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(-0.050)(+0.055), 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 +/- 0.045 for the normal hierarchy case, gamma = 0.661(-0.050)(+0.044) Mol for the degenerate hierarchy case, and gamma = 0.668(-0.051)(+0.045) 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. (C) 2018 The Authors. Published by Elsevier B.V.