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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., Comment: A report to NASA from the Roman Supernova Science Investigation Teams

Type Ia Supernovae (SNe Ia) are powerful standardizable candles for constraining cosmological models and provided the first evidence of the accelerated expansion of the universe. Their precision derives from empirical correlations, now measured from $>1000$ SNe Ia, between their luminosities, light-curve shapes, colors and most recently with the stellar mass of their host galaxy. As mass correlates with other galaxy properties, alternative parameters have been investigated to improve SN Ia standardization though none have been shown to significantly alter the determination of cosmological parameters. We re-examine a recent claim, based on 34 SN Ia in nearby passive host galaxies, of a 0.05 mag/Gyr dependence of standardized SN Ia luminosity on host age which if extrapolated to higher redshifts, would be a bias up to 0.25 mag, challenging the inference of dark energy. We reanalyze this sample of hosts using both the original method and a Bayesian hierarchical model and find after a fuller accounting of the uncertainties the significance of a dependence on age to be $\leq2\sigma$ and $\sim1\sigma$ after the removal of a single poorly-sampled SN Ia. To test the claim that a trend seen in old stellar populations can be applied to younger ages, we extend our analysis to a larger sample which includes young hosts. We find the residual dependence of host age (after all standardization typically employed for cosmological measurements) to be consistent with zero for 254 SNe Ia from the Pantheon sample, ruling out the large but low significance trend seen in passive hosts., Comment: 9 pages, 3 figures, 3 tables. Accepted for publication in ApJL