Constraints on the Epoch of Reionization with Roman Space Telescope and the Void Probability Function of Lyman-Alpha Emitters

We use large simulations of Lyman-Alpha Emitters with different fractions of ionized intergalactic medium to quantify the clustering of Ly$\alpha$ emitters as measured by the Void Probability function (VPF), and how it evolves under different ionization scenarios. We quantify how well we might be able to distinguish between these scenarios with a deep spectroscopic survey using the future Nancy Grace Roman Space Telescope. Since Roman will be able to carry out blind spectroscopic surveys of Ly$\alpha$ emitters continuously between $7 3-4\sigma$ at several redshifts between $75-8\sigma$) across the epoch of reionization, and would yield a detailed history of the reionization of the IGM and its effect on Lyman-$\alpha$ Emitter clustering.