A Decade to Map the Diffuse Universe: FRB-QSO Pairs with HST/COS Spectroscopy

Jointly analyzing the sightlines of arcsecond-localized fast radio bursts (FRBs) and UV-bright quasars (QSOs) nearby in projection has the potential to provide strong constraints on the phases, mass distributions, and magnetic structure of the diffuse universe. Each probe supplies what the other cannot: FRBs provide integrated electron columns (DM), line-of-sight magnetic field estimates (RM), and scattering constraints ($\tau_{\rm scatt}$) that are independent of gas phase; QSOs provide the redshift- and phase-resolved column densities needed to interpret them. Today, there are only $\sim100$ arcsecond-localized FRBs at $z < 1$, making statistical FRB-QSO pair surveys impossible. By 2035, there will be $\sim10^{5}$. Using the most recent FRB localization forecasts and UV-bright QSO catalogs, we estimate that next-generation interferometers will yield thousands of FRB--QSO pairs at angular separations $\theta < 10'$, including $\sim100$ pairs at $\theta < 1'$, over a common 20,000\,deg$^2$ footprint by 2035. We outline the science enabled by this sample: constraints on CGM ionization fractions and baryon masses; observational constraints on the role of magnetic fields and turbulence in the CGM and cosmic web; sightline-by-sightline partitioning of the cosmic DM budget; and three-dimensional mapping of the multiphase Milky Way and M31 halos. Together, these measurements directly address the physics of feedback, non-thermal pressure support, and energy balance in the diffuse gas that regulates galaxy growth. HST/COS is the only instrument that can carry out this program, and the 2030s are the only decade in which to do it before Habitable Worlds Observatory (HWO) defines the next era of diffuse universe science.