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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 subsample which we employ in this study contains 81 971 galaxies distributed over 17 000 degree 2  with an effective redshift  z  eff = 0.067. By modelling the 2D galaxy correlation function, , we measure the parameter combination  f ( z  eff )σ 8 ( z  eff ) = 0.423 ± 0.055, where  is the growth rate of cosmic structure and σ 8  is the rms of matter fluctuations in 8  h  −1  Mpc spheres.  Alternatively, by assuming standard gravity we can break the degeneracy between σ 8  and the galaxy bias parameter  b . Combining our data with the Hubble constant prior from Riess et al., we measure σ 8 = 0.76 ± 0.11 and Ω m = 0.250 ± 0.022, consistent with constraints from other galaxy surveys and the cosmic microwave background data from  Wilkinson Microwave Anisotropy Probe  7 ( WMAP 7).  Combining our measurement of  f σ 8  with  WMAP 7 allows us to test the cosmic growth history and the relationship between matter and gravity on cosmic scales by constraining the growth index of density fluctuations, γ. Using only 6dFGS and  WMAP 7 data we find γ= 0.547 ± 0.088, consistent with the prediction of General Relativity. We note that because of the low effective redshift of the 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  f σ 8  for the Wide‐field Australian SKA Pathfinder telescope  L ‐band Legacy All‐sky Blind surveY (WALLABY) and the proposed Transforming Astronomical Imaging surveys through Polychromatic Analysis of Nebulae (TAIPAN) survey. The WALLABY survey will be able to measure  f σ 8  with a precision of 4–10 per cent, 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, demonstrating that low‐redshift surveys have a significant role to play in future tests of dark energy and modified gravity.

The 6dF Galaxy Survey: z ≈ 0 measurements of the growth rate and σ 8