Are peculiar velocity surveys competitive as a cosmological probe?
  Peculiar velocity surveys, which measure galaxy peculiar velocities directly
from standard candles in addition to redshifts, can provide strong constraints
on the linear growth rate of cosmological large-scale structure at low
redshift. The improvement originates from the physical relationship between
galaxy density and peculiar velocity, which substantially reduces cosmic
variance. We present the results of Fisher matrix forecasts of correlated
fields of galaxy density and velocity. Peculiar velocity can improve the growth
rate constraints by about a factor of two compared to density alone, if we can
use all the information for wavenumber k < 0.2 h/Mpc. Future peculiar velocity
surveys, TAIPAN, and the all-sky HI surveys, WALLABY and WNSHS, can measure the
growth rate, f*sigma8 to 3 per cent at z ~ 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 0.01 h/Mpc in the range 0.02 h/Mpc < k < 0.1
h/Mpc, 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 use
N-body simulations to improve the modelling of auto- and cross-power spectra of
galaxy density and peculiar velocity by introducing a new redshift-space
distortion term to the velocity, which has been neglected in previous studies.
The velocity power spectrum has a damping in redshift space, which is larger
than that naively expected from the similar effect in the galaxy power
spectrum.
