Rogue worlds meet the dark side: revealing terrestrial-mass primordial black holes with the Nancy Grace Roman Space Telescope

Gravitational microlensing is one of the strongest observational techniques to observe non-luminous astrophysical bodies. Existing microlensing observations provide tantalizing evidence of a population of low-mass objects whose origin is unknown. These events may be caused by terrestrial-mass free-floating planets or by exotic objects such as primordial black holes. However, the nature of these objects cannot be resolved on an event-by-event basis, as the induced light curve is degenerate for lensing bodies of identical mass. One must instead statistically compare \textit{distributions} of lensing events to determine the nature of the lensing population. While existing surveys lack the statistics required to identify multiple subpopulations of lenses, this will change with the launch of the Nancy Grace Roman Space Telescope. Roman's Galactic Bulge Time Domain Survey is expected to observe hundreds of low-mass microlensing events, enabling a robust statistical characterization of this population. In this paper, we show that by exploiting features in the distribution of lensing event durations, Roman will be sensitive to a subpopulation of primordial black holes hidden amongst a background of free-floating planets. Roman's reach will extend to primordial black hole dark matter fractions as low as $f_\text{PBH} = 10^{-4}$ at peak sensitivity, and will be able to conclusively determine the origin of existing ultrashort-timescale microlensing events. A positive detection would provide evidence that a significant fraction of the cosmological dark matter consists of macroscopic, non-luminous objects.