Preprint typeset using LATEX style emulateapj v. 08/22/09 RECONSTRUCTING GRAVITY BEYOND THE LOCAL UNIVERSE WITH PECULIAR VELOCITIES

We study a maximum probability approach to reconstructing spatial maps of the Newtonian gravitational potential Ψ from peculiar velocities of galaxies at redshifts beyond z ∼ 0.1, where peculiar velocities have been measured from distance indicators (DI) such as the Tully-Fisher relation. With the large statistical uncertainties associated with DIs (of the order ∼ 20 % in distance), our reconstruction method aims to recover the underlying true peculiar velocity field with sufficient precision to be used as a cosmological probe of gravity, by reducing these statistical 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 δg and the second makes use of the matter linear density power spectrum Pk. Through the use of N-body simulations we demonstrate that, with mea-surements with a suitably high signal-to-noise, we can successfully reconstruct the velocity and gravitational potential field out to z. 0.3. This will prove useful for future tests of gravity, as these relatively deep maps are complementary to weak lensing maps at the same redshift. Subject headings: methods: data analysis,numerical,statistical – galaxies: distances and redshifts – cosmology: large-scale structure of Universe 1