🔭 astrophysics

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

This paper presents a scalable hierarchical inference tool to forecast the cosmological constraining power of a simulated LSST sample of 800 strongly lensed AGNs, demonstrating that incorporating this large dataset can achieve a ~2.5% constraint on H0 and significantly improve the dark energy figure of merit compared to smaller, high-fidelity samples.

Original authors: 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

Published 2026-07-15

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: 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

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe is a giant, expanding balloon, and scientists are trying to figure out exactly how fast it's inflating and what's pushing it to expand faster. For a long time, they've been using a few special "cosmic lighthouses"—bright, distant galaxies called Active Galactic Nuclei (AGN)—that are bent by gravity into multiple images. This bending creates a time delay; light from one image arrives a few days or weeks later than light from another. By measuring this delay, astronomers can calculate the universe's expansion history.

But here's the catch: until now, they've only had a handful of these lighthouses to study—about eight. It's like trying to guess the weather pattern of an entire continent by looking at a single cloud. The paper you're reading simulates a massive upgrade: what if we had 800 of these lenses, as predicted by the upcoming Vera C. Rubin Observatory (LSST)?

The Big Discovery: More Data, Even if It's "Messier"

The team ran a huge simulation (a computer experiment, not a real observation yet) to see what happens when you combine a small group of super-precise lenses with a massive crowd of "good enough" lenses.

Their main finding is surprisingly simple: Quantity has a massive impact.

They found that adding 600 lenses that rely on standard LSST data (which are less precise than the high-end ones) to a base of 200 better lenses tripled the ability to measure Dark Energy.

Before: With just the high-quality lenses, the "Dark Energy Figure of Merit" (a score for how well we know the rules of the universe) was 2.4.
After: Adding the 600 extra lenses boosted that score to 6.7.

Think of it like trying to hear a whisper in a noisy room. If you have one person shouting the message clearly, you can hear it. But if you have 600 people whispering the same message at once, the combined sound becomes loud and clear, even if each individual whisper is fuzzy. The simulation suggests that this "crowd" of 800 lenses could pin down the expansion rate of the universe ( $H_0$ ) to within 2.5% and give us a much sharper picture of Dark Energy.

The "How-To" Guide: What Matters Most?

The authors didn't just count lenses; they tested different strategies to see where to spend telescope time and money. They treated the universe like a puzzle and tried different pieces to see which ones fit best.

1. The Kinematics Question: Fewer Deep Dives or Many Shallow Dips?
To solve the puzzle, scientists need to know how stars move inside the lensing galaxies (kinematics). They tested two approaches:

Option A: Use powerful telescopes to get incredibly detailed, 3D maps of star movements for a few lenses (using IFU technology).
Option B: Use smaller telescopes to get a single, average speed measurement for many more lenses.

The simulation showed that both strategies work equally well for improving the Dark Energy score (boosting it by about 30% in both cases). However, if the goal is specifically to measure the expansion rate ( $H_0$ ) more precisely, the detailed 3D maps (Option A) are the winners, squeezing the uncertainty down from ~2.5% to ~2%.

2. The Image Quality Question: Do We Need Perfect Photos?
Scientists wondered if they needed to spend months creating perfect, high-resolution computer models of every galaxy (Forward Modeling) or if quick, automated models were enough.

The Result: In their simulation, upgrading the image models from "automated" to "perfect" didn't make a huge difference in the final Dark Energy score.
The Catch: The authors are careful to say this might be because their simulation of the "perfect" models wasn't fully realistic yet. They suspect that in the real world, better models might help more, but based on this specific simulation, the time-delay measurements are the real bottleneck, not the image quality.

3. The Time-Delay Question: The 2-Day Magic Number
This was the most exciting finding. The team tested how much better the results would be if they could measure the time delays more accurately.

Current Plan: LSST might measure delays with a precision of 5 days.
The Simulation: They tested improving this to 4 days, 3 days, and finally 2 days.
The Verdict: Nothing much changed until they hit 2 days. Once the precision reached 2 days, the ability to measure Dark Energy jumped significantly.
The Takeaway: It's not just about having more lenses; it's about making sure the timing measurements are sharp. If the community can push LSST data analysis to reach that 2-day precision threshold, the results will be game-changing.

The Redshift Twist: Where You Look Matters

The paper also played with the "location" of the lenses. They simulated lenses at different distances (redshifts).

The Finding: It turns out the distance of the lens (the galaxy bending the light) matters a lot, but the distance of the source (the bright background object) doesn't seem to matter much.
The Sweet Spot: Surprisingly, lenses that are closer to us (lower redshift) provided better constraints on the expansion rate and Dark Energy than those very far away. It's a bit counter-intuitive, like finding that a nearby streetlamp helps you see the shape of a hill better than a distant mountain peak.

What This Means (And What It Doesn't)

The authors are very clear: This is a simulation. They haven't found these 800 lenses yet; they've built a computer model to predict what will happen when the Vera C. Rubin Observatory starts its survey.

They explicitly rule out the idea that we need to wait for a few perfect lenses to get good results. Instead, they argue that the "messy" data from hundreds of lenses is incredibly valuable. They also suggest that while better images are nice, the real key to unlocking the secrets of Dark Energy is getting those time-delay measurements down to a 2-day precision and gathering as many lenses as possible.

In short, the universe is holding a massive secret about Dark Energy. This paper suggests that we don't need a single, perfect key to unlock it; we just need a giant keyring with 800 keys, and we need to make sure the teeth on those keys are cut with a precision of 2 days. If we do that, we might finally understand the invisible force pushing our universe apart.

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

Problem Statement
Time-delay cosmography (TDC) using strongly lensed Active Galactic Nuclei (AGN) provides a direct, single-step measurement of angular diameter distances in the late Universe, offering an independent probe of the expansion history. While current TDC samples (e.g., TDCOSMO) have successfully constrained the Hubble constant ( $H_0$ ) to $\sim4\%$ , their constraining power on the dark energy (DE) equation of state parameters ( $w_0, w_a$ ) remains weak. The Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) is forecasted to discover $\sim1,000$ to $3,500$ new lensed AGN, with $\sim800$ expected to have measurable time delays. The challenge lies in scaling the hierarchical Bayesian inference required to combine these hundreds of lenses while accounting for complex degeneracies (mass-sheet and mass-anisotropy) and varying levels of observational fidelity (from high-resolution space-based follow-up to LSST-only data).

Methodology
The authors introduce a scalable hierarchical inference framework, implemented in a new code named fasttdc, designed to compute cosmological likelihoods for hundreds of lenses simultaneously. The analysis is divided into two stages:

Data Vector Generation: Individual lens models and measurements are summarized into static data vectors. This includes samples from image-based mass modeling posteriors ( $\xi_{lens}$ ), pre-computed Fermat potential differences ( $\Delta\phi$ ) and Jeans model quantities ( $J$ ), external convergence predictions ( $\kappa_{ext}$ ), and observed time delays and velocity dispersions. The authors emulate these data vectors for a simulated sample of 800 lenses drawn from the OM10 catalog, assuming a ground-truth $\Lambda$ CDM cosmology ( $H_0=70, \Omega_m=0.3, w_0=-1, w_a=0$ ).
Hierarchical Inference: The data vectors are fed into a joint Bayesian inference framework (using the emcee MCMC sampler) to infer the population-level cosmological parameters ( $\Omega = \{H_0, \Omega_m, w_0, w_a\}$ ) and hyperparameters describing the lens population distributions for the internal mass-sheet ( $\lambda_{int}$ ) and anisotropy ( $\beta_{ani}$ ). The likelihood evaluation utilizes importance sampling to marginalize over individual lens properties, fully accounting for the mass-sheet and mass-anisotropy degeneracies without condensing the Fermat potential and time delay into a single distance posterior prematurely.

The study simulates a baseline sample of 800 lenses categorized by follow-up fidelity:

Platinum (50 lenses): Spatially resolved kinematics (IFU), dedicated time-delay monitoring, and high-resolution imaging (JWST or HST).
Gold (150 lenses): Single-aperture kinematics, LSST time-delay monitoring, and HST imaging.
Silver (600 lenses): LSST time-delay monitoring and LSST imaging, with or without single-aperture kinematics.

Key Contributions

Scalable Inference Tool: Development of fasttdc, a vectorized likelihood evaluation code capable of handling $\mathcal{O}(1000)$ lenses simultaneously, overcoming the computational bottlenecks of previous hierarchical methods.
Realistic Emulation: A comprehensive emulation pipeline that generates data vectors for image modeling (using Neural Posterior Estimation and forward modeling), time-delay measurements, stellar kinematics (IFU and aperture), and line-of-sight convergence, reflecting varying levels of observational fidelity.
Systematic Strategy Testing: A series of experiments quantifying how different follow-up strategies (kinematic types, imaging quality, time-delay precision) and redshift configurations impact cosmological constraints.

Results

Sample Size Impact: Incorporating the full LSST-scale sample (800 lenses) significantly improves constraints compared to smaller, high-precision samples. Adding 600 "Silver" lenses (LSST-only time delays) to a 200-lens sample increases the Dark Energy Figure of Merit (DE FOM) from 2.9 to 6.7 and improves $H_0$ precision from $\sim3.5\%$ to $\sim2.5\%$ .
Kinematic Follow-up: Expanding the sample of lenses with stellar kinematics is crucial. Increasing the number of lenses with spatially resolved IFU kinematics (from 50 to 122) improves the DE FOM to 9.1 and $H_0$ precision to $\sim2\%$ . Alternatively, increasing single-aperture kinematics (from 150 to 450 lenses) improves the DE FOM to 8.9, though it does not improve $H_0$ precision as effectively as the IFU strategy.
Time-Delay Precision: Improving time-delay measurement precision is a primary driver for DE constraints. Achieving a 2-day precision on time delays (either via dedicated monitoring for a subset or improved LSST light-curve modeling for the whole sample) yields the most significant gains. Experiment 3.1 (60 lenses at 2-day precision) reaches a DE FOM of 12.0, while Experiment 3.4 (all LSST lenses at 2-day precision) reaches a DE FOM of 10.1 with superior $H_0$ and $\Omega_m$ precision.
Mass Model Precision: Upgrading mass models from automated LSST-based modeling to higher-precision HST-based forward modeling showed mixed results. While it improved $\Omega_m$ precision in some scenarios, it did not consistently improve the DE FOM, suggesting that at current time-delay and kinematic precisions, mass model precision is not the limiting factor.
Redshift Configuration: The lens redshift ( $z_{lens}$ ) is the dominant factor in constraining power. Lower lens redshifts ( $z_{lens} \approx 0.2$ ) yield higher DE FOMs and better $H_0$ constraints compared to higher redshifts ( $z_{lens} \approx 1.0$ ), whereas source redshift has a negligible effect.

Significance and Claims
The paper claims that the LSST sample of lensed AGN, when analyzed with a scalable hierarchical framework, offers a powerful, independent probe of dark energy. The authors demonstrate that the statistical power gained from incorporating a large number of lower-precision lenses (LSST-only data) is substantial, improving the DE FOM by nearly a factor of 3 compared to relying solely on high-precision follow-up samples.

The study concludes that to maximize the DE constraining power of TDC, the community should prioritize:

Time-delay precision: Efforts to improve LSST light-curve modeling to achieve $\sim2$ -day precision on time delays are critical.
Kinematic follow-up: While both IFU and aperture strategies improve constraints, IFU measurements are uniquely valuable for tightening $H_0$ constraints.
Redshift selection: Lower lens redshifts are advantageous for constraining $H_0$ and $w_0$ .

The authors emphasize that their results are based on emulated data and that future work must incorporate more realistic mass model posteriors and systematic effects. However, the framework established provides a necessary foundation for the LSST Dark Energy Science Collaboration to deliver the first cosmological constraints from LSST lensed AGN.

The Big Discovery: More Data, Even if It's "Messier"

The "How-To" Guide: What Matters Most?

The Redshift Twist: Where You Look Matters

What This Means (And What It Doesn't)

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