The 6dF Galaxy Survey: cosmological constraints from the velocity power spectrum

We present scale-dependent measurements of the normalized growth rate of structure f sigma 8(k, z = 0) using only the peculiar motions of galaxies. We use data from the 6-degree Field Galaxy Survey velocity sample together with a newly compiled sample of low-redshift (z < 0.07) Type Ia supernovae. We constrain the growth rate in a series of Delta k similar to 0.03 h Mpc(-1) bins to similar to 35 per cent precision, including a measurement on scales > 300 h(-1) Mpc, which represents one of the largest scale growth rate measurement to date. We find no evidence for a scale-dependence in the growth rate, or any statistically significant variation from the growth rate as predicted by the Planck cosmology. Bringing all the scales together, we determine the normalized growth rate at z = 0 to similar to 15 per cent in a manner independent of galaxy bias and in excellent agreement with the constraint from the measurements of redshift-space distortions from 6-degree Field Galaxy Survey. We pay particular attention to systematic errors. We point out that the intrinsic scatter present in Fundamental Plane and Tully-Fisher relations is only Gaussian in logarithmic distance units; wrongly assuming it is Gaussian in linear (velocity) units can bias cosmological constraints. We also analytically marginalize over zero-point errors in distance indicators, validate the accuracy of all our constraints using numerical simulations, and demonstrate how to combine different (correlated) velocity surveys using a matrix 'hyperparameter' analysis. Current and forthcoming peculiar velocity surveys will allow us to understand in detail the growth of structure in the low-redshift universe, providing strong constraints on the nature of dark energy.