Sydney Erickson, Martin Millon, Padmavathi Venkatraman, Tian Li, Philip Holloway, Phil Marshall, Anowar Shajib, Simon Birrer, Xiang-Yu Huang, Timo Anguita, Steven Dillmann, Narayan Khadka, Kate Napier, Aaron Roodman, The LSST Dark Energy Science Collaboration

Strongly lensed Active Galactic Nuclei (AGN) with an observable time delay can be used to constrain the expansion history of the Universe through time-delay cosmography (TDC). As the sample of time-delay lenses grows to statistical size, with $\mathcal{O}$(1000) lensed AGN forecast to be observed by the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST), there is an emerging opportunity to use TDC as an independent probe of dark energy. To take advantage of this statistical sample, we implement a scalable hierarchical inference tool which computes the cosmological likelihood for hundreds of strong lenses simultaneously. With this new technique, we investigate the cosmological constraining power from a simulation of the full LSST sample. We start from individual lenses, and emulate the full joint hierarchical TDC analysis, including image-based modeling, time-delay measurement, velocity dispersion measurement, and external convergence prediction. We fully account for the mass-sheet and mass-anisotropy degeneracies. We assume a sample of 800 lenses, with varying levels of follow-up fidelity based on existing campaigns. With our baseline assumptions, within a flexible $w_0w_a$CDM cosmology, we simultaneously forecast a $\sim$2.5% constraint on H0 and a dark energy figure of merit (DE FOM) of 6.7. We show that by expanding the sample from 50 lenses to include an additional 750 lenses with plausible LSST time-delay measurements, we improve the forecasted DE FOM by nearly a factor of 3, demonstrating the value of incorporating this portion of the sample. We also investigate different follow-up campaign strategies, and find significant improvements in the DE FOM with additional stellar kinematics measurements and higher-precision time-delay measurements. We also demonstrate how the redshift configuration of time-delay lenses impacts constraining power in $w_0w_a$CDM.