Exploring neutrino mass and mass hierarchy in the scenario of vacuum energy interacting with cold dark matter

TL;DR

This work investigates how a vacuum-energy–dark-matter interaction affects cosmological constraints on the total neutrino mass and its mass hierarchy. Two IDE forms, $Q=βH ho_{ m c}$ and $Q=βH ho_{ m Lambda}$, are analyzed using the parameterized post-Friedmann framework and a Planck+BAO+SNIa+RSD dataset, with an additional $N_{ m eff}$ parameter when $H_0$ is included. The results show that $Q∝ρ_{ m c}$ yields substantially looser bounds on $∑ m_ν$ than ΛCDM, while $Q∝ρ_{ m Lambda}$ gives modestly tighter bounds, and the normal hierarchy is mildly preferred over the inverted one with $Δχ^2_{ m min} ≈ 2$–$3$ in some cases. Furthermore, the coupling is consistent with zero for $Q=βH ho_{ m c}$, while negative $β$ values are favored for $Q=βH ho_{Lambda}$ when $H_0$ is included, illustrating how dark-sector interactions and dataset choices shape neutrino-mass inferences.

Abstract

We investigate the constraints on total neutrino mass in the scenario of vacuum energy interacting with cold dark matter. We focus on two typical interaction forms, i.e., $Q=βHρ_{\rm c}$ and $Q=βHρ_Λ$. To avoid the occurrence of large-scale instability in interacting dark energy cosmology, we adopt the parameterized post-Friedmann approach to calculate the perturbation evolution of dark energy. We employ observational data, including the Planck cosmic microwave background temperature and polarization data, baryon acoustic oscillation data, a JLA sample of type Ia supernovae observation, direct measurement of the Hubble constant, and redshift space distortion data. We find that, compared with those in the $Λ$CDM model, much looser constraints on $\sum m_ν$ are obtained in the $Q=βHρ_{\rm c}$ model, whereas slightly tighter constraints are obtained in the $Q=βHρ_Λ$ model. Consideration of the possible mass hierarchies of neutrinos reveals that the smallest upper limit of $\sum m_ν$ appears in the degenerate hierarchy case. By comparing the values of $χ^2_{\rm min}$, we find that the normal hierarchy case is favored over the inverted one. In particular, we find that the difference $Δχ^2_{\rm min} \equiv χ^2_{\rm IH; min}-χ^2_{\rm NH; min}> 2$ in the $Q=βHρ_{\rm c}$ model. In addition, we find that $β=0$ is consistent with the current observations in the $Q=βHρ_{\rm c}$ model, and $β< 0$ is favored at more than the $1σ$ level in the $Q=βHρ_Λ$ model.

Figures (4)

• Figure 1: Two-dimensional marginalized contours ($1\sigma$ and $2\sigma$) of the $\sum m_\nu$--$\beta$ plane in the I$\Lambda$CDM1 ($Q=\beta H \rho_{\rm c}$)+$\sum m_\nu$ model using the Planck TT, TE, EE + lowP + BAO + SNIa + RSD data combination for various neutrino mass hierarchies.
• Figure 2: Two-dimensional marginalized contours ($1\sigma$ and $2\sigma$) of the $\sum m_\nu$--$\beta$ plane in the I$\Lambda$CDM1 ($Q=\beta H \rho_{\rm c}$)+$\sum m_\nu$+$N_{\rm eff}$ model using the Planck TT, TE, EE + lowP + BAO + SNIa + RSD +$H_0$ data combination for various neutrino mass hierarchies.
• Figure 3: Two-dimensional marginalized contours ($1\sigma$ and $2\sigma$) of the $\sum m_\nu$--$\beta$ plane and the $\Omega_{\rm m}$--$\beta$ plane in the I$\Lambda$CDM2 ($Q=\beta H \rho_{\Lambda}$)+$\sum m_\nu$ model using the Planck TT, TE, EE + lowP + BAO + SNIa + RSD data combination for various neutrino mass hierarchies.
• Figure 4: Two-dimensional marginalized contours ($1\sigma$ and $2\sigma$) of the $\sum m_\nu$--$\beta$ plane and the $\Omega_{\rm m}$--$\beta$ plane in the I$\Lambda$CDM2 ($Q=\beta H \rho_{\Lambda}$)+$\sum m_\nu$+$N_{\rm eff}$ model using the Planck TT, TE, EE +lowP +BAO + SNIa + RSD + $H_0$ data combination for various neutrino mass hierarchies.