Fisher Forecasts for Cosmological Yields from $3\!\times\!2$pt Analysis of the Roman Space Telescope High Latitude Imaging Survey

The High Latitude Imaging Survey (HLIS) of NASA's Nancy Grace Roman Space Telescope will provide powerful tests of cosmological models through sensitive measurements of cosmic shear, galaxy-galaxy lensing (GGL), and galaxy clustering. As part of the HLIS Project Infrastructure Team's Data Challenge 1 (DC1), we carry out Fisher forecasts of cosmological parameter constraints from combinations of these probes, focusing on inverse-variance figures of merit (FoMs) for the parameters $σ_8$ and $Ω_{\rm{m}}$, which scale the amplitude of weak lensing signals. We find good agreement between Fisher analysis and Markov chain Monte Carlo (MCMC) analysis of the DC1 baseline data vector, and we investigate varied priors on cosmological parameters and on nuisance parameters describing unknown biases in photometric redshifts or shear measurements. The DC1 benchmark modeling assumes a ``lens $=$ source'' analysis with linear galaxy bias and no marginalization over baryonic physics. Under these assumptions, the forecast constraints from GGL+clustering are substantially stronger than those from cosmic shear, with the combination of all three probes (``$3\!\times\!2$pt'') providing moderate further improvement. Adding tight external priors on the power spectrum shape parameters $n_{\rm{s}}$, $Ω_{\rm{b}}$, and $h_0$ can improve the $(σ_8, Ω_{\rm{m}})$ FoMs by factors of $1.2$--$3.5$. The smallest scale angular bins provide much more information than the largest scale bins, and the highest redshift tomographic bins provide more information than the lowest redshift bins. Factor-of-two changes in the priors on photo-$z$ and shear biases, relative to the benchmark values based on anticipated calibration accuracy, produce changes of $\lesssim 20\%$ in FoMs.