Direct geometrical measurement of the Hubble constant from galaxy
  parallax: predictions for the Vera C. Rubin Observatory and Nancy Grace Roman
  Space Telescope
  We investigate the possibility that a statistical detection of the galaxy
parallax shift due to the Earth's motion with respect to the CMB frame (cosmic
secular parallax) could be made by the Vera C. Rubin Observatory Legacy Survey
of Space and Time (LSST) or by the Nancy Grace Roman Space Telescope (NGRST),
and used to measure the Hubble constant. We make mock galaxy surveys which
extend to redshift z=0.06 from a large N-body simulation, and include
astrometric errors from the LSST and NGRST science requirements, redshift
errors and peculiar velocities. We include spectroscopic redshifts for the
brightest galaxies (r < 18) in the fiducial case. We use these catalogues to
make measurements of parallax versus redshift,for various assumed survey
parameters and analysis techniques. We find that in order to make a competitive
measurement it will be necessary to model and correct for the peculiar velocity
component of galaxy proper motions. It will also be necessary to push
astrometry of extended sources into a new regime, and combine information from
the different elements of resolved galaxies. In an appendix we describe some
simple tests of galaxy image registration which yield relatively promising
results. For our fiducial survey parameters, we predict an rms error on the
direct geometrical measurement of H0 of 2.8% for LSST and 0.8% for NGRST.
