  The extragalactic distance scale is fundamental to our understanding of
astrophysics and cosmology. In recent years, the surface brightness fluctuation
(SBF) method, applied in the near-IR, has proven especially powerful for
measuring galaxy distances, first with HST and now with a new JWST program to
calibrate the method directly from the tip of the red giant branch (TRGB). So
far, however, the distances from space have been gathered slowly, one or two at
a time. With the Roman Space Telescope, we have the opportunity to measure
uniformly high-quality SBF distances to thousands of galaxies out to hundreds
of Mpc. The impact of these data on cosmology and galaxy studies depends on the
specifics of the survey, including the filter selection, exposure depth, and
(especially) the sky coverage. While the baseline HLWAS survey in four filters
plus the grism would yield useful data, the impact would be limited by the
relatively small area. A more optimal approach would concentrate on the most
efficient passband (F146), adopt an exposure time sufficient to measure good
quality distances well out into the Hubble flow, and then maximize the sky
coverage within the total time constraints. Grism observations over the same
area can provide the needed information on redshifts and spectral energy
distributions for compact sources, while colors for larger objects can be
obtained from lower resolution surveys. The proposed plan will enable accurate
determination of the physical properties of thousands of nearby galaxies, an
independent measure of the Hubble constant $H_0$ with negligible statistical
error, and competitive constraints on $S_8{\,=\,}\sigma_8(\Omega_m/0.3)^{0.5}$.
The resulting data set will be a phenomenal resource for a wide range of
studies in astrophysics and cosmology.
