  The dark matter subhalo mass function is a promising way of distinguishing
between dark matter models. While cold dark matter predicts halos down to
Earth-sized masses, other dark matter models typically predict a cut-off in the
subhalo mass function. Thus a definitive detection or limits on the existence
of subhalos at small masses can give us insight into the nature of dark matter.
If these subhalos exist in the Milky Way, they would produce weak lensing
signatures, such as modified apparent positions, on background stars. These
signatures would generate correlations in the apparent velocities and
accelerations of these stars, which could be observable given sufficient
astrometric resolution and cadence. The Nancy Grace Roman Space Telescope's
Exoplanet Microlensing Survey will be perfectly suited to measuring the
acceleration signatures of these halos. Here we forward model these
acceleration signatures and explore the Roman Space Telescope's future
constraints on lens profiles and populations. We find that the Roman Space
Telescope could place competitive bounds on point source, Gaussian, and
Navarro-Frenk-White (NFW) profile lenses that are complementary to other
proposed methods. In particular, it could place 95% upper limits on the NFW
concentration, $c_{200} < 10^{2.5}$. We discuss possible systematic effects
that could hinder these efforts, but argue they should not prevent the Roman
Space Telescope from placing strong limits. We also discuss further analysis
methods for improving these constraints.
