Search for sterile neutrinos in a universe of vacuum energy interacting with cold dark matter

TL;DR

This paper investigates sterile neutrino constraints in a universe where vacuum energy interacts with cold dark matter (IvCDM) under two coupling forms $Q_1=βHρ_{ m v}$ and $Q_2=βHρ_{ m c}$. It uses the parametrized post-Friedmann (PPF) framework to stabilize perturbations and analyzes Planck 2015 TT,TE,EE+lowP data together with BAO, SN, $H_0$, weak lensing, RSD, and Planck lensing, forming Planck+BSH and Planck+BSH+LSS data combinations. The results show that IvCDM1+$ u_s$ yields $N_{ m eff}<3.641$ and $m_{ u,{ m sterile}}^{ m eff}<0.312$ eV (Planck+BSH) and $N_{ m eff}<3.522$, $m_{ u,{ m sterile}}^{ m eff}<0.576$ eV (Planck+BSH+LSS), closely matching $ u_s$-free or mildly modified constraints, whereas IvCDM2+$ u_s$ gives $N_{ m eff}<3.498$, $m_{ u,{ m sterile}}^{ m eff}<0.875$ eV (Planck+BSH) and $N_{ m eff}=3.204^{+0.049}_{-0.135}$, $m_{ u,{ m sterile}}^{ m eff}=0.410^{+0.150}_{-0.330}$ eV (Planck+BSH+LSS), implying $ riangle N_{ m eff} eq0$ at ~1σ and a nonzero sterile mass at ~1σ. The coupling $eta$ is consistent with zero in IvCDM1 but prefers $eta>0$ in IvCDM2, with growth data significantly tightening the sterile-neutrino constraints and yielding a modest improvement on the $H_0$ tension, which remains around 2σ with Planck+BSH+LSS. Overall, the interaction form substantially influences sterile-neutrino inferences, and a partially thermalized eV-scale sterile neutrino remains a possible, though not definitive, outcome under current data and the PPF treatment.

Abstract

We investigate the cosmological constraints on sterile neutrinos in a universe in which vacuum energy interacts with cold dark matter by using latest observational data. We focus on two specific interaction models, $Q=βHρ_{\rm v}$ and $Q=βHρ_{\rm c}$. To overcome the problem of large-scale instability in the interacting dark energy scenario, we employ the parametrized post-Friedmann (PPF) approach for interacting dark energy to do the calculation of perturbation evolution. The observational data sets used in this work include the Planck 2015 temperature and polarization data, the baryon acoustic oscillation measurements, the type-Ia supernova data, the Hubble constant direct measurement, the galaxy weak lensing data, the redshift space distortion data, and the Planck lensing data. Using the all-data combination, we obtain $N_{\rm eff}<3.522$ and $m_{ν,{\rm sterile}}^{\rm eff}<0.576$ eV for the $Q=βHρ_{\rm v}$ model, and $N_{\rm eff}=3.204^{+0.049}_{-0.135}$ and $m_{ν,{\rm sterile}}^{\rm eff}=0.410^{+0.150}_{-0.330}$ eV for the $Q=βHρ_{\rm c}$ model. The latter indicates $ΔN_{\rm eff}>0$ at the 1.17$σ$ level and a nonzero mass of sterile neutrino at the 1.24$σ$ level. In addition, for the $Q=βHρ_{\rm v}$ model, we find that $β=0$ is consistent with the current data, and for the $Q=βHρ_{\rm c}$ model, we find that $β>0$ is obtained at more than 1$σ$ level.

Figures (10)

• Figure 1: The one-dimensional posterior distributions and two-dimensional marginalized contours (1$\sigma$ and 2$\sigma$) for parameters $\beta$, $\sigma_8$, $N_{\rm eff}$, and $m_{\nu,{\rm sterile}}^{\rm eff}$ of the I$\Lambda$CDM1 ($Q=\beta H\rho_{\rm v}$)+$\nu_s$ model by using the Planck+BSH ( blue) and the Planck+BSH+LSS ( green) data combinations.
• Figure 2: The one-dimensional posterior distributions and two-dimensional marginalized contours (1$\sigma$ and 2$\sigma$) for parameters $\beta$, $\sigma_8$, $N_{\rm eff}$, and $m_{\nu,{\rm sterile}}^{\rm eff}$ of the IvCDM2 ($Q=\beta H\rho_c$)+$\nu_s$ model by using the Planck+BSH ( blue) and the Planck+BSH+LSS ( green) data combinations.
• Figure 3: The one-dimensional posterior distributions and two-dimensional marginalized contours (1$\sigma$ and 2$\sigma$) for parameters $m_{\nu,{\rm sterile}}^{\rm eff}$ and $N_{\rm eff}$ of the $\Lambda$CDM+$\nu_s$, IvCDM1 ($Q=\beta H\rho_{\rm v}$)+$\nu_s$, and IvCDM2 ($Q=\beta H\rho_{\rm c}$)+$\nu_s$ models by using the Planck+BSH+LSS data combination.
• Figure 4: The one-dimensional posterior distributions and two-dimensional marginalized contours (1$\sigma$ and 2$\sigma$) for parameters $\beta$, $\sigma_8$, $N_{\rm eff}$, $m_{\nu,{\rm sterile}}^{\rm eff}$, and $\sum m_\nu$ of the IvCDM1 ($Q=\beta H\rho_{\rm de}$)+$\nu_s$+$\nu_a$ model by using the Planck+BSH ( blue) and Planck+BSH+LSS ( green) data combinations.
• Figure 5: The one-dimensional posterior distributions and two-dimensional marginalized contours (1$\sigma$ and 2$\sigma$) for parameters $\beta$, $\sigma_8$, $N_{\rm eff}$, $m_{\nu,{\rm sterile}}^{\rm eff}$, and $\sum m_\nu$ of the IvCDM2 ($Q=\beta H\rho_{\rm c}$)+$\nu_s$+$\nu_a$ model by using the Planck+BSH ( blue) and Planck+BSH+LSS ( green) data combinations.