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 $γ$ using the measurements of redshift-space distortions (RSD) in conjunction with other observations. In previous studies, deviations from the GR expected value of $γ\approx 0.55$ at the 2--3$σ$ level were found. In this work, we reconsider the measurement of $γ$ 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, $γ=0.584^{+0.047}_{-0.048}$, well consistent with the GR expected value (the consistency is at the 0.6$σ$ level). For the parameters of sterile neutrino, we obtain $N_{\rm{eff}}=3.62^{+0.26}_{-0.42}$ and $m_{ν,{\rm{sterile}}}^{\rm{eff}}=0.48^{+0.11}_{-0.14}$ 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.

Figures (3)

• Figure 1: Constraint results for the $\Lambda$CDM+$\nu_s$ model from the CMB+BAO+$H_0$+PlaSZ+Shear+RSD data combination. Upper panel: one-dimensional marginalized posterior distribution for the growth index $\gamma$. Lower panel: two-dimensional marginalized posterior distribution contours (68.3% and 95.4% CL) in the $\Omega_m$--$\gamma$ plane. The constraint results of the $\Lambda$CDM model (without sterile neutrino) using the CMB+BAO+RSD data are also shown for a comparison with the model with sterile neutrino. The vertical (upper) and horizontal (lower) red dashed lines indicate the GR expected value of $\gamma=0.55$.
• Figure 2: Two-dimensional marginalized constraints (68.3% and 95.4% CL) on the $\Lambda$CDM+$\nu_s$ model from the CMB+BAO+$H_0$+PlaSZ+Shear+RSD data combination in the $m_{\nu,{\rm{sterile}}}^{\rm{eff}}$--$N_{\rm{eff}}$ plane.
• Figure 3: Joint constraint results (68.3% and 95.4% CL) for the $\Lambda$CDM+$r$+$\nu_s$ model from the CMB+BAO+$H_0$+PlaSZ+Shear+RSD+BICEP2 data combination in the $\Omega_m$--$\gamma$ plane (upper) and in the $m_{\nu,{\rm{sterile}}}^{\rm{eff}}$--$N_{\rm{eff}}$ plane (lower). The horizontal red dashed line in the upper panel indicates the GR expected value of $\gamma=0.55$.