Unveiling secret interactions among sterile neutrinos with big-bang nucleosynthesis

TL;DR

The paper addresses the tension between eV-scale sterile neutrinos and cosmology by studying secret sterile self-interactions mediated by a gauge boson X (with M_X << M_W). Using a (2+1) flavor system in an averaged-momentum framework, it derives the in-medium Hamiltonian and collisional terms that govern active-sterile oscillations and finds that resonances can both suppress and enhance sterile production, increasing N_eff and distorting electron-neutrino spectra. By embedding the resulting N_eff and nu_e distortions into the BBN code PArthENoPE, the authors confront predictions with observed primordial abundances of $^4$He and deuterium, and Planck-derived baryon densities. The main outcome is that deuterium data impose strong constraints on the secret-interaction parameter space (e.g., M_X ≤ 40 MeV at Planck best-fit), while helium bounds are weak with current uncertainties; overall, the secret-interaction scenario is tightly constrained unless the mediator is very light ($M_X o 0$), a regime requiring separate analysis. These results significantly challenge the viability of secret ν_s–ν_s interactions as a mechanism to reconcile sterile neutrinos with cosmology.

Abstract

Short-baseline neutrino anomalies suggest the existence of low-mass ( m \sim O(1)~eV) sterile neutrinos ν_s. These would be efficiently produced in the early universe by oscillations with active neutrino species, leading to a thermal population of the sterile states seemingly incompatible with cosmological observations. In order to relieve this tension it has been recently speculated that new "secret" interactions among sterile neutrinos, mediated by a massive gauge boson X (with M_X << M_W), can inhibit or suppress the sterile neutrino thermalization, due to the production of a large matter potential term. We note however, that they also generate strong collisional terms in the sterile neutrino sector that induce an efficient sterile neutrino production after a resonance in matter is encountered, increasing their contribution to the number of relativistic particle species N_ eff. Moreover, for values of the parameters of the ν_s-ν_s interaction for which the resonance takes place at temperature T\lesssim few MeV, significant distortions are produced in the electron (anti)neutrino spectra, altering the abundance of light element in Big Bang Nucleosynthesis (BBN). Using the present determination of $^4$He and deuterium primordial abundances we determine the BBN constraints on the model parameters. We find that $^2$H/H density ratio exclude much of the parameter space if one assume a baryon density at the best fit value of Planck experiment, Ω_B h^2= 0.02207, while bounds become weaker for a higher Ω_B h^2=0.02261, the 95 % C.L. upper bound of Planck. Due to the large error on its experimental determination, the helium mass fraction Y_p gives no significant bounds.

Figures (6)

• Figure 1: Neutrino refractive and collisional rates (normalized in terms of the Hubble rate) versus temperature $T$ for $G_X=10^3$$G_F$. Left panel corresponds to $g_X=10^{-1}$, while right panel to $g_X=10^{-2}$. The curves correspond to the active-sterile vacuum term (solid curve), the secret matter potential for $\rho_{ss}=10^{-2}$ (dashed curve), the standard collisional term (dotted curve) and the collisional term associated with $G_X^2$ (dot-dashed curve) .
• Figure 2: Resonance temperature $T_{\rm res}$ in the plane $(G_X, g_X)$. Dashed curves represent constant $T_{\rm res}$ contours, while on solid curves $M_X$ is constant. The values shown for both parameters are expressed in MeV. The case of $T_{\rm res}=1$ MeV is highlighted with a tick dot-dashed style, and correspond to the order of magnitude of BBN onset in the standard case, when neutron to proton density ratio freezes out.
• Figure 3: Flavor evolution as functions of temperature $T$ for different cases for $G_X=10^{3}$$G_F$. Upper panel is the standard case without secret interactions. Middle and lower plots are for $g_X=10^{-1}$ and $g_X=10^{-2}$, respectively. In the left panels we report $\rho_{ee}$ (continuous curve), $\rho_{\mu\mu}$ (dotted curve) and $\rho_{ss}$ (dashed curve). Right panels show the corresponding $\Delta N_{\rm eff}$.
• Figure 4: The asymptotic values of $\Delta N_{\rm eff}$ versus $G_X$ and $g_X$. Colours from blue (lower right corner) to red (upper left corner) correspond to increasing values. Dashed curves show some reference values.
• Figure 5: ${}^{4}$He results. The dark region is the $1.5\sigma$ allowed parameter space for the helium mass fraction $Y_p$ using the experimental result of Eq. (\ref{['he4exp']}), varying the baryon density parameter in the range $0.02153 \leq \Omega_B h^2 \leq 0.02261$, corresponding to the 95 % C.L. Planck range. The solid line bounds the permitted region if we fix $\Omega_B h^2 = 0.02207$, the best fit quoted by Planck collaboration. At $2\sigma$ the whole region shown for $G_X$ and $g_X$would be allowed, while at $1\sigma$ it is all excluded.