Joint analysis of 6dFGS and SDSS peculiar velocities for the growth rate of cosmic structure and tests of gravity

Measurement of peculiar velocities by combining redshifts and distance indicators is a powerful way to measure the growth rate of a cosmic structure and test theories of gravity at low redshift. Here we constrain the growth rate of the structure by comparing observed Fundamental Plane peculiar velocities for 15 894 galaxies from the 6dF Galaxy Survey (6dFGS) and Sloan Digital Sky Survey (SDSS) with predicted velocities and densities from the 2M++ redshift survey. We measure the velocity scale parameter beta = Omega(gamma)(m)/b = 0.372(-0.050)(+0.034) and 0.314(-0.047)(+0.031) for 6dFGS and SDSS, respectively, where Omega(m) is the mass density parameter, gamma is the growth index, and b is the bias parameter normalized to the characteristic luminosity of galaxies, L*. Combining 6dFGS and SDSS, we obtain beta = 0.341 +/- 0.024, implying that the amplitude of the product of the growth rate and the mass fluctuation amplitude is f sigma(8) = 0.338 +/- 0.027 at an effective redshift z = 0.035. Adopting Omega(m) = 0.315 +/- 0.007, as favoured by Planck and using gamma = 6/11 for General Relativity and gamma = 11/16 for DGP gravity, we get S-8(z = 0) = sigma(8)root Omega(m)/0.3 = 0.637 +/- 0.054 and 0.741 +/- 0.062 for GR and DGP, respectively. This measurement agrees with other low-redshift probes of large-scale structure but deviates by more than 3 sigma from the latest Planck CMB measurement. Our results favour values of the growth index gamma > 6/11 or a Hubble constant H-0 > 70 km s(-1) Mpc(-1) or a fluctuation amplitude sigma(8) < 0.8 or some combination of these. Imminent redshift surveys such as Taipan, DESI, WALLABY, and SKA1-MID will help to resolve this tension by measuring the growth rate of cosmic structure to 1 per cent in the redshift range 0 < z < 1.