We present scale-dependent measurements of the normalised 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 ( 6dFGSv ) 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 \sim 0.03 h { Mpc ^ { -1 } } bins to \sim 35 \% 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 normalised growth rate at z = 0 to \sim 15 \% in a manner independent of galaxy bias and in excellent agreement with the constraint from the measurements of redshift-space distortions from 6dFGS .
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 marginalise 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 ‘ hyper-parameter ’ 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 .