Are peculiar velocity surveys competitive as a cosmological probe?

Peculiar velocity surveys, which measure galaxy velocities directly from standard candles in addition to redshifts, can provide strong constraints on the growth rate of structure at low redshift. The improvement originates from the physical relationship between galaxy density and peculiar velocity, which substantially reduces cosmic variance. We use Fisher matrix forecasts to show that peculiar velocity data can improve the growth rate constraints by about a factor of 2 compared to density alone for surveys with galaxy number density of 10(-2) (h(-1) Mpc)(-3), if we can use all the information for wavenumber k <= 0.2 h Mpc(-1). In the absence of accurate theoretical models at k = 0.2 h Mpc(-1), the improvement over redshift-only surveys is even larger - around a factor of 5 for k <= 0.1 h Mpc(-1). Future peculiar velocity surveys, Transforming Astronomical Imaging surveys through Polychromatic Analysis of Nebulae (TAIPAN), and the all-sky H I surveys, Widefield ASKAP L-band Legacy All-sky Blind Survey (WALLABY) and Westerbork Northern Sky H I Survey (WNSHS), can measure the growth rate to 3 per cent at z similar to 0.025. Although the velocity subsample is about an order of magnitude smaller than the redshift sample from the same survey, it improves the constraint by 40 per cent compared to the same survey without velocity measurements. Peculiar velocity surveys can also measure the growth rate as a function of wavenumber with 15-30 per cent uncertainties in bins with widths Delta k = 0.01 h Mpc(-1) in the range k <= 0.1 h Mpc(-1), which is a large improvement over galaxy density only. Such measurements on very large scales can detect signatures of modified gravity or non-Gaussianity through scale-dependent growth rate or galaxy bias. We test our modelling in detail using N-body simulations.