  We present a realistic 2000 deg$^{2}$ H$\alpha$ galaxy mock catalog with
$1<z<2$ for the Nancy Grace Roman Space Telescope galaxy redshift survey, the
High Latitude Spectroscopic Survey (HLSS), created using Galacticus, a
semi-analytical galaxy formation model, and high resolution cosmological N-body
simulations. Galaxy clustering can probe dark energy and test gravity via
baryon acoustic oscillation (BAO) and redshift space distortion (RSD)
measurements. Using our realistic mock as the simulated Roman HLSS data, and a
covariance matrix computed using a large set of approximate mocks created using
EZmock, we investigate the expected precision and accuracy of the BAO and RSD
measurements using the same analysis techniques used in analyzing real data. We
find that the Roman H$\alpha$ galaxy survey alone can measure the angular
diameter distance with 2\% uncertainty, the Hubble parameter with 3-6\%
uncertainty, and the linear growth parameter with 7\% uncertainty, in each of
four redshift bins. Our realistic forecast illustrates the power of the Roman
galaxy survey in probing the nature of dark energy and testing gravity.
