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 = \beta H \rho _ { v } and Q = \beta H \rho _ { 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 _ { eff } < 3.522 and m _ { \nu, { sterile } } ^ { eff } < 0.576 eV for the Q = \beta H \rho _ { v } model , and N _ { eff } = 3.204 ^ { +0.049 } _ { -0.135 } and m _ { \nu, { sterile } } ^ { eff } = 0.410 ^ { +0.150 } _ { -0.330 } eV for the Q = \beta H \rho _ { c } model .
The latter indicates \Delta N _ { eff } > 0 at the 1.17 \sigma level and a nonzero mass of sterile neutrino at the 1.24 \sigma level .
In addition , for the Q = \beta H \rho _ { v } model , we find that \beta = 0 is consistent with the current data , and for the Q = \beta H \rho _ { c } model , we find that \beta > 0 is obtained at more than 1 \sigma level .