Cosmological Forecasts for Combined and Next Generation Peculiar Velocity Surveys

Peculiar velocity surveys present a very promising route to measuring the growth rate of large-scale structure and its scale dependence. However, individual peculiar velocity surveys suffer from large statistical errors due to the intrinsic scatter in the relations used to infer a galaxy's true distance. In this context we use a Fisher Matrix formalism to investigate the statistical benefits of combining multiple peculiar velocity surveys. We find that for all cases we consider there is a marked improvement on constraints on the linear growth rate $f\sigma_{8}$. For example, the constraining power of only a few peculiar velocity measurements is such that the addition of the 2MASS Tully-Fisher survey (containing only $\sim2,000$ galaxies) to the full redshift and peculiar velocity samples of the 6-degree Field Galaxy Survey (containing $\sim 110,000$ redshifts and $\sim 9,000$ velocities) can improve growth rate constraints by $\sim20\%$. Furthermore, the combination of the future TAIPAN and WALLABY+WNSHS surveys has the potential to reach a $\sim3\%$ error on $f\sigma_{8}$, which will place tight limits on possible extensions to General Relativity. We then turn to look at potential systematics in growth rate measurements that can arise due to incorrect calibration of the peculiar velocity zero-point and from scale-dependent spatial and velocity bias. For next generation surveys, we find that neglecting velocity bias in particular has the potential to bias constraints on the growth rate by over $5\sigma$, but that an offset in the zero-point has negligible impact on the velocity power spectrum.