Measuring growth index in a universe with massive neutrinos: A revisit
  of the general relativity test with the latest observations
  We make a consistency test for the general relativity (GR) through measuring
the growth index $\gamma$ in a universe with massive (sterile/active)
neutrinos. We employ the redshift space distortion measurements to do the
analysis. To constrain other cosmological parameters, we also use other
cosmological measurements, including the Planck 2015 cosmic microwave
background temperature and polarization data, the baryon acoustic oscillation
data, the type Ia supernova JLA data, the weak lensing galaxy shear data, and
the Planck 2015 lensing data. In a universe with massive sterile neutrinos, we
obtain $\gamma=0.624^{+0.055}_{-0.050}$, with the tension with the GR
prediction $\gamma=0.55$ at the 1.48$\sigma$ level, showing that the
consideration of sterile neutrinos still cannot make the true measurement of
$\gamma$ be well consistent with the GR prediction. In a universe with massive
active neutrinos, we obtain $\gamma=0.663\pm0.045$ for the normal hierarchy
case, $\gamma=0.661^{+0.044}_{-0.050}$ for the degenerate hierarchy case, and
$\gamma=0.668^{+0.045}_{-0.051}$ for the inverted hierarchy case, with the
tensions with GR all at beyond the 2$\sigma$ level. We find that the
consideration of massive active neutrinos (no matter what mass hierarchy is
considered) almost does not influence the measurement of the growth index
$\gamma$.
