The 6dF Galaxy Survey: z \approx 0 measurement of the growth rate and
  sigma_8
  We present a detailed analysis of redshift-space distortions in the two-point
correlation function of the 6dF Galaxy Survey (6dFGS). The K-band selected
sub-sample which we employ in this study contains 81971 galaxies distributed
over 17000deg^2 with an effective redshift z = 0.067. By modelling the 2D
galaxy correlation function, xi(r_p,pi), we measure the parameter combination
f(z)sigma_8(z) = 0.423 +/- 0.055. Alternatively, by assuming standard gravity
we can break the degeneracy between sigma_8 and the galaxy bias parameter, b.
Combining our data with the Hubble constant prior from Riess et al (2011), we
measure sigma_8 = 0.76 +/- 0.11 and Omega_m = 0.250 +/- 0.022, consistent with
constraints from other galaxy surveys and the Cosmic Microwave Background data
from WMAP7. Combining our measurement of fsigma_8 with WMAP7 allows us to test
the relationship between matter and gravity on cosmic scales by constraining
the growth index of density fluctuations, gamma. Using only 6dFGS and WMAP7
data we find gamma = 0.547 +/- 0.088, consistent with the prediction of General
Relativity. We note that because of the low effective redshift of 6dFGS our
measurement of the growth rate is independent of the fiducial cosmological
model (Alcock-Paczynski effect). We also show that our conclusions are not
sensitive to the model adopted for non-linear redshift-space distortions. Using
a Fisher matrix analysis we report predictions for constraints on fsigma_8 for
the WALLABY survey and the proposed TAIPAN survey. The WALLABY survey will be
able to measure fsigma_8 with a precision of 4-10%, depending on the modelling
of non-linear structure formation. This is comparable to the predicted
precision for the best redshift bins of the Baryon Oscillation Spectroscopic
Survey (BOSS), demonstrating that low-redshift surveys have a significant role
to play in future tests of dark energy and modified gravity.
