Fast Radio Bursts in the Era of the Vera C. Rubin Observatory's Legacy Survey of Space and Time
Identifying the host galaxies of fast radio bursts (FRBs), and comparing their redshifts and dispersion measures, has unlocked a new probe of the cosmological distribution of ionised gas. However the necessary optical observations to identify FRB hosts, and measure their redshifts, are becoming increasingly onerous as the detection rate of precisely localised FRBs increases. Here we analyse the ability of the Legacy Survey of Space and Time (LSST), being conducted by the Vera C. Rubin Observatory, to identify FRB host galaxies, and the utility of LSST photometric redshifts for FRB cosmology. By combining a model of FRB host galaxy r-band magnitudes, $m_r$, with predictions for the FRB z-DM distribution, we create a method to predict the $m_r(z)$ distribution for the host galaxies of FRBs detected by radio surveys. We then predict these distributions for the coherent modes of the Australian Square Kilometre Array Pathfinder (ASKAP) and MeerKAT. We find that even a single visit with Rubin will be able to identify 65% of FRB host galaxies detected by ASKAP's coherent upgrade, `CRACO'; while the final 10 year co-added images will identify 81% of those from MeerKAT's tied array beams. We also simulate the impact of using photometric redshifts for a simplified analysis to determine $H_0$, finding that estimated photo-z errors result in a decreased precision of only 7% on $H_0$ for ASKAP's CRACO system. The impact of missing faint FRB hosts, which are likely at higher redshifts, is more significant, and might degrade sensitivity to $H_0$ by 47%, or 62% when combined with photo-z errors. All told, Rubin's LSST will be an incredibly powerful survey for facilitating FRB cosmology, although supplemental observations may be useful for particularly faint and distant host galaxies.