2018ApJ...868...69T

The transverse peculiar velocities caused by the mass distribution of large-scale structure (LSS) provide a test of the theoretical matter power spectrum and the cosmological parameters that contribute to its shape. Typically, the matter density distribution of the nearby universe is measured through redshift or line-of-sight peculiar velocity surveys. However, both methods require model-dependent distance measures to place the galaxies or to differentiate peculiar velocity from the Hubble expansion. In this paper, we use the correlated proper motions of galaxy pairs from the VLBA Extragalactic Proper Motion Catalog to place limits on the transverse peculiar velocity of galaxy pairs with comoving separations <1500 Mpc without a reliance on precise distance measurements. The relative proper motions of galaxy pairs across the line of sight can be directly translated into relative peculiar velocities because no proper motion will occur in a homogeneous expansion. We place a 3σ limit on the relative proper motion of pairs with comoving separations <100 Mpc of -17.4 µas yr^–1< {dot}θ/sinθ< 19.8µas yr^–1. We also confirm that large-separation objects (>200 Mpc) are consistent with pure Hubble expansion to within ∼5.3 µas yr^–1 (1σ). Finally, we predict that Gaia end-of-mission proper motions will be able to significantly detect the mass distribution of LSS on length scales <25 Mpc. This future detection will allow a test of the shape of the theoretical mass power spectrum without a reliance on precise distance measurements.