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arxiv: 2605.05318 · v1 · submitted 2026-05-06 · 🌌 astro-ph.IM · astro-ph.CO· astro-ph.GA· astro-ph.HE

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HOLISMOKES XXI: Detecting strongly lensed type Ia supernovae from time series of multi-band LSST-like imaging data -- Part II

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Pith reviewed 2026-05-08 16:19 UTC · model grok-4.3

classification 🌌 astro-ph.IM astro-ph.COastro-ph.GAastro-ph.HE
keywords strongly lensed supernovaeType Ia supernovaeLSSTdeep learningtime seriesgravitational lensingtransient detectionimage classification
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The pith

A deep learning model using convolutional LSTM detects strongly lensed Type Ia supernovae from realistic multi-band time-series images, achieving approximately 60 percent true-positive rate at a false-positive rate of order 10 to the minus

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper extends a previous deep-learning approach for finding rare strongly lensed supernovae Ia in upcoming LSST data. It tests the model on more realistic simulations that include varying point-spread functions between epochs, variance corrections, and supernovae occurring in the foreground lens galaxy as contaminants. The core result is that the classifier still performs well, updating its classification as new observations arrive. Sympathetic readers would care because prompt detection is needed to trigger expensive follow-up observations that can measure time delays and study the lens system. The work shows the method is robust enough to handle real survey conditions.

Core claim

We extend the previous convolutional LSTM framework by constructing realistic image time series from HSC PDR3 observations, introducing epoch-to-epoch PSF variations with variance-map corrections, simulated lensed arcs, SN light-curve variations, Poisson noise, and foreground SN Ia contaminants. Despite these additions, the model reaches a true-positive rate of ~60% at a false-positive rate of O(10^{-4}) by the seventh observation and ~80% by the tenth. We also examine confusion with sibling SNe in LRGs and identify mimicking configurations.

What carries the argument

The convolutional LSTM architecture that processes multi-band, multi-epoch image cutouts to capture spatiotemporal correlations and update classifications with each new observation.

If this is right

  • The classifier supports real-time LSN searches in LSST alert streams.
  • Detection performance improves rapidly with additional epochs of observation.
  • Foreground lens-galaxy supernovae form an important false-positive class that must be distinguished.
  • Specific configurations of sibling supernovae can be used to improve model robustness.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The robustness suggests the model is ready for deployment on early LSST data without extensive additional tuning.
  • Similar time-series approaches could be tested for detecting other lensed transients such as core-collapse supernovae or quasars.
  • If the low false-positive rate holds on real data, it would greatly reduce the resources needed for spectroscopic follow-up of candidates.

Load-bearing premise

The HSC PDR3-based simulations with injected lensed arcs, SN light-curve variations, Poisson noise, and PSF variations sufficiently capture the statistical properties of real LSST observations and all relevant false-positive classes.

What would settle it

Comparing the model's receiver operating characteristic curves on actual LSST observations against the simulated performance curves would confirm or refute the reported true-positive and false-positive rates.

Figures

Figures reproduced from arXiv: 2605.05318 by Alejandra Melo, Irham Taufik Andika, Ming Kei Chan, Raoul Canameras, Satadru Bag, Sherry H. Suyu, Stefan Schuldt, Stefan Taubenberger.

Figure 1
Figure 1. Figure 1: Two representative examples of LSNe Ia are shown in the two rows using view at source ↗
Figure 2
Figure 2. Figure 2: Time series of LSNe Ia illustrating the effect of varying PSF conditions across epochs. Three representative view at source ↗
Figure 3
Figure 3. Figure 3: Two examples of SN Ia occurring in the foreground lens galaxy of a lensing system, representing the “SN in lenses” view at source ↗
Figure 4
Figure 4. Figure 4: Receiver operating characteristic (ROC) curves for the multi-band classification results obtained from 14 observa view at source ↗
Figure 5
Figure 5. Figure 5: Each panel shows FPR as a function of score threshold separately for different negative components. The four view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of model-predicted score distributions within the positive LSNe Ia class, split into systems with view at source ↗
Figure 7
Figure 7. Figure 7: Distribution of model-predicted scores for LSNe Ia divided into three bins of offset between the SN and the host view at source ↗
Figure 8
Figure 8. Figure 8: ROC curves comparing classification performance view at source ↗
read the original abstract

Strong gravitationally lensed supernovae (LSNe) are rare but extremely valuable probes of cosmology and astrophysics. Prompt identification within the alert streams of time-domain surveys such as the Rubin Legacy Survey of Space and Time (LSST) is essential for timely follow-up observations. In our previous study, Bag et al. (2026), we introduced a deep-learning framework for detecting LSNe Ia directly from multi-band, multi-epoch image cutouts. The model employs a convolutional LSTM architecture to capture spatiotemporal correlations in time-series imaging data, enabling classification updates as new observations arrive. In this work, we extend that framework by incorporating greater realism into the simulations. In particular, we present a method to construct realistic image time series from single-epoch observations by introducing epoch-to-epoch point spread function variations with corresponding variance-map corrections. The dataset is based on HSC PDR3 observations and includes simulated lensed host-galaxy arcs, SN light-curve variations, and Poisson noise. We also introduce an additional negative class consisting of SN Ia occurring in the foreground lens galaxy, representing a challenging source of false positives. Despite these additional complexities, the model retains strong performance. The receiver operating characteristic improves rapidly during the first few observations, reaching a true-positive rate of $\sim60\%$ at a false-positive rate of $\mathcal{O}(10^{-4})$ by the seventh observation and $\sim80\%$ by the tenth. We also investigate potential confusion with sibling SNe occurring in LRGs and identify the configurations that best mimic lensed systems. These results demonstrate that the image-time-series approach remains robust under more realistic observing conditions, and is well suited for real-time LSN searches in LSST and other time-domain surveys.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. This paper extends a prior convolutional LSTM framework for detecting strongly lensed Type Ia supernovae (LSNe Ia) from multi-band, multi-epoch image cutouts. It adds realism to HSC PDR3-based simulations by introducing epoch-to-epoch PSF variations with variance-map corrections, Poisson noise, simulated lensed host arcs, SN light-curve variations, and an extra negative class of foreground SN Ia in the lens galaxy. Despite these complexities, the model shows rapid improvement in ROC performance, reaching a true-positive rate of ~60% at a false-positive rate of O(10^{-4}) by the seventh observation and ~80% by the tenth, with additional analysis of confusion from sibling SNe in LRGs. The work concludes that the approach is robust and suitable for real-time LSST searches.

Significance. If the simulations prove representative, the results provide concrete evidence that a spatiotemporal deep-learning classifier can maintain useful detection efficiency under realistic multi-epoch conditions, which is valuable for prompt follow-up of rare LSNe Ia in LSST alert streams. The explicit addition of PSF variations, variance corrections, and a challenging foreground contaminant class strengthens the practical relevance beyond the earlier study.

major comments (1)
  1. [Abstract and dataset construction] The central performance claim (TPR ~60% at FPR O(10^{-4}) by epoch 7, ~80% by epoch 10) is obtained exclusively on a test set constructed from HSC PDR3 single-epoch images with added epoch-to-epoch PSF variations, variance-map corrections, Poisson noise, injected lensed arcs, SN light-curve variations, and foreground SN Ia contaminants. This construction implicitly assumes that the resulting statistical properties match those of real LSST difference imaging; unmodeled effects such as correlated read noise, filter-dependent depth variations, or additional variable-source classes (AGN, stellar flares) could alter the decision boundary. Because this assumption is load-bearing for the claim that the method is 'well suited for real-time LSN searches in LSST', a quantitative sensitivity test or direct comparison against more comprehensive LSST mocks is required.
minor comments (2)
  1. [Abstract] The abstract employs both ~ and mathcal{O} notation; ensure identical usage and explicit definitions appear in the main text and figure captions.
  2. [Methods] A table listing the exact simulation parameters (PSF variation model, noise levels, number of injected arcs, etc.) would improve reproducibility.

Simulated Author's Rebuttal

1 responses · 1 unresolved

We thank the referee for their careful and constructive review of our manuscript. The concern about the degree of realism in our simulations relative to full LSST difference imaging is valid, and we have revised the text to acknowledge limitations while preserving the core results.

read point-by-point responses
  1. Referee: The central performance claim (TPR ~60% at FPR O(10^{-4}) by epoch 7, ~80% by epoch 10) is obtained exclusively on a test set constructed from HSC PDR3 single-epoch images with added epoch-to-epoch PSF variations, variance-map corrections, Poisson noise, injected lensed arcs, SN light-curve variations, and foreground SN Ia contaminants. This construction implicitly assumes that the resulting statistical properties match those of real LSST difference imaging; unmodeled effects such as correlated read noise, filter-dependent depth variations, or additional variable-source classes (AGN, stellar flares) could alter the decision boundary. Because this assumption is load-bearing for the claim that the method is 'well suited for real-time LSN searches in LSST', a quantitative sensitivity test or direct comparison against more comprehensive LSST mocks is required.

    Authors: We agree that our simulations, although they incorporate PSF variations, variance-map corrections, Poisson noise, lensed host arcs, SN light-curve variations, and foreground SN Ia contaminants, do not capture every possible effect present in real LSST difference imaging. Unmodeled contributions such as correlated read noise, filter-dependent depth variations, and additional variable-source classes (e.g., AGN or stellar flares) could in principle shift the decision boundary. In the revised manuscript we have added a new subsection (Section 5.3) that explicitly discusses these limitations and qualitatively assesses their likely impact on classifier performance. We have also revised the abstract and concluding paragraph to replace the phrase 'well suited for real-time LSN searches in LSST' with the more cautious statement that the approach 'shows promise under LSST-like conditions and merits further validation with more complete simulations.' A quantitative sensitivity test or direct comparison against comprehensive LSST mocks would require generation or access to substantially more advanced mock datasets and is outside the scope of the present study; such work is planned for a follow-up investigation. revision: partial

standing simulated objections not resolved
  • Quantitative sensitivity tests to unmodeled effects (correlated read noise, AGN, stellar flares, filter-dependent depth variations) or direct comparison against full LSST mocks cannot be performed within the current revision.

Circularity Check

0 steps flagged

Minor self-citation to prior architecture paper; new performance metrics computed on independently generated simulations with added realism

full rationale

The paper cites Bag et al. (2026) only to introduce the convolutional LSTM framework and then evaluates an extended version on a fresh set of HSC PDR3-based simulations that inject epoch-to-epoch PSF variations, variance-map corrections, Poisson noise, lensed arcs, SN light-curve variations, and foreground SN Ia contaminants. The reported TPR/FPR values (∼60 % at O(10^{-4}) by epoch 7, ∼80 % by epoch 10) are measured directly on this new test set and do not reduce to any fitted parameter or self-cited equation by construction. No self-definitional loops, fitted-input-as-prediction, or load-bearing uniqueness theorems appear in the derivation chain. The self-citation is therefore non-load-bearing and the overall circularity remains minimal.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central performance claims rest on the assumption that the HSC-based simulation pipeline faithfully reproduces LSST observing conditions and that the chosen negative class covers the dominant false-positive sources; the model itself contains many learned parameters whose values are determined by training on these simulations.

free parameters (2)
  • convLSTM architecture hyperparameters
    Network depth, filter sizes, learning rate, and training schedule are chosen and optimized on the simulated training set.
  • PSF variation model parameters
    Parameters controlling epoch-to-epoch PSF changes and variance-map corrections are introduced to match HSC data properties.
axioms (1)
  • domain assumption HSC PDR3 single-epoch images plus injected lensed arcs and SN light curves plus Poisson noise plus PSF variations statistically match future LSST observations
    All reported detection rates are measured on data generated under this assumption.

pith-pipeline@v0.9.0 · 5673 in / 1487 out tokens · 33664 ms · 2026-05-08T16:19:46.757886+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

200 extracted references · 185 canonical work pages · 4 internal anchors

  1. [1]

    HOLISMOKES. IX. Neural network inference of strong-lens parameters and uncertainties from ground-based images. , keywords =. doi:10.1051/0004-6361/202244325 , archivePrefix =. 2206.11279 , primaryClass =

  2. [2]

    HOLISMOKES. I. Highly Optimised Lensing Investigations of Supernovae, Microlensing Objects, and Kinematics of Ellipticals and Spirals. , keywords =. doi:10.1051/0004-6361/202037757 , archivePrefix =. 2002.08378 , primaryClass =

  3. [3]

    , keywords =

    A targeted search for strongly lensed supernovae with the Las Cumbres Observatory. , keywords =. doi:10.1093/mnras/stae2103 , archivePrefix =. 2111.01680 , primaryClass =

  4. [4]

    2007, ApJS, 172, 1, doi: 10.1086/516585

    The Cosmic Evolution Survey (COSMOS): Overview. , keywords =. doi:10.1086/516585 , archivePrefix =. astro-ph/0612305 , primaryClass =

  5. [5]

    S., Aguilar, G., et al

    The Fourteenth Data Release of the Sloan Digital Sky Survey: First Spectroscopic Data from the Extended Baryon Oscillation Spectroscopic Survey and from the Second Phase of the Apache Point Observatory Galactic Evolution Experiment. , keywords =. doi:10.3847/1538-4365/aa9e8a , archivePrefix =. 1707.09322 , primaryClass =

  6. [6]

    , year = 2018, month =

    The SDSS-IV Extended Baryon Oscillation Spectroscopic Survey: Baryon Acoustic Oscillations at Redshift of 0.72 with the DR14 Luminous Red Galaxy Sample. , keywords =. doi:10.3847/1538-4357/aacea5 , archivePrefix =. 1712.08064 , primaryClass =

  7. [7]

    , keywords =

    Lensed quasar search via time variability with the HSC transient survey. , keywords =. doi:10.1051/0004-6361/201936806 , archivePrefix =. 1910.01140 , primaryClass =

  8. [8]

    , keywords =

    Strongly lensed candidates from the HSC transient survey. , keywords =. doi:10.1051/0004-6361/202039376 , archivePrefix =. 2009.07854 , primaryClass =

  9. [9]

    Publications of the Astronomical Society of the Pacific , author =

    Cosmic-Ray Rejection by Laplacian Edge Detection. , keywords =. doi:10.1086/323894 , archivePrefix =. astro-ph/0108003 , primaryClass =

  10. [10]

    , keywords =

    Second data release of the Hyper Suprime-Cam Subaru Strategic Program. , keywords =. doi:10.1093/pasj/psz103 , archivePrefix =. 1905.12221 , primaryClass =

  11. [11]

    2014, ARA&A, 52, 107, https://doi.org/10.1146/annurev-astro-082812-141031

    Observational Clues to the Progenitors of Type Ia Supernovae. , keywords =. doi:10.1146/annurev-astro-082812-141031 , archivePrefix =. 1312.0628 , primaryClass =

  12. [12]

    2018, PASJ, 70, S4, doi: 10.1093/pasj/psx066

    The Hyper Suprime-Cam SSP Survey: Overview and survey design. , keywords =. doi:10.1093/pasj/psx066 , archivePrefix =. 1704.05858 , primaryClass =

  13. [13]

    The Subaru/XMM-Newton Deep Survey (SXDS). II. Optical Imaging and Photometric Catalogs. , keywords =. doi:10.1086/527321 , archivePrefix =. 0801.4017 , primaryClass =

  14. [15]

    Planck 2015 results. XIII. Cosmological parameters. , archivePrefix = "arXiv", eprint =. doi:10.1051/0004-6361/201525830 , adsurl =

  15. [16]

    Strong-lens candidates at all mass scales and their environments from the Hyper-Suprime Cam and deep learning

    HOLISMOKES: XIII. Strong-lens candidates at all mass scales and their environments from the Hyper-Suprime Cam and deep learning. , keywords =. doi:10.1051/0004-6361/202450927 , archivePrefix =. 2405.20383 , primaryClass =

  16. [17]

    , keywords =

    The Hyper Suprime-Cam SSP transient survey in COSMOS: Overview. , keywords =. doi:10.1093/pasj/psz050 , archivePrefix =. 1904.09697 , primaryClass =

  17. [18]

    2022, MNRAS, 509, 3966, doi: 10.1093/mnras/stab2093

    Galaxy Zoo DECaLS: Detailed visual morphology measurements from volunteers and deep learning for 314 000 galaxies. , keywords =. doi:10.1093/mnras/stab2093 , archivePrefix =. 2102.08414 , primaryClass =

  18. [19]

    2023, MNRAS, 526, 4768, doi: 10.1093/mnras/stad2919 38Pfeifle et al

    Galaxy Zoo DESI: Detailed morphology measurements for 8.7M galaxies in the DESI Legacy Imaging Surveys. , keywords =. doi:10.1093/mnras/stad2919 , archivePrefix =. 2309.11425 , primaryClass =

  19. [20]

    , keywords =

    The Hubble Ultra Deep Field. , keywords =. doi:10.1086/507302 , archivePrefix =. astro-ph/0607632 , primaryClass =

  20. [21]

    The MUSE Hubble Ultra Deep Field Survey. II. Spectroscopic redshifts and comparisons to color selections of high-redshift galaxies. , keywords =. doi:10.1051/0004-6361/201731195 , archivePrefix =. 1710.03773 , primaryClass =

  21. [22]

    HOLISMOKES. IV. Efficient mass modeling of strong lenses through deep learning. , keywords =. doi:10.1051/0004-6361/202039574 , archivePrefix =. 2010.00602 , primaryClass =

  22. [23]

    HOLISMOKES. VI. New galaxy-scale strong lens candidates from the HSC-SSP imaging survey. , keywords =. doi:10.1051/0004-6361/202141758 , archivePrefix =. 2107.07829 , primaryClass =

  23. [24]

    Evaluation of supervised neural networks for strong-lens searches in ground-based imaging surveys

    HOLISMOKES: XI. Evaluation of supervised neural networks for strong-lens searches in ground-based imaging surveys. , keywords =. doi:10.1051/0004-6361/202347072 , archivePrefix =. 2306.03136 , primaryClass =

  24. [25]

    HOLISMOKES. II. Identifying galaxy-scale strong gravitational lenses in Pan-STARRS using convolutional neural networks. , keywords =. doi:10.1051/0004-6361/202038219 , archivePrefix =. 2004.13048 , primaryClass =

  25. [26]

    , keywords =

    The strong gravitational lens finding challenge. , keywords =. doi:10.1051/0004-6361/201832797 , archivePrefix =. 1802.03609 , primaryClass =

  26. [27]

    , keywords =

    An Extended Catalog of Galaxy-Galaxy Strong Gravitational Lenses Discovered in DES Using Convolutional Neural Networks. , keywords =. doi:10.3847/1538-4365/ab26b6 , archivePrefix =. 1905.10522 , primaryClass =

  27. [28]

    , keywords =

    Finding strong gravitational lenses in the Kilo Degree Survey with Convolutional Neural Networks. , keywords =. doi:10.1093/mnras/stx2052 , archivePrefix =. 1702.07675 , primaryClass =

  28. [29]

    , keywords =

    Prediction of Supernova Rates in Known Galaxy-Galaxy Strong-lens Systems. , keywords =. doi:10.3847/1538-4357/aad5ea , archivePrefix =. 1803.07569 , primaryClass =

  29. [30]

    arXiv e-prints , keywords =

    Detectability and Characterisation of Strongly Lensed Supernova Lightcurves in the Zwicky Transient Facility. arXiv e-prints , keywords =. doi:10.48550/arXiv.2406.00052 , archivePrefix =. 2406.00052 , primaryClass =

  30. [31]

    , keywords =

    Rates and Properties of Supernovae Strongly Gravitationally Lensed by Elliptical Galaxies in Time-domain Imaging Surveys. , keywords =. doi:10.3847/1538-4365/ab1fe0 , archivePrefix =. 1809.10147 , primaryClass =

  31. [32]

    Ivezi ´c, S

    LSST: From Science Drivers to Reference Design and Anticipated Data Products. , keywords =. doi:10.3847/1538-4357/ab042c , archivePrefix =. 0805.2366 , primaryClass =

  32. [33]

    TDCOSMO. I. An exploration of systematic uncertainties in the inference of H _ 0 from time-delay cosmography. , keywords =. doi:10.1051/0004-6361/201937351 , archivePrefix =. 1912.08027 , primaryClass =

  33. [34]

    , keywords =

    STRIDES: a 3.9 per cent measurement of the Hubble constant from the strong lens system DES J0408-5354. , keywords =. doi:10.1093/mnras/staa828 , archivePrefix =. 1910.06306 , primaryClass =

  34. [35]

    Cosmology Intertwined: A Review of the Particle Physics, Astrophysics, and Cosmology Associated with the Cosmological Tensions and Anomalies

    Cosmology intertwined: A review of the particle physics, astrophysics, and cosmology associated with the cosmological tensions and anomalies. Journal of High Energy Astrophysics , keywords =. doi:10.1016/j.jheap.2022.04.002 , archivePrefix =. 2203.06142 , primaryClass =

  35. [36]

    Statistical strong lensing. II. Cosmology and galaxy structure with time-delay lenses. , keywords =. doi:10.1051/0004-6361/202142062 , archivePrefix =. 2109.00009 , primaryClass =

  36. [38]

    , keywords =

    2237+0305 : a new and unusual gravitational lens. , keywords =. doi:10.1086/113777 , adsurl =

  37. [40]

    TDCOSMO. IV. Hierarchical time-delay cosmography - joint inference of the Hubble constant and galaxy density profiles. , keywords =. doi:10.1051/0004-6361/202038861 , archivePrefix =. 2007.02941 , primaryClass =

  38. [41]

    2003, MNRAS, 340, 1214, doi: 10.1046/j.1365-8711.2003.06380.x

    The Cosmic Lens All-Sky Survey - II. Gravitational lens candidate selection and follow-up. , keywords =. doi:10.1046/j.1365-8711.2003.06257.x , archivePrefix =. astro-ph/0211069 , primaryClass =

  39. [42]

    Overview and classification of candidates selected by two techniques

    The STRong lensing Insights into the Dark Energy Survey (STRIDES) 2016 follow-up campaign - I. Overview and classification of candidates selected by two techniques. , keywords =. doi:10.1093/mnras/sty2329 , archivePrefix =. 1808.04838 , primaryClass =

  40. [43]

    W., McMahon, R., et al

    The STRong lensing Insights into the Dark Energy Survey (STRIDES) 2017/2018 follow-up campaign: discovery of 10 lensed quasars and 10 quasar pairs. , keywords =. doi:10.1093/mnras/staa652 , archivePrefix =. 1912.09133 , primaryClass =

  41. [44]

    COSMOGRAIL. XVII. Time delays for the quadruply imaged quasar PG 1115+080. , keywords =. doi:10.1051/0004-6361/201833287 , archivePrefix =. 1804.09183 , primaryClass =

  42. [45]

    , keywords =

    Deconvolution with Correct Sampling. , keywords =. doi:10.1086/305187 , archivePrefix =. astro-ph/9704059 , primaryClass =

  43. [46]

    J., Lucas, P

    Gravitationally lensed quasars and supernovae in future wide-field optical imaging surveys. , keywords =. doi:10.1111/j.1365-2966.2010.16639.x , archivePrefix =. 1001.2037 , primaryClass =

  44. [47]

    2019, Reports on Progress in Physics, 82, 126901, doi: 10.1088/1361-6633/ab4fc5

    Strong gravitational lensing of explosive transients. Reports on Progress in Physics , keywords =. doi:10.1088/1361-6633/ab4fc5 , archivePrefix =. 1907.06830 , primaryClass =

  45. [48]

    Nature Communications , keywords =

    Strongly lensed repeating fast radio bursts as precision probes of the universe. Nature Communications , keywords =. doi:10.1038/s41467-018-06303-0 , archivePrefix =. 1708.06357 , primaryClass =

  46. [49]

    Nature Communications , keywords =

    Precision cosmology from future lensed gravitational wave and electromagnetic signals. Nature Communications , keywords =. doi:10.1038/s41467-017-01152-9 , archivePrefix =. 1703.04151 , primaryClass =

  47. [50]

    G., Yuan, W., Macri, L

    Riess, Adam G. and others. A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s ^ −1 Mpc ^ −1 Uncertainty from the Hubble Space Telescope and the SH0ES Team. Astrophys. J. Lett. 2022. doi:10.3847/2041-8213/ac5c5b. arXiv:2112.04510

  48. [51]

    , keywords =

    Time delay cosmography. , keywords =. doi:10.1007/s00159-016-0096-8 , archivePrefix =. 1605.05333 , primaryClass =

  49. [52]

    2010, ARA&A, 48, 87, doi: 10.1146/annurev-astro-081309-130924

    Strong Lensing by Galaxies. , keywords =. doi:10.1146/annurev-astro-081309-130924 , archivePrefix =. 1003.5567 , primaryClass =

  50. [53]

    , keywords =

    Discovering Gravitational Lenses through Measurements of Their Time Delays. , keywords =. doi:10.1086/430048 , archivePrefix =. astro-ph/0501518 , primaryClass =

  51. [54]

    Crossing Statistic: Reconstructing the Expansion History of the Universe

    Shafieloo, Arman. Crossing Statistic: Reconstructing the Expansion History of the Universe. JCAP. 2012. doi:10.1088/1475-7516/2012/08/002. arXiv:1204.1109

  52. [55]

    Fast and Reliable Time Delay Estimation of Strong Lens Systems Using the Smoothing and Cross-correlation Methods

    Aghamousa, Amir and Shafieloo, Arman. Fast and Reliable Time Delay Estimation of Strong Lens Systems Using the Smoothing and Cross-correlation Methods. Astrophys. J. 2015. doi:10.1088/0004-637X/804/1/39. arXiv:1410.8122

  53. [56]

    Gallazzi, S

    Shafieloo, Arman and Alam, Ujjaini and Sahni, Varun and Starobinsky, Alexei A. Smoothing Supernova Data to Reconstruct the Expansion History of the Universe and its Age. Mon. Not. Roy. Astron. Soc. 2006. doi:10.1111/j.1365-2966.2005.09911.x. arXiv:astro-ph/0505329

  54. [57]

    J., Almaini, O., et al

    Shafieloo, Arman. Model Independent Reconstruction of the Expansion History of the Universe and the Properties of Dark Energy. Mon. Not. Roy. Astron. Soc. 2007. doi:10.1111/j.1365-2966.2007.12175.x. arXiv:astro-ph/0703034

  55. [58]

    Shafieloo and C

    Shafieloo, Arman and Clarkson, Chris. Model independent tests of the standard cosmological model. Phys. Rev. D. 2010. doi:10.1103/PhysRevD.81.083537. arXiv:0911.4858

  56. [59]

    and Linder, Eric V

    Bag, Satadru and Kim, Alex G. and Linder, Eric V. and Shafieloo, Arman. Be It Unresolved: Measuring Time Delays from Lensed Supernovae. Astrophys. J. 2021. doi:10.3847/1538-4357/abe238. arXiv:2010.03774

  57. [60]

    , keywords =

    Discovering strongly lensed QSOs from unresolved light curves. , keywords =. doi:10.1093/mnras/stab241 , archivePrefix =. 2011.04667 , primaryClass =

  58. [61]

    , keywords =

    The light-curve reconstruction method for measuring the time delay of gravitational lens systems. , keywords =. doi:10.1093/mnras/282.2.530 , archivePrefix =. astro-ph/9601164 , primaryClass =

  59. [62]

    Using a flux time series that is a linear combination of time-shifted light curves

    Measuring time delays - I. Using a flux time series that is a linear combination of time-shifted light curves. , keywords =. doi:10.1093/mnras/stab1600 , archivePrefix =. 2101.11017 , primaryClass =

  60. [63]

    Using observations of the unresolved flux and astrometry

    Measuring time delays - II. Using observations of the unresolved flux and astrometry. , keywords =. doi:10.1093/mnras/stab2432 , archivePrefix =. 2101.11024 , primaryClass =

  61. [66]

    Strong Lens Time Delay Challenge: II

    Liao, Kai and others. Strong Lens Time Delay Challenge: II. Results of TDC1. Astrophys. J. 2015. doi:10.1088/0004-637X/800/1/11. arXiv:1409.1254

  62. [67]

    2020a, Astron

    Aghanim, N. and others. Planck 2018 results. VI. Cosmological parameters. Astron. Astrophys. 2020. doi:10.1051/0004-6361/201833910. arXiv:1807.06209

  63. [68]

    Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics Beyond LambdaCDM

    Riess, Adam G. and Casertano, Stefano and Yuan, Wenlong and Macri, Lucas M. and Scolnic, Dan. Large Magellanic Cloud Cepheid Standards Provide a 1\. Astrophys. J. 2019. doi:10.3847/1538-4357/ab1422. arXiv:1903.07603

  64. [69]

    A 2.4 per cent measurement of H _ 0 from lensed quasars: 5.3 tension between early- and late-Universe probes

    Wong, Kenneth C. and others. H0LiCOW XIII. A 2.4 per cent measurement of H0 from lensed quasars: 5.3 tension between early- and late-Universe probes. Mon. Not. Roy. Astron. Soc. 2020. doi:10.1093/mnras/stz3094. arXiv:1907.04869

  65. [70]

    , title = "

    Refsdal, Sjur and Bondi, H. , title = ". Monthly Notices of the Royal Astronomical Society , volume =. 1964 , month =. doi:10.1093/mnras/128.4.295 , url =

  66. [71]

    , year = 1964, month = jan, volume =

    Refsdal, Sjur , title = ". Monthly Notices of the Royal Astronomical Society , volume =. 1964 , month =. doi:10.1093/mnras/128.4.307 , url =

  67. [72]

    , keywords =

    The Hubble Time Inferred from 10 Time Delay Lenses. , keywords =. doi:10.1086/507583 , archivePrefix =. astro-ph/0607240 , primaryClass =

  68. [73]

    doi:10.1086/513093 , url =

    Masamune Oguri , title =. doi:10.1086/513093 , url =

  69. [74]

    and Courbin, F

    H0LiCOW - V. New COSMOGRAIL time delays of HE 0435-1223: H _ 0 to 3.8 per cent precision from strong lensing in a flat CDM model. , keywords =. doi:10.1093/mnras/stw3006 , archivePrefix =. 1607.01790 , primaryClass =

  70. [75]

    TDCOSMO. V. Strategies for precise and accurate measurements of the Hubble constant with strong lensing. , keywords =. doi:10.1051/0004-6361/202039179 , archivePrefix =. 2008.06157 , primaryClass =

  71. [76]

    MNRAS , author =

    Mao, Shu-de and Schneider, Peter. Evidence for substructure in lens galaxies?. Mon. Not. Roy. Astron. Soc. 1998. doi:10.1046/j.1365-8711.1998.01319.x. arXiv:astro-ph/9707187

  72. [77]

    Benton and Madau, Piero

    Metcalf, R. Benton and Madau, Piero. Compound gravitational lensing as a probe of dark matter substructure within galaxy halos. Astrophys. J. 2001. doi:10.1086/323695. arXiv:astro-ph/0108224

  73. [78]

    , keywords =

    Direct Detection of Cold Dark Matter Substructure. , keywords =. doi:10.1086/340303 , archivePrefix =. astro-ph/0111456 , primaryClass =

  74. [79]

    Pooley and S

    D. Pooley and S. Rappaport and J. Blackburne and P. L. Schechter and J. Schwab and J. Wambsganss , title =. The Astrophysical Journal , abstract =. doi:10.1088/0004-637x/697/2/1892 , url =

  75. [80]

    and Falco, Emilio E

    Oguri, Masamune and Rusu, Cristian E. and Falco, Emilio E. , title = ". Monthly Notices of the Royal Astronomical Society , volume =. 2014 , month =. doi:10.1093/mnras/stu106 , url =

  76. [81]

    C. Y. Peng and C. D. Impey and E. E. Falco and C. S. Kochanek and J. Lehar and B. A. McLeod and H.-W. Rix and C. R. Keeton and J. A. Munoz , title =. The Astrophysical Journal , abstract =. doi:10.1086/307860 , url =

  77. [82]

    , keywords =

    Mortlock, Daniel J. and Webster, Rachel L. and Francis, Paul J. , title = ". Monthly Notices of the Royal Astronomical Society , volume =. 1999 , month =. doi:10.1046/j.1365-8711.1999.02872.x , url =

  78. [83]

    J. Jim. The Initial Mass Function of Lens Galaxies from Quasar Microlensing , journal =. doi:10.3847/1538-4357/ab46b8 , url =

  79. [84]

    L., Rodney, S

    Kelly, Patrick L. and others. Multiple Images of a Highly Magnified Supernova Formed by an Early-Type Cluster Galaxy Lens. Science. 2015. doi:10.1126/science.aaa3350. arXiv:1411.6009

  80. [85]

    R., et al

    Goobar, A. and others. iPTF16geu: A multiply imaged, gravitationally lensed type Ia supernova. Science. 2017. doi:10.1126/science.aal2729. arXiv:1611.00014

Showing first 80 references.