A covariant treatment of cosmic parallax
  The Gaia satellite will soon probe parallax on cosmological distances. Using
the covariant formalism and considering the angle between a pair of sources, we
find parallax for both spacelike and timelike separation between observation
points. Our analysis includes both intrinsic parallax and parallax due to
observer motion. We propose a consistency condition that tests the FRW metric
using the parallax distance and the angular diameter distance. This test is
purely kinematic and relies only on geometrical optics, it is independent of
matter content and its relation to the spacetime geometry. We study
perturbations around the FRW model, and find that they should be taken into
account when analysing observations to determine the parallax distance.
