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 _ { 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 _ { 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 _ { 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 .