The Hubble Expansion is Isotropic in the Epoch of Dark Energy
  The isotropy of the universal Hubble expansion is a fundamental tenet of
physical cosmology, but it has not been precisely tested during the current
epoch, when dark energy is dominant. Anisotropic expansion will produce a
shearing velocity field, causing objects to stream toward directions of faster
expansion and away from directions of slower expansion. This work tests the
basic cosmological assumption of isotropic expansion and thus the isotropy of
dark energy. The simplest anisotropy will manifest as a quadrupolar curl-free
proper motion vector field. We derive this theoretical signature using a
tri-axial expanding metric with a flat geometry (Bianchi I model), generalizing
and correcting previous work. We then employ the best current data, the Titov &
Lambert (2013) proper motion catalog of 429 objects, to measure the isotropy of
universal expansion. We demonstrate that the Hubble expansion is isotropic to
7% (1 $\sigma$), corresponding to streaming motions of 1 microarcsecond/yr, in
the best-constrained directions (-19% and +17% in the least-constrained
directions) and does not significantly deviate from isotropy in any direction.
The Gaia mission, which is expected to obtain proper motions for 500,000
quasars, will likely constrain the anisotropy below 1%.
