Measuring growth index in a universe with sterile neutrinos
  Consistency tests for the general relativity (GR) can be performed by
constraining the growth index $\gamma$ using the measurements of redshift-space
distortions (RSD) in conjunction with other observations. In previous studies,
deviations from the GR expected value of $\gamma\approx 0.55$ at the
2--3$\sigma$ level were found. In this work, we reconsider the measurement of
$\gamma$ in a universe with sterile neutrinos. We constrain the sterile
neutrino cosmological model using the RSD measurements combined with the cosmic
microwave background data (Planck temperature data plus WMAP 9-yr polarization
data), the baryon acoustic oscillation data, the Hubble constant direct
measurement, the Planck Sunyaev-Zeldovich cluster counts data, and the galaxy
shear data. We obtain the constraint result of the growth index,
$\gamma=0.584^{+0.047}_{-0.048}$, well consistent with the GR expected value
(the consistency is at the 0.6$\sigma$ level). For the parameters of sterile
neutrino, we obtain $N_{\rm{eff}}=3.62^{+0.26}_{-0.42}$ and
$m_{\nu,{\rm{sterile}}}^{\rm{eff}}=0.48^{+0.11}_{-0.14}$ eV. We also consider
the BICEP2 data and perform an analysis on the model with tensor modes. Similar
fit results are obtained, showing that once light sterile neutrino is
considered in the universe, GR will become well consistent with the current
observations.
