Probing Dark Matter Models through Weak Lensing with the Nancy Grace Roman Space Telescope

Dark matter (DM) primarily reveals itself through gravitational interactions, forming large halos that contain smaller gravitationally bound structures known as subhalos. Although we have yet to observe direct interactions between DM and normal matter, weak gravitational lensing offers a compelling method to detect DM's influence on visible matter. This study explores the gravitational lensing effects caused by DM subhalos within the Milky Way using high-precision astrometry to detect subtle changes in the apparent accelerations of background stars over time. We model subhalo mass functions for DM models such as cold dark matter, warm dark matter, and primordial black holes to enhance the representation of subhalo distribution and abundance. This improvement enables the simulation of observations from astrometric surveys, like the upcoming Nancy Grace Roman Space Telescope. Using Markov Chain Monte Carlo (MCMC) sampling, we analyze how varying DM mass functions and profiles impact stellar accelerations. We present results on constraints placed on various DM models, particularly CDM concentration parameters. This method has the potential to shed light on DM subhalo structure and properties, particularly in the low-mass regime.