Measuring growth index in a universe with massive neutrinos: A revisit of the general relativity test with the latest observations

TL;DR

This study tests general relativity by measuring the growth index in a universe with massive neutrinos using various cosmological observations, finding tensions with GR predictions that are not resolved by including sterile or active neutrinos.

Contribution

It provides the first comprehensive analysis of the growth index considering both sterile and active neutrinos with latest observational data.

Findings

Measured growth index with sterile neutrinos shows 1.48σ tension with GR.

Measured growth index with active neutrinos exceeds 2σ tension with GR.

Massive active neutrinos have negligible effect on the growth index measurement.

Abstract

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 $\gamma$.