Direct geometrical measurement of the Hubble constant from galaxy parallax: predictions for LSST/VRO and WFIRST

We investigate the possibility that a statistical detection of the galaxy parallax shifts due to the Earth's motion with respect to the CMB frame (cosmic secular parallax) could be made by the Vera Rubin Observatory or by the WFIRST satellite, 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 WFIRST 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. 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 WFIRST.