Search for sterile neutrinos in a universe of vacuum energy interacting
  with cold dark matter
  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, $Q=\beta
H\rho_{\rm v}$ and $Q=\beta H\rho_{\rm c}$. 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 $N_{\rm eff}<3.522$ and $m_{\nu,{\rm sterile}}^{\rm eff}<0.576$ eV
for the $Q=\beta H\rho_{\rm v}$ model, and $N_{\rm
eff}=3.204^{+0.049}_{-0.135}$ and $m_{\nu,{\rm sterile}}^{\rm
eff}=0.410^{+0.150}_{-0.330}$ eV for the $Q=\beta H\rho_{\rm c}$ model. The
latter indicates $\Delta N_{\rm eff}>0$ at the 1.17$\sigma$ level and a nonzero
mass of sterile neutrino at the 1.24$\sigma$ level. In addition, for the
$Q=\beta H\rho_{\rm v}$ model, we find that $\beta=0$ is consistent with the
current data, and for the $Q=\beta H\rho_{\rm c}$ model, we find that $\beta>0$
is obtained at more than 1$\sigma$ level.
