Reconstructing the velocity field beyond the local universe

We present a maximum probability approach to reconstructing spatial maps of the peculiar velocity field at redshifts $z\sim0.1$, where the velocities have been measured from distance indicators (DI) such as $D_n-\sigma$ relations or Tully-Fisher. With the large statistical uncertainties associated with DIs, our reconstruction method aims to recover the underlying true peculiar velocity field by reducing these errors with the use of two physically motivated filtering prior terms. The first constructs an estimate of the velocity field derived from the galaxy over-density {\deltag} and the second makes use of the matter linear density power spectrum {\pk}. Using $N$-body simulations we find, with an SDSS-like sample ($N_{gal}\simeq33$ per deg$^2$), an average correlation coefficient value of $r=0.55\pm{0.02}$ between our reconstructed velocity field and that of the true velocity field from the simulation. However, with a suitably high number density of galaxies from the next generation surveys (e.g. $N_{gal}\simeq140$ per deg$^2$) we can achieve an average $r=0.70\pm{0.02}$ out to moderate redshifts $z\sim0.1$. This will prove useful for future tests of gravity, as these relatively deep maps are complementary to weak lensing maps at the same redshift.