  The Nancy Grace Roman Space Telescope (Roman) will perform a Galactic
Exoplanet Survey (RGES) to discover bound exoplanets with semi-major axes
greater than 1 au using gravitational microlensing. Roman will even be
sensitive to planetary mass objects that are not gravitationally bound to any
host star. Such free-floating planetary mass objects (FFPs) will be detected as
isolated microlensing events with timescales shorter than a few days. A
measurement of the abundance and mass function of FFPs is a powerful diagnostic
of the formation and evolution of planetary systems, as well as the physics of
the formation of isolated objects via direct collapse. We show that Roman will
be sensitive to FFP lenses that have masses from that of Mars ($0.1 M_\oplus$)
to gas giants ($M\gtrsim100M_\oplus$) as isolated lensing events with
timescales from a few hours to several tens of days, respectively. We
investigate the impact of the detection criteria on the survey, especially in
the presence of finite-source effects for low-mass lenses. The number of
detections will depend on the abundance of such FFPs as a function of mass,
which is at present poorly constrained. Assuming that FFPs follow the fiducial
mass function of cold, bound planets adapted from Cassan et al. (2012), we
estimate that Roman will detect $\sim250$ FFPs with masses down to that of Mars
(including $\sim 60$ with masses $\le M_\oplus$). We also predict that Roman
will improve the upper limits on FFP populations by at least an order of
magnitude compared to currently-existing constraints.
