Astrometric Effects of Gravitational Wave Backgrounds with non-Luminal
  Propagation Speeds
  A passing gravitational wave causes a deflection in the apparent astrometric
positions of distant stars. The effect of the speed of the gravitational wave
on this astrometric shift is discussed. A stochastic background of
gravitational waves would result in a pattern of astrometric deflections which
are correlated on large angular scales. These correlations are quantified and
investigated for backgrounds of gravitational waves with sub- and super-luminal
group velocities. The statistical properties of the correlations are depicted
in two equivalent and related ways: as correlation curves and as angular power
spectra. Sub-(super-)luminal gravitational wave backgrounds have the effect of
enhancing (suppressing) the power in low-order angular modes. Analytical
representations of the redshift-redshift and redshift-astrometry correlations
are also derived. The potential for using this effect for constraining the
speed of gravity is discussed.
