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

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 $\Delta k \sim 0.03 h{\rm Mpc^{-1}}$ bins to $\sim35\%$ precision, including a measurement on scales $>300 h^{-1}{\rm Mpc}$, 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 {\it Planck} cosmology. Bringing all the scales together, we determine the normalised growth rate at $z=0$ to $\sim15\%$ in a manner {\it 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.