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.
