspond to recoupling after and before $A'$ decay, respectively.
• Figure 3: (a) Three-dimensional matter power spectrum $P_M(|\vec{k}|)$ derived from the SDSS Luminous Red Galaxy (LRG) Sample Tegmark:2006az and (b) one-dimensional flux power spectrum $\Delta^2(k) = k\,P_F(k) / \pi$ of Lyman-$\alpha$ photons at various redshifts, compared to the qualitative predictions of sterile neutrino models with (red dashed curves) and without (green dotted curves) self-interactions. Note that the relation between $P_M(|\vec{k}|)$ and $P_F(k)$ is non-linear, see e.g. Rossi:2014wsa. The assumed self-interaction parameters are $e_s = 0.1$, $M = 0.1$ MeV, and the assumed sterile neutrino mass is 1 eV. The data points and the SM prediction (solid green curves) are taken from Tegmark:2006az and and from Viel:2013fqw, respectively. The predictions including sterile neutrinos are obtained by multiplying the SM predictions by the $k$-dependent suppression profile from Fig. 7 of Lesgourgues:2012uu, shifted such that the onset of the suppression is at our calculated damping scale $k_s$ (Eq.(\ref{['eq:ks']}); see text for details), and scaled such that the maximum suppression is given by Eq. \ref{['eq:DeltaP-lin']} for panel (a) and by \ref{['eq:DeltaP-nonlin']} for panel (b). Note that the error bars shown here are statistical only, and large systematic uncertainties, especially at small scales (large $k$) should be kept in mind.
• Figure 4: Schematic illustration of the parameter space for eV-scale sterile neutrinos coupled to a new "secret" gauge boson with mass $M$ and a secret fine structure constant $\alpha_s$. The vacuum mixing angle between active and sterile neutrinos was taken to be $\theta_0 = 0.1$. The white region in the lower half of the plot is allowed by all constraints, while the narrow white band in the upper left part satisfies all constraints except possibly large scale structure (LSS) limits from Lyman-$\alpha$ data at the smallest scales. The red stars show representative models in scenarios (i) and (ii). The colored regions are excluded, either by LSS observations (blue vertically hatched), by the requirement that active neutrinos should free stream early enough (red shaded), or by a combination of CMB and BBN data (yellow cross-hatched).
• Figure 5: Kinetic temperature $T_s$ and chemical potential $\mu_s$ of sterile neutrinos, as functions of the scale factor $a(t)$ during the transition from the relativistic regime to the non-relativistic regime, with initial conditions $T_s = T_i \gg m_s$ and $\mu_s = 0$ at $a=a_i$.