Investigating the Dark Energy Constraint from Strongly Lensed AGN at LSST-Scale

TL;DR

This work develops a scalable, hierarchical time-delay cosmography framework (fasttdc) to exploit LSST-scale samples of strongly lensed AGN for dark energy constraints. By simulating an 800-lens LSST-like catalog and performing a joint inference over cosmology and lens-population hyperparameters, the authors quantify gains in H_0 precision and the Dark Energy Task Force figure of merit (DE FOM) as a function of follow-up fidelity (kinematics, image-modeling quality, and time-delay precision) and redshift configuration. Key findings show that adding hundreds of LSST lenses can substantially improve DE constraints (DE FOM rising from ~2.4 to ~6.7 in the baseline case), with additional improvements driven by higher-precision time delays and spatially resolved kinematics; mass-model fidelity, while important, may have nuanced effects depending on modeling realism. The study also emphasizes the strategic value of targeted follow-up and redshift distribution planning, and outlines future roadmap toward a full DESC TDC cosmology analysis with more realistic mass models and faster likelihood evaluation. Overall, the work demonstrates the potential of LSST-era time-delay cosmography to provide competitive, independent constraints on dark energy and the expansion history of the Universe.

Abstract

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.

Figures (6)

• Figure 1: Diagram of the vectorized likelihood evaluation, isolated to the time-delay likelihood only (the kinematic likelihood is treated similarly). In step 1, samples of the modeling inputs ($\lambda_{int}$,$\kappa_{\text{ext}}$,$\Delta \phi$) are condensed into samples of the predicted time-delay, with a value tracked for every importance sample, across every lens. In step 2, the likelihood of the predicted time-delay is evaluated against the observed time-delay over every importance sample, averaged, and then multiplied across every lens, to produce the final likelihood. See Equation \ref{['eqn:imp_sampling_lklhd']}.
• Figure 2: We demonstrate how growing the sample size impacts the cosmological inference from the baseline experiment configuration (Table \ref{['table:baseline']}). We start with 50 platinum lenses only (light purple), then add in 150 gold lenses with LSST time-delay measurements (light blue), and finally add in 600 silver lenses with LSST time-delays and image-based mass models (blue-green). We see that the addition of the 750 lenses that depend on LSST measurements simultaneously improves the DE FOM from 2.4 to 6.7, and the $H_0$ precision from $\sim$3.5% to $\sim$2.5%.
• Figure 3: Cosmological posteriors from four experiments, testing additional follow-up compared to the baseline. The baseline posterior is shown in grey. On the top left, we test adding IFU observation on 72 lenses (dark green). On the top right, we test adding aperture kinematics on 300 lenses (light green). On the bottom left, we test a conservative long-term monitoring campaign, increasing the time-delay precision to 2 days for 60 lenses (light blue). On the bottom right, we test a more optimistic scenario, assuming a 2-day time-delay precision for all LSST measurements (purple).
• Figure 4: Cosmological constraint from a sample of 10 lenses, changing the redshift populations. For each plot, the source redshift population is constant, with $\mu(z_{\text{src}})$=2.0, and the lens redshift changes from $\mu(z_{\text{lens}})$=1.0 (red) to $\mu(z_{\text{lens}})$=0.5 (purple) to $\mu(z_{\text{lens}})$=0.2 (blue). The left plot has a uniform $\Omega_m$ prior, the right plot has an informative $\Omega_m$ prior.
• Figure 5: We compare cosmological contours from the forecast in shajib_SLSC (orange), to our baseline experiment (grey), and our experiment 3.1 with extra long-term time-delay monitoring (blue).