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Strong gravitational lenses are a singular probe of the Universe’s small-scale structure—they are sensitive to the gravitational effects of low-mass (<10¹⁰M_⊙) halos even without a luminous counterpart. Recent strong-lensing analyses of dark matter structure rely on simulation-based inference (SBI). Modern SBI methods, which leverage neural networks as density estimators, have shown promise in extracting the halo-population signal. However, it is unclear whether the constraints from these models are limited by the methodology or the data. In this study, we introduce an accelerator-optimized simulation pipeline that can generate lens images with realistic subhalo populations in milliseconds. Leveraging this simulator, we identify the main limitation of our fiducial SBI analysis: training set size. We then adopt a sequential neural posterior estimation (SNPE) approach, allowing us to refine the training distribution to align with the observed data. Using only one-fifth as many mock Hubble Space Telescope images, SNPE matches the constraints on the low-mass halo population produced by our best nonsequential model. Our experiments suggest that an over 3 order-of-magnitude increase in training set size and GPU hours would be required to achieve an equivalent result without sequential methods. While the full potential of the existing lens sample remains to be explored, the notable improvement in constraining power enabled by our sequential approach highlights that current constraints are limited primarily by methodology and not the data itself. Moreover, our results emphasize the need to treat training set generation and model optimization as interconnected stages of any cosmological analysis using SBI.

 

Strong gravitational lensing provides a purely gravitational means to infer properties of dark matter haloes and thereby constrain the particle nature of dark matter. Strong lenses sometimes appear as four lensed images of a background quasar accompanied by spatially resolved emission from the quasar host galaxy encircling the main deflector (lensed arcs). We present methodology to simultaneously reconstruct lensed arcs and relative image magnifications (flux ratios) in the presence of full populations of subhaloes and line-of-sight haloes. To this end, we develop a new approach for multiplane ray tracing that accelerates lens mass and source light reconstruction by factors of $\sim\!\! 100\!\!-\!\!1000$. Using simulated data, we show that simultaneous reconstruction of lensed arcs and flux ratios isolates small-scale perturbations to flux ratios by dark matter substructure from uncertainties associated with the main deflector mass profile on larger angular scales. Relative to analyses that use only image positions and flux ratios to constrain the lens model, incorporating arcs strengthens likelihood ratios penalizing warm dark matter with a suppression scale $m_{\rm {hm}} / {\rm M}_{\odot }$ in the ranges of $\left[10^7 \!\!-\!\! 10^{7.5}\right]$, $\left[10^{7.5} \!\!-\!\! 10^{8}\right]$, $\left[10^8 \!\!-\!\! 10^{8.5}\right]$, and $\left[10^{8.5} \!\!-\!\! 10^{9}\right]$ by factors of 1.3, 2.5, 5.6, and 13.1, respectively, for a cold dark matter ground truth. The 95 per cent exclusion limit improves by 0.5 dex in $\log _{10} m_{\rm {hm}}$. The enhanced sensitivity to low-mass haloes enabled by these methods pushes the observational frontier of substructure lensing to the threshold of galaxy formation, enabling stringent tests of any theory that alters the properties of dark matter haloes.

 

This is the second in a series of papers in which we use JWST MIRI multiband imaging to measure the warm dust emission in a sample of 31 multiply imaged quasars, to be used as a probe of the particle nature of dark matter. We present measurements of the relative magnifications of the strongly lensed warm dust emission in a sample of 9 systems. The warm dust region is compact and sensitive to perturbations by populations of halos down to masses ∼106 M⊙. Using these warm dust flux-ratio measurements in combination with 5 previous narrow-line flux-ratio measurements, we constrain the halo mass function. In our model, we allow for complex deflector macromodels with flexible third and fourth-order multipole deviations from ellipticity, and we introduce an improved model of the tidal evolution of subhalos. We constrain a WDM model and find an upper limit on the half-mode mass of 107.6M⊙ at posterior odds of 10:1. This corresponds to a lower limit on a thermally produced dark matter particle mass of 6.1 keV. This is the strongest gravitational lensing constraint to date, and comparable to those from independent probes such as the Lyα forest and Milky Way satellite galaxies. 

Strongly lensed supernovae are rare and valuable probes of cosmology and astrophysics. Upcoming wide-field time-domain surveys, such as the Vera C. Rubin Observatory’s Legacy Survey of Space and Time (LSST), are expected to discover an order-of-magnitude more lensed supernovae than have previously been observed. In this work, we investigate the cosmological prospects of lensed type Ia supernovae (SNIa) in LSST by quantifying the expected annual number of detections, the impact of stellar microlensing, follow-up feasibility, and how to best separate lensed and unlensed SNIa. We simulate SNIa lensed by galaxies, using the current LSST baseline v3.0 cadence, and find an expected number of 44 lensed SNIa detections per year. Microlensing effects by stars in the lensing galaxy are predicted to lower the lensed SNIa detections by ∼8 per cent. The lensed events can be separated from the unlensed ones by jointly considering their colours and peak magnitudes. We define a ‘gold sample’ of ∼10 lensed SNIa per year with time delay >10 d, >5 detections before light curve peak, and sufficiently bright (mi < 22.5 mag) for follow-up observations. In 3 yr of LSST operations, such a sample is expected to yield a 1.5 per cent measurement of the Hubble constant.

 

The mass distribution in massive elliptical galaxies encodes their evolutionary history, thus providing an avenue to constrain the baryonic astrophysics in their evolution. The power-law assumption for the radial mass profile in ellipticals has been sufficient to describe several observables to the noise level, including strong lensing and stellar dynamics. In this paper, we quantitatively constrained any deviation, or the lack thereof, from the power-law mass profile in massive ellipticals through joint lensing–dynamics analysis of a large statistical sample with 77 galaxy–galaxy lens systems. We performed an improved and uniform lens modelling of these systems from archival Hubble Space Telescope imaging using the automated lens modelling pipeline dolphin. We combined the lens model posteriors with the stellar dynamics to constrain the deviation from the power law after accounting for the line-of-sight lensing effects, a first for analyses on galaxy–galaxy lenses. We find that the Sloan Lens ACS Survey lens galaxies with a mean redshift of 0.2 are consistent with the power-law profile within 1.1σ (2.8σ) and the Strong Lensing Legacy Survey lens galaxies with a mean redshift of 0.6 are consistent within 0.8σ (2.1σ), for a spatially constant (Osipkov–Merritt) stellar anisotropy profile. We adopted the spatially constant anisotropy profile as our baseline choice based on previous dynamical observables of local ellipticals. However, spatially resolved stellar kinematics of lens galaxies are necessary to differentiate between the two anisotropy models. Future studies will use our lens models to constrain the mass distribution individually in the dark matter and baryonic components.

 

One of the frontiers for advancing what is known about dark matter lies in using strong gravitational lenses to characterize the population of the smallest dark matter haloes. There is a large volume of information in strong gravitational lens images – the question we seek to answer is to what extent we can refine this information. To this end, we forecast the detectability of a mixed warm and cold dark matter scenario using the anomalous flux ratio method from strong gravitational lensed images. The halo mass function of the mixed dark matter scenario is suppressed relative to cold dark matter but still predicts numerous low-mass dark matter haloes relative to warm dark matter. Since the strong lensing signal receives a contribution from a range of dark matter halo masses and since the signal is sensitive to the specific configuration of dark matter haloes, not just the halo mass function, degeneracies between different forms of suppression in the halo mass function, relative to cold dark matter, can arise. We find that, with a set of lenses with different configurations of the main deflector and hence different sensitivities to different mass ranges of the halo mass function, the different forms of suppression of the halo mass function between the warm dark matter model and the mixed dark matter model can be distinguished with 40 lenses with Bayesian odds of 30:1.

 

We present JWST and Atacama Large Millimeter/submillimeter Array (ALMA) imaging for the lensing system SPT0418−47, which includes a strongly lensed, dusty, star-forming galaxy at redshiftz= 4.225 and an associated multiply imaged companion. The JWST NIRCam and MIRI imaging observations presented in this paper were acquired as part of the Early Release Science program Targeting Extremely Magnified Panchromatic Lensed Arcs and Their Extended Star formation (TEMPLATES). This data set provides robust mutiwavelength detections of stellar light in both the main (SPT0418A) and companion (SPT0418B) galaxies, while the ALMA detection of [Cii] emission confirms that SPT0418B lies at the same redshift as SPT0418A. We infer that the projected physical separation of the two galaxies is 4.42 ± 0.05 kpc. We derive total magnifications ofμ= 29 ± 1 andμ= 4.1 ± 0.7 for SPT0418A and SPT0418B, respectively. We use bothprospectorandcigaleto derive stellar masses. We find that SPT0418A has a stellar mass of$M_{*}={3.4}_{-0.6}^{+1.1}\times {10}^{10}{M}_{\odot }$fromprospector orM_*= 1.5 ± 0.3 × 10¹⁰M_⊙fromcigale. The stellar mass ratio of SPT0418A and SPT0418B is roughly between 4 and 7 (${4.2}_{-1.6}^{+1.9}$forprospectorand 7.5 ± 3.7 forcigale). We see evidence of extended structure associated with SPT0418A that is suggestive of a tidal feature. These features, along with the close projected proximity, imply that the system is interacting. Interestingly, the star formation rates and stellar masses of both galaxies are consistent with the main sequence of star-forming galaxies at this epoch, indicating that this ongoing interaction has not noticeably elevated the star formation levels.

 

Strong-lensing time delays enable the measurement of the Hubble constant ( H 0 ) independently of other traditional methods. The main limitation to the precision of time-delay cosmography is mass-sheet degeneracy (MSD). Some of the previous TDCOSMO analyses broke the MSD by making standard assumptions about the mass density profile of the lens galaxy, reaching 2% precision from seven lenses. However, this approach could potentially bias the H 0 measurement or underestimate the errors. For this work, we broke the MSD for the first time using spatially resolved kinematics of the lens galaxy in RXJ1131−1231 obtained from the Keck Cosmic Web Imager spectroscopy, in combination with previously published time delay and lens models derived from Hubble Space Telescope imaging. This approach allowed us to robustly estimate H 0 , effectively implementing a maximally flexible mass model. Following a blind analysis, we estimated the angular diameter distance to the lens galaxy D d  = 865 −81 +85 Mpc and the time-delay distance D Δt  = 2180 −271 +472 Mpc, giving H 0  = 77.1 −7.1 +7.3 km s −1 Mpc −1 – for a flat Λ cold dark matter cosmology. The error budget accounts for all uncertainties, including the MSD inherent to the lens mass profile and line-of-sight effects, and those related to the mass–anisotropy degeneracy and projection effects. Our new measurement is in excellent agreement with those obtained in the past using standard simply parametrized mass profiles for this single system ( H 0  = 78.3 −3.3 +3.4 km s −1 Mpc −1 ) and for seven lenses ( H 0  = 74.2 −1.6 +1.6 km s −1 Mpc −1 ), or for seven lenses using single-aperture kinematics and the same maximally flexible models used by us ( H 0  = 73.3 −5.8 +5.8 km s −1 Mpc −1 ). This agreement corroborates the methodology of time-delay cosmography. 

Constraining the distribution of small-scale structure in our universe allows us to probe alternatives to the cold dark matter paradigm. Strong gravitational lensing offers a unique window into small dark matter halos (<10¹⁰M_⊙) because these halos impart a gravitational lensing signal even if they do not host luminous galaxies. We create large data sets of strong lensing images with realistic low-mass halos, Hubble Space Telescope (HST) observational effects, and galaxy light from HST’s COSMOS field. Using a simulation-based inference pipeline, we train a neural posterior estimator of the subhalo mass function (SHMF) and place constraints on populations of lenses generated using a separate set of galaxy sources. We find that by combining our network with a hierarchical inference framework, we can both reliably infer the SHMF across a variety of configurations and scale efficiently to populations with hundreds of lenses. By conducting precise inference on large and complex simulated data sets, our method lays a foundation for extracting dark matter constraints from the next generation of wide-field optical imaging surveys.