Testing general relativity with growth rate measurement from Sloan digital sky survey - III. Baryon oscillations spectroscopic survey galaxies

The measured redshift (z) of an astronomical object is a combination of Hubble recession, gravitational redshift and peculiar velocity. The line-of-sight distance to a galaxy inferred from redshift is affected by the peculiar velocity component of galaxy redshift, which is observed as an anisotropy in the correlation function. This anisotropy allows us to measure the linear growth rate of matter (fσ₈). We measure the fσ₈ at z = 0.57 using the CMASS sample from Data Release 11 of Sloan Digital Sky Survey III (SDSS III) Baryon Oscillations Spectroscopic Survey (BOSS). The galaxy sample consists of 690 826 massive galaxies in the redshift range 0.43-0.7 covering 8498 deg². Here, we report the first simultaneous measurement of fσ₈ and background cosmological parameters using Convolution Lagrangian Perturbation Theory (CLPT) with Gaussian streaming model (Gaussian Streaming Redshift Space Distortions - GSRSD).We arrive at a constraint of fσ₈ = 0.462 ± 0.041 (9 per cent accuracy) at effective redshift (-z = 0.57) when we include Planck cosmic microwave background likelihood while marginalizing over all other cosmological parameters. We also measure bσ₈ =1.19±0.03, H(z=0.57)=89.2±3.6 kms^-1 Mpc^-1 andD_A(z=0.57)=1401 ± 23 Mpc. Our analysis also improves the constraint on Ω_c h² = 0.1196 ± 0.0009 by a factor of 3 when compared to the Planck only measurement(Ω_c h² = 0.1196 ± 0.0031). Our results are consistent with Planck Λ cold dark matter (CDM)-general relativity (GR) prediction and all other CMASS measurements, even though our theoretical models are fairly different. This consistency suggests that measurement of fσ₈ from redshift space distortions at multiple redshifts will be a sensitive probe of the theory of gravity that is largely model independent, allowing us to place model-independent constraints on alternative models of gravity.