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 for surveys with galaxy number density of about 10 ^ { -2 } ( h ^ { -1 } \mathrm { Mpc } ) ^ { -3 } , if we can use all the information for wavenumber k \leq 0.2 h \mathrm { Mpc } ^ { -1 } .
In the absence of accurate theoretical models at k = 0.2 h \textrm { Mpc } ^ { -1 } , the improvement over redshift-only surveys is even larger — around a factor of 5 for k \leq 0.1 h \mathrm { Mpc } ^ { -1 } .
Future peculiar velocity surveys , TAIPAN , and the all-sky H i surveys , WALLABY and WNSHS , can measure the growth rate , f \sigma _ { 8 } to 3 per cent at z \sim 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 \mathrm { Mpc } ^ { -1 } in the range 0.02 h \mathrm { Mpc } ^ { -1 } \la k \leq 0.1 h \mathrm { 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 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 .