A Reference Survey for Supernova Cosmology with the Nancy Grace Roman Space Telescope

This note presents an initial survey design for the Nancy Grace Roman High-latitude Time Domain Survey. This is not meant to be a final or exhaustive list of all the survey strategy choices, but instead presents a viable path towards achieving the desired precision and accuracy of dark energy measurements using Type Ia supernovae (SNe Ia). We describe a survey strategy that use six filters (RZYJH and F) and the prism on the Roman Wide Field Instrument. This survey has two tiers, one "wide" which targets SNe Ia at redshifts up to 1 and one "deep" targeting redshifts up to 1.7; for each, four filters are used (with Y and J used in both tiers). We propose one field each in the north and south continuous viewing zones, and expect to obtain high-quality distances of $\sim$12,000 SNe Ia with $\sim$5,000 at z > 1. We propose a wide-tier area of $\sim$19 deg$^2$ and a deep tier of $\sim$5 deg$^2$. Exposure times range from 100 s to 900 s for imaging and 900 s to 3600 s for the prism. These exposure times would reach $\sim$25.5 mag and $\sim$26.5 mag for the wide and deep tiers respectively, with deep co-add stacks reaching $\sim$28 mag and $\sim$29 mag. The total survey spans two years, with a total allocation time of six months, and a cadence of $\sim$5 days.