Weighing neutrinos in the scenario of vacuum energy interacting with cold dark matter: application of the parameterized post-Friedmann approach

Abstract: We constrain the neutrino mass in the scenario of vacuum energy interacting with cold dark matter by using current cosmological observations. To avoid the large-scale instability problem in interacting dark energy models, we employ the parameterized post-Friedmann (PPF) approach to do the calculation of perturbation evolution, for the $Q=\beta H\rho_{\rm c}$ and $Q=\beta H\rho_{\Lambda}$ models. The current observational data sets used in this work include Planck (cosmic microwave background), BSH (baryon acoustic oscillations, type Ia supernovae, and Hubble constant), and LSS (redshift space distortions and weak lensing). According to the constraint results, we find that $\beta>0$ at more than $1\sigma$ level for the $Q=\beta H\rho_{\rm c}$ model, which indicates that cold dark matter decays into vacuum energy; while $\beta=0$ is consistent with the current data at $1\sigma$ level for the $Q=\beta H\rho_{\Lambda}$ model. Taking the $\Lambda$CDM model as a baseline model, we find that a smaller upper limit, $\sum m_{\nu}<0.11$ eV ($2\sigma$), is induced by the latest BAO BOSS DR12 data and the Hubble constant measurement $H_{0} = 73.00 \pm 1.75$ km~s$^{-1}$~Mpc$^{-1}$. For the $Q=\beta H\rho_{\rm c}$ model, we obtain $\sum m_{\nu}<0.20$ eV ($2\sigma$) from Planck+BSH. For the $Q=\beta H\rho_{\Lambda}$ model, $\sum m_{\nu}<0.10$ eV ($2\sigma$) and $\sum m_{\nu}<0.14$ eV ($2\sigma$) are derived from Planck+BSH and Planck+BSH+LSS, respectively. We show that these smaller upper limits on $\sum m_{\nu}$ are affected more or less by the tension between $H_{0}$ and other observational data.