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

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.