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 _ { eff } = 3.62 ^ { +0.26 } _ { -0.42 } and m _ { \nu, { sterile } } ^ { 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 .