Sterile Neutrinos in Light of Recent Cosmological and Oscillation Data: a Multi-Flavor Scheme Approach

TL;DR

This work develops a multi-flavor framework for sterile-neutrino production in the early Universe, combining an analytic small-mixing description with momentum-averaged density-matrix evolution to predict heavy-state abundances. It then performs a joint analysis of short-baseline oscillation data and cosmological observations under a $3+2$ sterile-neutrino hypothesis, using MCMC to map the viable parameter space. The results show that, within standard $\Lambda$CDM, the $3+2$ scenario is strongly disfavored by cosmology, with no 90% CL overlap with SBL-derived ranges for the sterile energy density, though a narrow compatibility window exists at the 99% CL and a global fit remains possible with lighter masses and partial thermalization (e.g., $\sim$44% for the fourth state). The study emphasizes that solving the full multi-flavor kinetics is crucial and that the main tension arises from internal SBL inconsistencies rather than cosmological data, guiding future experimental tests of sterile neutrinos.

Abstract

Light sterile neutrinos might mix with the active ones and be copiously produced in the early Universe. In the present paper, a detailed multi-flavor analysis of sterile neutrino production is performed. Making some justified approximations allows us to consider not only neutrino interactions with the primeval medium and neutrino coherence breaking effects, but also oscillation effects arising from the presence of three light (mostly-active) neutrino states mixed with two heavier (mostly-sterile) states. First, we emphasize the underlying physics via an analytical description of sterile neutrino abundances that is valid for cases with small mixing between active and sterile neutrinos. Then, we study in detail the phenomenology of (3+2) sterile neutrino models in light of short-baseline oscillation data, including the LSND and MiniBooNE results. Finally, by using the information provided by this analysis, we obtain the expected sterile neutrino cosmological abundances and then contrast them with the most recent available data from Cosmic Microwave Background and Large Scale Structure observations. We conclude that (3+2) models are significantly more disfavored by the internal inconsistencies between sterile neutrino interpretations of appearance and disappearance short-baseline data themselves, rather than by the used cosmological data.

Figures (9)

• Figure 1: Ratios $\rho_{ss}/\rho_{eq}$ and $\rho_{pp}/\rho_{eq}$ as a function of the temperature as given by Eq. (\ref{['eq:rhohh']}) with all approximations (see text) and when only some of these approximations are implemented. The black (red) solid lines refer to the case when all approximations are taken to obtain $\rho_{ss}$ ($\rho_{pp}$). The blue (orange) lines represent solutions to $\rho_{ss}$ ($\rho_{pp}$) with some approximations taken more accurately; dashed lines refer to the case when the momentum spread is taken into account, dot-dashed lines to the case when the exact form of the effective potential is considered and solid lines represent the case when both the momentum spread and the exact potential are assumed. The parameters we have taken are: $U_{e4} = U_{\mu 4} = 2 \times 10^{-3}$, $U_{e5} = U_{\mu 5} = 10^{-3}$, $m_4 = 1$ eV and $m_5 = \sqrt{10}$ eV.
• Figure 2: Flavor composition of neutrino mass eigenstates in $(3+2)$ sterile neutrino models. The hatched rectangles indicate active flavor content (electron, muon, tau, respectively, from left to right), and the empty rectangles indicate sterile flavor content.
• Figure 3: Evolution of sterile neutrino abundances, normalized to thermal equilibrium abundances $\rho_{\hbox{eq}}$, as a function of temperature $T$. The dashed red (solid blue) line indicate $\rho_{ss}/\rho_{\hbox{eq}}$ ($\rho_{pp}/\rho_{\hbox{eq}}$). The case shown corresponds to the $(3+2)$ model that describes SBL-only data best.
• Figure 4: $\Delta\chi^2$ profiles as a function of the sterile neutrino matter density $(\Omega_s+\Omega_p) h^2$. The red (blue) line indicates the case where cosmological-only (SBL-only) data are fitted. Three scenarios are shown for cosmological data fits: default data set and model (solid), data set including Lyman-$\alpha$ forest data and default model (dashed), default data set and cosmological model with free $w$ and $\Omega_k$ (dotted). The horizontal dotted lines define the 90% and 99% confidence level regions (1 dof).
• Figure 5: Allowed regions in ($\Delta m_{41}^2(|U_{e4}|^2+|U_{\mu 4}|^2)$, $\Delta m_{51}^2(|U_{e5}|^2+|U_{\mu 5}|^2)$) space, for SBL-only data (filled blue regions) and cosmology-only data (red contours). Light (dark) colors correspond to 90% (99%) confidence level regions (2 dof). The yellow star indicates the SBL-only best-fit point.