The High Latitude Spectroscopic Survey on the Nancy Grace Roman Space
  Telescope
  The Nancy Grace Roman Space Telescope will conduct a High Latitude
Spectroscopic Survey (HLSS) over a large volume at high redshift, using the
near-IR grism (1.0-1.93 $\mu$m, $R=435-865$) and the 0.28 deg$^2$ wide field
camera. We present a reference HLSS which maps 2000 deg$^2$ and achieves an
emission line flux limit of 10$^{-16}$ erg/s/cm$^2$ at 6.5$\sigma$, requiring
$\sim$0.6 yrs of observing time. We summarize the flowdown of the Roman science
objectives to the science and technical requirements of the HLSS. We construct
a mock redshift survey over the full HLSS volume by applying a semi-analytic
galaxy formation model to a cosmological N-body simulation, and use this mock
survey to create pixel-level simulations of 4 deg$^2$ of HLSS grism
spectroscopy. We find that the reference HLSS would measure $\sim$ 10 million
H$\alpha$ galaxy redshifts that densely map large scale structure at $z=1-2$
and 2 million [OIII] galaxy redshifts that sparsely map structures at $z=2-3$.
We forecast the performance of this survey for measurements of the cosmic
expansion history with baryon acoustic oscillations and the growth of large
scale structure with redshift space distortions. We also study possible
deviations from the reference design, and find that a deep HLSS at $f_{\rm
line}>7\times10^{-17}$erg/s/cm$^2$ over 4000 deg$^2$ (requiring $\sim$1.5 yrs
of observing time) provides the most compelling stand-alone constraints on dark
energy from Roman alone. This provides a useful reference for future
optimizations. The reference survey, simulated data sets, and forecasts
presented here will inform community decisions on the final scope and design of
the Roman HLSS.
