Measuring growth index in a universe with sterile neutrinos

Abstract

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, $\gamma =0.584_{-0.048}^{+0.047}$, well consistent with the GR expected value (the consistency is at the 0.6$\sigma$ level). For the parameters of sterile neutrino, we obtain $N_{\mathrm{eff}}=3.62_{-0.42}^{+0.26}$ and $m_{\nu ,\mathrm{sterile}}^{\mathrm{eff}}=0.48_{-0.14}^{+0.11}$ 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.

5 pages, 3 figures; accepted for publication in Physics Letters B

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• Galaxy-Scale Test of General Relativity with Strong Gravitational Lensing
• Prospects for searching for sterile neutrinos with gravitational wave and $\gamma$-ray burst joint observations
• Testing General Relativity on Galactic Scales via DESI-BAO and Strong Lensing: Circumventing Assumptions on the Hubble Constant, Sound Horizon, and Dark Energy