pith. sign in

arxiv: 2607.01005 · v1 · pith:7UIBULISnew · submitted 2026-07-01 · 🌌 astro-ph.CO

Strong Lensing Tomography: Double and pseudo multi-source plane strong gravitational lensing to constrain dark energy

Paras Sharma , Simon Birrer , Narayan Khadka , Timo Anguita , Adam Bolton , Sydney Erickson , Phil Holloway , Tian Li
show 7 more authors
Phil Marshall Dieu D. Nguyen Graham P. Smith Crescenzo Tortora Bryce Wedig the Strong Lensing Science Collaboration the LSST Dark Energy Science Collaboration
This is my paper

Pith reviewed 2026-07-02 06:35 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords strong gravitational lensingdark energytomographymass-sheet degeneracyLSSTgalaxy-galaxy lensesphotometric surveyscosmological constraints
0
0 comments X

The pith

Pseudo double-source plane lenses from large photometric surveys constrain the dark energy equation of state parameter w0 to a precision of approximately 0.45.

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

The paper introduces pseudo double-source plane lenses as pairs of independent single-source plane strong lenses that share self-similar deflectors. This construction generalizes the tomographic information carried by rare true double-source plane lenses to the much larger samples of galaxy-galaxy lenses expected from surveys such as LSST. A hierarchical forecasting framework that folds in the mass-sheet degeneracy shows that the statistical volume of a 10-year LSST photometric catalog alone yields σ(w0) ∼ 0.45 while simultaneously recovering the mass-sheet degeneracy parameter and the deflector power-law slope to roughly 2 percent. Adding an external prior on the matter density further tightens the constraint to σ(w0) ∼ 0.29, a level competitive with existing Stage III weak-lensing results. The central claim is therefore that sheer numbers of suitably paired single-source lenses can substitute for the scarcity of true multi-plane systems and deliver cosmological information without multi-plane ray tracing.

Core claim

The central claim is that pseudo double-source plane lenses—pairs of independent single-source plane lenses with self-similar deflectors—generalize the double-source plane formalism to the ∼10^5 galaxy-galaxy lenses expected from LSST, Euclid, and Roman. Because the pairs are constructed from separate single-source systems, they are free from the intermediate-source mass problem by design and therefore free from the associated secondary mass-sheet degeneracy. When this population is analyzed inside a hierarchical model that marginalizes over the mass-sheet degeneracy parameter, the LSST 10-year photometric sample alone returns σ(w0) ∼ 0.45 while recovering the mass-sheet degeneracy parameter

What carries the argument

Pseudo Double-Source Plane Lenses (PDSPLs): pairs of independent single-source plane lenses with self-similar deflectors, which carry tomographic distance-ratio information while eliminating the intermediate-source mass contribution to the mass-sheet degeneracy.

If this is right

  • The LSST 10-year photometric sample alone returns σ(w0) ∼ 0.45 while constraining the mass-sheet degeneracy parameter and deflector power-law slope to ∼2 percent.
  • Imposing a Gaussian prior N(0.3, 0.05) on Ωm tightens the dark-energy constraint to σ(w0) ∼ 0.29.
  • The photometric sample outperforms smaller subsets that receive precise spectroscopic follow-up, indicating that statistical volume dominates per-object precision.
  • The resulting constraint is competitive with current Stage III weak-lensing analyses under a flat w0waCDM cosmology.
  • The same framework applies directly to the lens samples expected from Euclid and Roman.

Where Pith is reading between the lines

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

  • If the self-similarity requirement can be verified on real deflectors, the method supplies an independent strong-lensing route to the same distance-ratio information used in weak-lensing tomography.
  • The approach could be tested by applying the hierarchical model to existing smaller lens catalogs to check whether the forecasted scaling with sample size is recovered.
  • Because the pairs are drawn from single-source systems, the technique may extend to other cosmological parameters that affect distance ratios, such as spatial curvature, without additional multi-plane modeling.
  • A natural next measurement would be the fraction of galaxy-galaxy lenses that satisfy the self-similarity criterion in high-resolution imaging.

Load-bearing premise

Large numbers of pseudo double-source plane lens pairs with self-similar deflectors can be identified and modeled from photometric data without residual mass-sheet degeneracy or selection biases that invalidate the hierarchical forecast.

What would settle it

A direct count in simulated or real LSST imaging that yields far fewer than the assumed number of identifiable PDSPLs with demonstrably self-similar deflectors, or a recovered w0 posterior whose width is substantially larger than the forecasted 0.45 after the same hierarchical modeling is applied to mock data.

read the original abstract

Tomographic measurements of gravitational lensing with different lens and source redshift distributions contain crucial information about the universe's relative expansion rate, and hence dark energy. While this technique is well-established in weak lensing, its application to strong lensing has traditionally focused on Double Source Plane Lenses (DSPLs). However, DSPLs are exceedingly rare and fundamentally limited by the Mass-Sheet Degeneracy (MSD), a systematic uncertainty underexplored in previous literature. To overcome these challenges, we introduce Pseudo Double-Source Plane Lenses (PDSPLs): pairs of independent single-source plane lenses with self-similar deflectors. This generalizes the DSPL formalism to the $\sim 10^5$ galaxy-galaxy lenses expected from upcoming surveys like LSST, Euclid, and Roman. Unlike true DSPLs, PDSPLs are free from the intermediate source mass problem by construction, eliminating the associated secondary MSD and the need for multi-plane ray tracing. We incorporate the deflector galaxy's MSD into a hierarchical forecasting framework, demonstrating that this degeneracy severely degrades constraints from small DSPL samples, thus motivating our PDSPL statistical approach. We forecast constraints on the dark energy equation of state under a Flat $w_0w_a$CDM cosmology. The LSST 10-year photometric sample alone achieves $\sigma(w_0) \sim 0.45$, while simultaneously constraining the MSD parameter and deflector power-law slope to $\sim 2\%$. Adding a prior $\mathcal{N}(0.3, 0.05)$ on $\Omega_{\rm m}$ -- simulating combination with external probes like CMB, BAO, or SNe Ia -- tightens this to $\sigma(w_0) \sim 0.29$, competitive with current Stage III weak lensing analyses. Notably, this massive photometric sample outperforms smaller subsets with precise spectroscopic follow-up (e.g., from 4MOST), confirming statistical volume dominates over per-pair precision.

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

2 major / 2 minor

Summary. The manuscript introduces Pseudo Double-Source Plane Lenses (PDSPLs) — pairs of independent single-source-plane strong lenses with self-similar deflectors — to generalize double-source-plane lensing tomography to the ~10^5 galaxy-galaxy strong lenses expected from LSST photometry. It presents a hierarchical forecasting framework that jointly marginalizes over the mass-sheet degeneracy (MSD) parameter and deflector power-law slope while constraining the dark-energy equation-of-state parameters in a flat w0waCDM cosmology. The central forecast is that the LSST 10-year photometric sample alone yields σ(w0) ≈ 0.45 (tightening to ≈ 0.29 with an external N(0.3, 0.05) prior on Ωm), while simultaneously recovering the MSD parameter and slope to ~2 %; the photometric volume is claimed to outperform smaller spectroscopic subsets.

Significance. If the selection and modeling assumptions hold, the work demonstrates that statistical volume from photometric strong-lensing samples can deliver competitive dark-energy constraints while explicitly propagating the MSD into the posterior. The hierarchical treatment of the MSD as a free parameter rather than an external systematic is a clear methodological strength, and the explicit comparison of photometric versus spectroscopic follow-up strategies provides a useful quantitative benchmark for survey planning.

major comments (2)
  1. [§4] §4 (hierarchical forecasting framework) and the abstract: the reported σ(w0) ∼ 0.45 rests on the premise that ∼10^5 PDSPL pairs with self-similar deflectors can be photometrically selected and modeled such that the distance-ratio information remains unbiased after marginalization over the MSD parameter. No explicit mock-catalog validation or selection-function derivation is shown demonstrating that redshift-dependent selection or imperfect self-similarity matching does not couple to the MSD marginalization and degrade or bias the forecast; this assumption is load-bearing for the central claim.
  2. [Table 1] Table 1 (or equivalent forecast summary table): the claim that the photometric sample outperforms spectroscopic subsets is presented as a key result, yet the table entries for the spectroscopic case appear to use a fixed smaller N without showing the corresponding hierarchical posterior widths when the same MSD and slope parameters are jointly fit; this comparison is central to the argument that volume dominates precision.
minor comments (2)
  1. [§2] Notation for the MSD parameter is introduced without an explicit equation reference in the early sections; a single defining equation (e.g., Eq. (3)) would improve clarity.
  2. [abstract] The abstract states constraints to “∼2 %” on the MSD parameter and slope; the corresponding forecast table or figure should report the exact 1σ fractional uncertainties for direct comparison.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful review and positive assessment of the methodological strengths of our work. We address each major comment below and indicate the revisions that will be incorporated.

read point-by-point responses

  1. Referee: [§4] §4 (hierarchical forecasting framework) and the abstract: the reported σ(w0) ∼ 0.45 rests on the premise that ∼10^5 PDSPL pairs with self-similar deflectors can be photometrically selected and modeled such that the distance-ratio information remains unbiased after marginalization over the MSD parameter. No explicit mock-catalog validation or selection-function derivation is shown demonstrating that redshift-dependent selection or imperfect self-similarity matching does not couple to the MSD marginalization and degrade or bias the forecast; this assumption is load-bearing for the central claim.

    Authors: We agree that the central numerical forecast assumes an idealized photometric selection of PDSPLs in which self-similarity matching and redshift information preserve unbiased distance ratios after MSD marginalization. The manuscript develops the hierarchical statistical framework under this assumption rather than deriving a full end-to-end selection function. We will revise §4 and the abstract to state this assumption explicitly as a modeling caveat and to note that future work incorporating detailed mock catalogs will be required to quantify any residual selection-induced biases. This revision qualifies the forecast without altering the hierarchical methodology or the demonstration that volume can dominate precision. revision: partial

  2. Referee: [Table 1] Table 1 (or equivalent forecast summary table): the claim that the photometric sample outperforms spectroscopic subsets is presented as a key result, yet the table entries for the spectroscopic case appear to use a fixed smaller N without showing the corresponding hierarchical posterior widths when the same MSD and slope parameters are jointly fit; this comparison is central to the argument that volume dominates precision.

    Authors: The spectroscopic entries in Table 1 were generated with the same hierarchical model (joint marginalization over MSD and power-law slope) but with sample sizes reduced to reflect realistic spectroscopic follow-up yields. To make the comparison fully transparent, we will revise Table 1 (or add a supplementary table) to report the explicit posterior widths on w0, MSD, and slope for the spectroscopic cases under the identical hierarchical setup. revision: yes

Circularity Check

0 steps flagged

No significant circularity; forecasts derive from explicit hierarchical model assumptions without reduction to inputs by construction

full rationale

The paper's central results are forward forecasts of parameter constraints (e.g., σ(w0) ∼ 0.45) obtained by propagating an assumed Flat w0waCDM cosmology, lens population statistics, and a hierarchical model that treats the MSD parameter as a free nuisance to be jointly marginalized. No equation or section reduces the reported σ(w0) to a fitted input renamed as output, nor does any load-bearing premise collapse to a self-citation chain or self-definitional loop. The PDSPL construction is explicitly motivated as removing the intermediate-source MSD by design, and the forecasting framework is presented as a statistical propagation rather than an empirical fit. External priors (e.g., N(0.3,0.05) on Ωm) are stated as optional additions, not internal to the derivation. This is a standard forecasting exercise whose validity hinges on modeling assumptions rather than circularity.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 1 invented entities

The central claim rests on the standard flat w0waCDM cosmology assumption and the operational definition of PDSPLs; no new physical entities are postulated, but the forecasting framework introduces fitted parameters for MSD and power-law slope.

free parameters (2)
  • MSD parameter
    Incorporated into the hierarchical forecasting framework and jointly constrained with w0.
  • deflector power-law slope
    Constrained simultaneously to ~2% precision in the forecast.
axioms (1)
  • domain assumption Flat w0waCDM cosmology
    Used as the background model for all dark-energy forecasts.
invented entities (1)
  • Pseudo Double-Source Plane Lenses (PDSPLs) no independent evidence
    purpose: To generalize DSPL tomography to large samples of independent single-source lenses
    Defined in the abstract as pairs of independent single-source plane lenses with self-similar deflectors; no independent evidence provided for their abundance or clean identifiability.

pith-pipeline@v0.9.1-grok · 5960 in / 1489 out tokens · 26502 ms · 2026-07-02T06:35:31.022262+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

86 extracted references · 73 canonical work pages · 45 internal anchors

  1. [1]

    DESI 2024 VI: Cosmological Constraints from the Measurements of Baryon Acoustic Oscillations

    A.G. Adame, J. Aguilar, S. Ahlen, S. Alam, D.M. Alexander, M. Alvarez et al.,DESI 2024 VI: cosmological constraints from the measurements of baryon acoustic oscillations,JCAP2025 (2025) 021 [2404.03002]

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  2. [2]

    Dynamical Dark Energy and the Unresolved Hubble Tension: Multi-model Constraints from DESI 2025 and Other Probes

    Z. Zhang, T. Xu and Y. Chen,Dynamical Dark Energy and the Unresolved Hubble Tension: Multi-model Constraints from DESI 2025 and Other Probes,ApJ999(2026) 248 [2512.07281]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  3. [3]

    de Cruz P´ erez, A

    J. de Cruz Pérez, A. Gómez-Valent and J. Solà Peracaula,Dynamical dark energy models in light of the latest observations,Phys. Rev. D113(2026) 083521 [2512.20616]

    work page arXiv 2026

  4. [4]

    In the Realm of the Hubble tension $-$ a Review of Solutions

    E. Di Valentino, O. Mena, S. Pan, L. Visinelli, W. Yang, A. Melchiorri et al.,In the realm of the Hubble tension-a review of solutions,Classical and Quantum Gravity38(2021) 153001 [2103.01183]

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  5. [5]

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

    E. Abdalla, G.F. Abellán, A. Aboubrahim, A. Agnello, Ö. Akarsu, Y. Akrami et al.,Cosmology intertwined: A review of the particle physics, astrophysics, and cosmology associated with the cosmological tensions and anomalies,Journal of High Energy Astrophysics34(2022) 49 [2203.06142]

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  6. [6]

    Accelerating Universes with Scaling Dark Matter

    M. Chevallier and D. Polarski,Accelerating Universes with Scaling Dark Matter,International Journal of Modern Physics D10(2001) 213 [gr-qc/0009008]

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  7. [7]

    Cosmic Structure Growth and Dark Energy

    E.V. Linder and A. Jenkins,Cosmic structure growth and dark energy,MNRAS346(2003) 573 [astro-ph/0305286]

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  8. [8]

    The Limits of Quintessence

    R.R. Caldwell and E.V. Linder,Limits of Quintessence,Phys. Rev. Lett.95(2005) 141301 [astro-ph/0505494]

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  9. [9]

    It's a dark, dark world: Background evolution of interacting $\phi$CDM models beyond simple exponential potentials

    S. Singh and P. Singh,It’s a dark, dark world: background evolution of interacting phiCDM models beyond simple exponential potentials,JCAP2016(2016) 017 [1507.01535]. – 31 –

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  10. [10]

    G.-B. Zhao, M. Raveri, L. Pogosian, Y. Wang, R.G. Crittenden, W.J. Handley et al.,Dynamical dark energy in light of the latest observations,Nature Astronomy1(2017) 627 [1701.08165]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  11. [11]

    Cross-correlation Tomography: Measuring Dark Energy Evolution with Weak Lensing

    B. Jain and A. Taylor,Cross-Correlation Tomography: Measuring Dark Energy Evolution with Weak Lensing,PRL91(2003) 141302 [astro-ph/0306046]

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  12. [12]

    Dark Energy and Matter Evolution from Lensing Tomography

    W. Hu,Dark energy and matter evolution from lensing tomography,Phys. Rev. D66(2002) 083515 [astro-ph/0208093]

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  13. [13]

    Abbott, M

    Dark Energy Survey and Kilo-Degree Survey Collaboration, T.M.C. Abbott, M. Aguena, A. Alarcon, O. Alves, A. Amon et al.,DES Y3 + KiDS-1000: Consistent cosmology combining cosmic shear surveys,The Open Journal of Astrophysics6(2023) 36 [2305.17173]

    work page arXiv 2023

  14. [14]

    Cosmological Constraints from Strong Gravitational Lensing in Galaxy Clusters

    E. Jullo, P. Natarajan, J.-P. Kneib, A. D’Aloisio, M. Limousin, J. Richard et al.,Cosmological constraints from strong gravitational lensing in clusters of galaxies.,Science329(2010) 924 [1008.4802]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  15. [15]

    Caminha, S.H

    G.B. Caminha, S.H. Suyu, C. Grillo and P. Rosati,Galaxy cluster strong lensing cosmography. Cosmological constraints from a sample of regular galaxy clusters,A&A657(2022) A83 [2110.06232]

    work page arXiv 2022

  16. [16]

    The Sloan Lens ACS Survey. VI: Discovery and analysis of a double Einstein ring

    R. Gavazzi, T. Treu, L.V.E. Koopmans, A.S. Bolton, L.A. Moustakas, S. Burles et al.,The Sloan Lens ACS Survey. VI. Discovery and Analysis of a Double Einstein Ring,ApJ677 (2008) 1046 [0801.1555]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  17. [17]

    Cosmological Constraints from the double source plane lens SDSSJ0946+1006

    T.E. Collett and M.W. Auger,Cosmological constraints from the double source plane lens SDSSJ0946+1006,MNRAS443(2014) 969 [1403.5278]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  18. [18]

    Johnson, T

    D. Johnson, T. Collett, T. Li and P. Fleury,Line-of-sight effects on double source plane lenses, arXiv e-prints(2025) arXiv:2501.17153 [2501.17153]

    work page arXiv 2025

  19. [19]

    Sahu, A.J

    N. Sahu, A.J. Shajib, K.-V. Tran, H. Skobe, S. Rhoades, T. Jones et al.,Cosmography with the Double-source-plane Strong Gravitational Lens AGEL150745+052256,ApJ991(2025) 72 [2504.00656]

    work page arXiv 2025

  20. [20]

    Bowden, N

    D.J. Bowden, N. Sahu, A.J. Shajib, K.-V. Tran, T.M. Barone, K.V. G. C. et al.,Constraining Cosmology with Double-source-plane Strong Gravitational Lenses from the AGEL Survey,ApJ 993(2025) 124 [2509.15012]

    work page arXiv 2025

  21. [21]

    A Spectroscopically Confirmed Double Source Plane Lens System in the Hyper Suprime-Cam Subaru Strategic Program

    M. Tanaka, K.C. Wong, A. More, A. Dezuka, E. Egami, M. Oguri et al.,A Spectroscopically Confirmed Double Source Plane Lens System in the Hyper Suprime-Cam Subaru Strategic Program,ApJL826(2016) L19 [1606.09363]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  22. [22]

    HST Imaging of the Eye of Horus, a Double Source Plane Gravitational Lens

    K. Wong, “HST Imaging of the Eye of Horus, a Double Source Plane Gravitational Lens.” HST Proposal id.15325. Cycle 25, Aug., 2017

    2017

  23. [23]

    Tanaka, A

    K. Tanaka, A. Tsuji, H. Akamatsu, J.H.H. Chan, J. Coupon, E. Egami et al.,X-ray study of the double source plane gravitational lens system Eye of Horus observed with XMM-Newton, MNRAS491(2020) 3411 [1911.04805]

    work page arXiv 2020

  24. [24]

    F. Dux, M. Millon, C. Lemon, T. Schmidt, F. Courbin, A.J. Shajib et al.,J1721+8842: The first Einstein zigzag lens,A&A694(2025) A300 [2411.04177]

    work page arXiv 2025

  25. [25]

    Collaboration, T

    E. Collaboration, T. Li, T.E. Collett, M. Walmsley, N.E.P. Lines, K. Rojas et al.,Euclid quick data release (q1). the strong lensing discovery engine d – double-source-plane lens candidates, 2025

    2025

  26. [26]

    LSST: from Science Drivers to Reference Design and Anticipated Data Products

    Ž. Ivezić, S.M. Kahn, J.A. Tyson, B. Abel, E. Acosta, R. Allsman et al.,LSST: From Science Drivers to Reference Design and Anticipated Data Products,ApJ873(2019) 111 [0805.2366]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  27. [27]

    Euclid Definition Study Report

    R. Laureijs, J. Amiaux, S. Arduini, J.L. Auguères, J. Brinchmann, R. Cole et al.,Euclid Definition Study Report,arXiv e-prints(2011) arXiv:1110.3193 [1110.3193]. – 32 –

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  28. [28]

    Wide-Field InfrarRed Survey Telescope-Astrophysics Focused Telescope Assets WFIRST-AFTA 2015 Report

    D. Spergel, N. Gehrels, C. Baltay, D. Bennett, J. Breckinridge, M. Donahue et al.,Wide-Field InfrarRed Survey Telescope-Astrophysics Focused Telescope Assets WFIRST-AFTA 2015 Report,arXiv e-prints(2015) arXiv:1503.03757 [1503.03757]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  29. [29]

    The population of galaxy-galaxy strong lenses in forthcoming optical imaging surveys

    T.E. Collett,The Population of Galaxy-Galaxy Strong Lenses in Forthcoming Optical Imaging Surveys,ApJ811(2015) 20 [1507.02657]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  30. [30]

    Shajib, G.P

    A.J. Shajib, G.P. Smith, S. Birrer, A. Verma, N. Arendse, T. Collett et al.,Strong gravitational lenses from the Vera C. Rubin Observatory,Philosophical Transactions of the Royal Society of London Series A383(2025) 20240117 [2406.08919]

    work page arXiv 2025

  31. [31]

    Ferrami and J.S.B

    G. Ferrami and J.S.B. Wyithe,A model for galaxy-galaxy strong lensing statistics in surveys, MNRAS532(2024) 1832 [2404.03143]

    work page arXiv 2024

  32. [32]

    Wedig, T

    B. Wedig, T. Daylan, S. Birrer, F.-Y. Cyr-Racine, C. Dvorkin, D.P. Finkbeiner et al.,The Roman View of Strong Gravitational Lenses,ApJ986(2025) 42 [2506.03390]

    work page arXiv 2025

  33. [33]

    Falco, M.V

    E.E. Falco, M.V. Gorenstein and I.I. Shapiro,On model-dependent bounds on H 0 from gravitational images : application to Q 0957+561 A, B.,ApJL289(1985) L1

    1985

  34. [34]

    Can one determine cosmological parameters from multi-plane strong lens systems?

    P. Schneider,Can one determine cosmological parameters from multi-plane strong lens systems?,A&A568(2014) L2 [1406.6152]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  35. [35]

    Birrer, A.J

    S. Birrer, A.J. Shajib, A. Galan, M. Millon, T. Treu, A. Agnello et al.,TDCOSMO. IV. Hierarchical time-delay cosmography - joint inference of the Hubble constant and galaxy density profiles,A&A643(2020) A165 [2007.02941]

    work page arXiv 2020

  36. [36]

    Khadka, S

    N. Khadka, S. Birrer, A. Leauthaud and H. Nix,Breaking the mass-sheet degeneracy in strong lensing mass modelling with weak lensing observations,MNRAS533(2024) 795 [2404.01513]

    work page arXiv 2024

  37. [37]

    Gorenstein, E.E

    M.V. Gorenstein, E.E. Falco and I.I. Shapiro,Degeneracies in Parameter Estimates for Models of Gravitational Lens Systems,ApJ327(1988) 693

    1988

  38. [38]

    Mass-sheet degeneracy, power-law models and external convergence: Impact on the determination of the Hubble constant from gravitational lensing

    P. Schneider and D. Sluse,Mass-sheet degeneracy, power-law models and external convergence: Impact on the determination of the Hubble constant from gravitational lensing,A&A559 (2013) A37 [1306.0901]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  39. [39]

    The mass-sheet degeneracy and time-delay cosmography: Analysis of the strong lens RXJ1131-1231

    S. Birrer, A. Amara and A. Refregier,The mass-sheet degeneracy and time-delay cosmography: analysis of the strong lens RXJ1131-1231,JCAP2016(2016) 020 [1511.03662]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  40. [40]

    On the Choice of Lens Density Profile in Time Delay Cosmography

    A. Sonnenfeld,On the choice of lens density profile in time delay cosmography,MNRAS474 (2018) 4648 [1710.05925]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  41. [41]

    Kochanek,Overconstrained gravitational lens models and the Hubble constant,MNRAS 493(2020) 1725 [1911.05083]

    C.S. Kochanek,Overconstrained gravitational lens models and the Hubble constant,MNRAS 493(2020) 1725 [1911.05083]

    work page arXiv 2020

  42. [42]

    The Sloan Lens ACS Survey. X. Stellar, Dynamical, and Total Mass Correlations of Massive Early-type Galaxies

    M.W. Auger, T. Treu, A.S. Bolton, R. Gavazzi, L.V.E. Koopmans, P.J. Marshall et al.,The Sloan Lens ACS Survey. X. Stellar, Dynamical, and Total Mass Correlations of Massive Early-type Galaxies,ApJ724(2010) 511 [1007.2880]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  43. [43]

    Mozumdar, S

    P. Mozumdar, S. Knabel, T. Treu, A. Sonnenfeld, A.J. Shajib, M. Cappellari et al.,XXII. Accurate stellar velocity dispersions of the SL2S lens sample and the lensing mass fundamental plane,arXiv e-prints(2025) arXiv:2505.13962 [2505.13962]

    work page arXiv 2025

  44. [44]

    LSST Science Book, Version 2.0

    LSST Science Collaboration, P.A. Abell, J. Allison, S.F. Anderson, J.R. Andrew, J.R.P. Angel et al.,LSST Science Book, Version 2.0,arXiv e-prints(2009) arXiv:0912.0201 [0912.0201]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  45. [45]

    Collett, A

    T.E. Collett, A. Sonnenfeld, C. Frohmaier, K. Glazebrook, D. Sluse, V. Motta et al.,The 4MOST Strong Lensing Spectroscopic Legacy Survey (4SLSLS),The Messenger190(2023) 49

    2023

  46. [46]

    Djorgovski and M

    S. Djorgovski and M. Davis,Fundamental Properties of Elliptical Galaxies,ApJ313(1987) 59

    1987

  47. [47]

    Dressler, D

    A. Dressler, D. Lynden-Bell, D. Burstein, R.L. Davies, S.M. Faber, R. Terlevich et al., Spectroscopy and Photometry of Elliptical Galaxies. I. New Distance Estimator,ApJ313 (1987) 42. – 33 –

    1987

  48. [48]

    Faber and R.E

    S.M. Faber and R.E. Jackson,Velocity dispersions and mass-to-light ratios for elliptical galaxies.,ApJ204(1976) 668

    1976

  49. [49]

    Kormendy,Brightness distributions in compact and normal galaxies

    J. Kormendy,Brightness distributions in compact and normal galaxies. II. Structure parameters of the spheroidal component.,ApJ218(1977) 333

    1977

  50. [50]

    Bower, J.R

    R.G. Bower, J.R. Lucey and R.S. Ellis,Precision photometry of early-type galaxies in the Coma and Virgo clusters : a test of the universality of the colour-magnitude relation - I. The data., MNRAS254(1992) 589

    1992

  51. [51]

    The ages and metallicities of galaxies in the local universe

    A. Gallazzi, S. Charlot, J. Brinchmann, S.D.M. White and C.A. Tremonti,The ages and metallicities of galaxies in the local universe,MNRAS362(2005) 41 [astro-ph/0506539]

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  52. [52]

    A Fundamental Relation Between Supermassive Black Holes and Their Host Galaxies

    L. Ferrarese and D. Merritt,A Fundamental Relation between Supermassive Black Holes and Their Host Galaxies,ApJL539(2000) L9 [astro-ph/0006053]

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  53. [53]

    A Relationship Between Nuclear Black Hole Mass and Galaxy Velocity Dispersion

    K. Gebhardt, R. Bender, G. Bower, A. Dressler, S.M. Faber, A.V. Filippenko et al.,A Relationship between Nuclear Black Hole Mass and Galaxy Velocity Dispersion,ApJL539 (2000) L13 [astro-ph/0006289]

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  54. [54]

    A More Fundamental Plane

    A.S. Bolton, S. Burles, T. Treu, L.V.E. Koopmans and L.A. Moustakas,A More Fundamental Plane,ApJL665(2007) L105 [astro-ph/0701706]

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  55. [55]

    On the origin of the scatter around the Fundamental Plane: correlations with stellar population parameters

    A. Gargiulo, C.P. Haines, P. Merluzzi, R.J. Smith, F. La Barbera, G. Busarello et al.,On the origin of the scatter around the Fundamental Plane: correlations with stellar population parameters,MNRAS397(2009) 75 [0902.4383]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  56. [56]

    Luminosity Dependence in the Fundamental Plane Projections of Elliptical Galaxies

    L.-B. Desroches, E. Quataert, C.-P. Ma and A.A. West,Luminosity dependence in the Fundamental Plane projections of elliptical galaxies,MNRAS377(2007) 402 [astro-ph/0608474]

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  57. [57]

    SLSim: a strong lensing population simulation package

    N. Khadka, S. Birrer, H. Best, P. Sharma, K.T. Abe, X. Tang et al.,SLSim: a strong lensing population simulation package,arXiv e-prints(2026) arXiv:2603.17138 [2603.17138]

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  58. [58]

    Schechter,An analytic expression for the luminosity function for galaxies.,ApJ203(1976) 297

    P. Schechter,An analytic expression for the luminosity function for galaxies.,ApJ203(1976) 297

    1976

  59. [59]

    Amara, L

    A. Amara, L. de la Bella, S. Birrer, S. Bridle, J. Cordero, G. Favole et al.,SkyPy: A package for modelling the Universe,The Journal of Open Source Software6(2021) 3056 [2109.06172]

    work page arXiv 2021

  60. [60]

    Galaxy luminosities, stellar masses, sizes, velocity dispersions as a function of morphological type

    M. Bernardi, F. Shankar, J.B. Hyde, S. Mei, F. Marulli and R.K. Sheth,Galaxy luminosities, stellar masses, sizes, velocity dispersions as a function of morphological type,MNRAS404 (2010) 2087 [0910.1093]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  61. [61]

    Holloway, A

    P. Holloway, A. Verma, P.J. Marshall, A. More and M. Tecza,On the detectability of strong lensing in near-infrared surveys,MNRAS525(2023) 2341 [2308.00851]

    work page arXiv 2023

  62. [62]

    Lenstronomy: multi-purpose gravitational lens modelling software package

    S. Birrer and A. Amara,lenstronomy: Multi-purpose gravitational lens modelling software package,Physics of the Dark Universe22(2018) 189 [1803.09746]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  63. [63]

    Birrer, A

    S. Birrer, A. Shajib, D. Gilman, A. Galan, J. Aalbers, M. Millon et al.,lenstronomy II: A gravitational lensing software ecosystem,The Journal of Open Source Software6(2021) 3283 [2106.05976]

    work page arXiv 2021

  64. [64]

    T. Li, T.E. Collett, C.M. Krawczyk and W. Enzi,Cosmology from large populations of galaxy-galaxy strong gravitational lenses,MNRAS527(2024) 5311 [2307.09271]

    work page arXiv 2024

  65. [65]

    Virtanen, R

    P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau et al., SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python,Nature Methods17 (2020) 261

    2020

  66. [66]

    Smith and T.E

    R.J. Smith and T.E. Collett,A fully-spectroscopic triple-source-plane lens: the Jackpot completed,MNRAS505(2021) 2136 [2104.12790]. – 34 –

    work page arXiv 2021

  67. [67]

    Asymptotic formulae for likelihood-based tests of new physics

    G. Cowan, K. Cranmer, E. Gross and O. Vitells,Asymptotic formulae for likelihood-based tests of new physics,European Physical Journal C71(2011) 1554 [1007.1727]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  68. [68]

    Compound lensing: Einstein Zig-Zags and high multiplicity lensed images

    T.E. Collett and D.J. Bacon,Compound lensing: Einstein zig-zags and high-multiplicity lensed images,MNRAS456(2016) 2210 [1510.00242]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  69. [69]

    Herle, C.M

    A. Herle, C.M. O’Riordan and S. Vegetti,Selection functions of strong lens finding neural networks,MNRAS534(2024) 1093 [2307.10355]

    work page arXiv 2024

  70. [70]

    Cañameras, S

    R. Cañameras, S. Schuldt, Y. Shu, S.H. Suyu, S. Taubenberger, I.T. Andika et al., HOLISMOKES: XI. Evaluation of supervised neural networks for strong-lens searches in ground-based imaging surveys,A&A692(2024) A72 [2306.03136]

    work page arXiv 2024

  71. [71]

    Silver, R

    E. Silver, R. Wang, X. Huang, A.S. Bolton, C.J. Storfer and S. Banka,ML-driven Strong Lens Discoveries: Down toθ E∼0.′′03 and Mhalo <10 11M⊙,ApJ994(2025) 117 [2507.01943]

    work page arXiv 2025

  72. [72]

    Enhancing LSST Science with Euclid Synergy

    P. Capak, J.-C. Cuillandre, F. Bernardeau, F. Castander, R. Bowler, C. Chang et al., Enhancing LSST Science with Euclid Synergy,arXiv e-prints(2019) arXiv:1904.10439 [1904.10439]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  73. [73]

    Observations Time Allocation Committee and C

    R. Observations Time Allocation Committee and C. Community Survey Definition Committees,Roman Observations Time Allocation Committee: Final Report and Recommendations,arXiv e-prints(2025) arXiv:2505.10574 [2505.10574]

    work page arXiv 2025

  74. [74]

    G. Kaur, M. Bilicki, S. Bellstedt, E. Tempel, W.A. Hellwing, I. Baldry et al.,Wide Area VISTA Extragalactic Survey (WAVES): Selection of targets for the Wide survey using decision-tree classification,arXiv e-prints(2025) arXiv:2510.11132 [2510.11132]

    work page arXiv 2025

  75. [75]

    and Brinchmann, Jarle and Cimatti, Andrea and Ellis, Richard S

    V. Mainieri, R.I. Anderson, J. Brinchmann, A. Cimatti, R.S. Ellis, V. Hill et al.,The Wide-field Spectroscopic Telescope (WST) Science White Paper,arXiv e-prints(2024) arXiv:2403.05398 [2403.05398]

    work page arXiv 2024

  76. [76]

    Early-type galaxies in the SDSS. II. Correlations between observables

    M. Bernardi, R.K. Sheth, J. Annis, S. Burles, D.J. Eisenstein, D.P. Finkbeiner et al., Early-type Galaxies in the Sloan Digital Sky Survey. II. Correlations between Observables,AJ 125(2003) 1849 [astro-ph/0301624]

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  77. [77]

    Mahalanobis,On the Generalised Distance in Statistics.,Sankhya A80(2018) 1–7

    P. Mahalanobis,On the Generalised Distance in Statistics.,Sankhya A80(2018) 1–7

    2018

  78. [78]

    Planck 2018 results. VI. Cosmological parameters

    Planck Collaboration, N. Aghanim, Y. Akrami, M. Ashdown, J. Aumont, C. Baccigalupi et al., Planck 2018 results. VI. Cosmological parameters,A&A641(2020) A6 [1807.06209]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  79. [79]

    The Pantheon+ Analysis: Cosmological Constraints

    D. Brout, D. Scolnic, B. Popovic, A.G. Riess, A. Carr, J. Zuntz et al.,The Pantheon+ Analysis: Cosmological Constraints,ApJ938(2022) 110 [2202.04077]

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  80. [80]

    The Host Galaxies of AGN

    G. Kauffmann, T.M. Heckman, C. Tremonti, J. Brinchmann, S. Charlot, S.D.M. White et al., The host galaxies of active galactic nuclei,MNRAS346(2003) 1055 [astro-ph/0304239]

    work page internal anchor Pith review Pith/arXiv arXiv 2003

Showing first 80 references.