{"id":"ae823159-1635-46c7-b2d4-f4452b74873a","arxiv_id":"2502.02536","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":3.0,"correctness_risk":"low","formal_verification":"none","parameter_count":0,"one_line_summary":"A review arguing that combining strong gravitational lensing of gravitational-wave and electromagnetic signals will enable new probes of cosmology, modified gravity, and compact-object merger physics.","lead":"This review lays out how strong gravitational lensing of gravitational waves and their electromagnetic counterparts could open new views of cosmology, gravity, and the origins of gamma-ray bursts and fast radio bursts. It gives the community a shared roadmap and estimates the rates at which such lensed multi-messenger events might be found.","discovery_kind":"review","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The headline rate estimates in Sec. 2(d)(ii) depend on the stated single-progenitor and aligned-jet assumptions; the predicted ~10 lensed GRBs yr−1 also sits in tension with the null Fermi lensed-GRB searches, so the quantitative claim needs an uncertainty/sensitivity analysis.","rationale":"The paper is a clearly written agenda/review; its science case for multi-messenger strong lensing is well supported by the cited literature, and the qualitative arguments regarding time-delay cosmology, tests of gravity, and source physics do not depend on the exact rate numbers. The single load-bearing quantitative element is the detectability estimate in Sec. 2(d)(ii). My concern is not that the authors hide their assumptions—they state them explicitly—but that the resulting rates are presented without uncertainty quantification and are not checked against the existing null result from Fermi searches for lensed GRBs. The reader's weakest_assumption identifies the same root cause, and I agree with it. A rerun of the linked notebook with plausible variations in progenitor mix and luminosity function is a concrete, feasible check. If the ~10 yr−1 figure is stable under factor-of-few shifts, the conditional verdict can be accepted; if it changes by orders of magnitude, the strongest quantitative claim should be framed as an upper limit rather than a prediction. Therefore I do not move the reader's CONDITIONAL verdict.","tokens_in":21302,"tokens_out":10892,"duration_ms":113588,"concrete_test":"Re-run the public Jupyter notebook [108] used for Sec. 2(d)(ii) under three variants: (i) replace the 100% BNS assumption with an observationally motivated BNS/NSBH fraction, e.g. 50-70% BNS; (ii) replace the single GRB 170817A-like luminosity with the sGRB luminosity function of [105] including a spread in jet opening angles; and (iii) compute the expected number of lensed GRBs that would have been seen in 11 years of Fermi GBM and compare with the null searches [97,98]. If the predicted ~10 yr−1 drops below ~1 yr−1, or if the model predicts more than one detectable lensed GRB in the Fermi sample, the headline quantitative claim is not robust as stated.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's most concrete quantitative claim is that ~10 GRB lens systems per year and 1 lensed GRB per 13 lensed GWs are detectable (Sec. 2(d)(ii); Fig. 4). These numbers, from 'Phurailatpam et al., in prep.' and the linked notebook [108], are derived under the explicitly simplifying assumptions that all detectable sGRBs come from BNS mergers, that their luminosity equals GRB 170817A, and that the GW inclination angle is aligned with the GRB jet axis. The text itself notes that NSBH mergers may contribute to sGRB and kilonova populations and that long-duration merger GRBs exist (Sec. 2(c)(i)), so the all-BNS assumption is not an innocent choice. If a substantial fraction of sGRBs are instead NSBH or have different jet structure or luminosity, the effective joint detection rate changes. No error bars, sensitivity ranges, or comparison with the 11-year Fermi GBM lensed-GRB searches [97,98] are provided. Since those searches found no confirmed lensed GRB, an estimate of ~10 detectable lensed systems per year requires an explanation of why the systems would have been missed; otherwise the estimate is likely optimistic. The qualitative science case for multi-messenger lensing does not collapse, but the concrete rate claims carry the abstract's quantitative promise and are not yet fully supported.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This review article argues that strong gravitational lensing of multi-messenger sources—gravitational waves, gamma-ray bursts, kilonovae, and fast radio bursts—will enable new probes of cosmology, tests of general relativity, and a better understanding of compact-object merger physics. It surveys time-delay cosmology, microlensing systematics, modified gravitational-wave propagation, progenitor physics, and search strategies for lensed counterparts. The most concrete new quantitative claims appear in Sec. 2(d)(ii): roughly 10 detectable GRB lens systems per year and a 1-in-13 chance of a lensed GRB counterpart to a detectable lensed GW event, based on simulations described as in preparation and a linked notebook.","tokens_in":21617,"tokens_out":5099,"duration_ms":48809,"significance":"If the rate estimates hold, multi-messenger strong lensing would indeed open an unprecedented observational window, and the article's qualitative science case is broadly persuasive and well grounded in the cited literature. The paper is commendably candid about idealizations (e.g., the Fermat-potential uncertainty results are explicitly stated to be valid only in idealized scenarios), and the inclusion of a public notebook for the GRB–GW rate calculation is a useful reproducibility step. The main quantitative rate estimates, however, rest on strong simplifying assumptions and are not yet supported by an uncertainty analysis or reconciled with existing null searches, so the paper's central quantitative promise needs strengthening before publication.","major_comments":[{"comment":"The estimates of \"approximately 10 yr−1\" detectable GRB lens systems and \"1 GRB lens out of 13 GW lenses\" are derived under the stated assumptions that all detectable sGRBs come from BNS mergers with GRB 170817A-like luminosity and with the GW inclination angle aligned with the GRB jet axis. The text itself notes (Sec. 2(c)(i) and Sec. 3(b)) that NSBH mergers can also produce sGRBs and kilonovae, so these assumptions are not innocuous. No sensitivity analysis, error bars, or dependence on the chosen luminosity function and jet structure is provided. Please add a quantitative assessment of how the rates change under plausible variations (e.g., NSBH contribution fraction, luminosity function, jet opening angle, or inclination distribution), or explicitly reframe these numbers as order-of-magnitude illustrations rather than predictive rates.","section":"Sec. 2(d)(ii), Fig. 4 and Eq. (2.1)"},{"comment":"The predicted ~10 detectable lensed GRB systems per year is not reconciled with the null results of the 11-year Fermi GBM lensed-GRB searches [97,98]. Since those searches found no confirmed lensed GRB, the paper should explain why the predicted systems would have been missed by existing searches (e.g., different time-delay ranges, flux thresholds, sky coverage, or the possibility that many lensed images are sub-threshold and only recoverable via the GW association). Without such a discussion, the estimate appears optimistic and is difficult to evaluate. The qualitative science case does not depend on this number, but as stated it is a load-bearing quantitative claim.","section":"Sec. 2(d)(ii)"}],"minor_comments":[{"comment":"The sentence \"These measurements are consistent with early-Universe probes but amplify the tension with late-Universe values\" is unclear: the quoted TDCOSMO value H0 = 65+23−14 km/s/Mpc is formally consistent with both Planck and SH0ES at the quoted uncertainties, so \"amplify\" may be misleading. Please rephrase.","section":"Sec. 2(a)"},{"comment":"The off-axis detection condition involving 1.61×10^8/(4π D_L^2) exp(−θ^2/(2×21.2^2)) ≥ 1 is not derived or referenced. Please define all variables and explain the origin of the numerical factor, or replace the equation with a reference to the source of this detection probability.","section":"Sec. 2(d)(ii), Eq. (2.1)"},{"comment":"Several references are incomplete: ref. 3 lacks authors, refs. 60, 84, and 86 lack author or title information. The reference list should be completed to journal standards.","section":"References"},{"comment":"The caption says \"See Sec. 2 d ii\" while the text uses \"Sec. 2(d)(ii)\"; please standardize the notation.","section":"Fig. 4 caption"},{"comment":"The abstract would benefit from one sentence summarizing the expected event rates, since the quantitative claims are a key part of the paper's forward-looking message.","section":"Abstract"}],"recommendation":"major_revision","confidential_remarks":"This is a review article for a themed issue, and the inclusion of unreviewed in-preparation results (the rate estimates of Sec. 2(d)(ii)) is somewhat unusual for a review. The authors should be encouraged to clearly mark these numbers as preliminary or to move them to a dedicated research paper. The self-citations are appropriate in context, but the dependence of the main quantitative claims on non-public work (Phurailatpam et al., in prep.; Ali & More, in prep.) should be flagged to the authors as a readability and assessability concern."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague —\n\nThe paper is a review/perspective for a theme issue: strong lensing as a tool for multi-messenger astronomy. It reads well and does what a good review should: organize the science case, connect literatures that usually live apart, and argue that lensed multi-messenger events would be uniquely informative for cosmology, gravity tests, and source physics. The writing is clear, the citation list is broad, and the authors are candid that their new pieces are idealised: the Fermat-potential uncertainty trends are valid in mock, no-noise conditions, and the rate estimates rest on explicit simplifying assumptions.\n\nThe genuinely new content is modest and clearly flagged as such. Two items stand out: (i) the claim that double-image lenses have smaller relative Fermat-potential errors than quads, with some quad configurations better than others (Ali & More, in prep); (ii) the GRB–GW lensing rate estimates: about 10 detectable lensed GRB systems per year, and 1 lensed GRB per 13 lensed GWs for a three-detector network at design sensitivity (Phurailatpam et al., in prep). Both are presented as work in progress, with the simulation notebook linked. That is an honest presentation for a review, though it means the quantitative claims should not be cited as settled numbers.\n\nThe soft spot is exactly the one the stress-test flags. The rate estimates assume all detectable sGRBs come from BNS mergers with a single luminosity (that of GRB 170817A) and aligned jet/inclination. The paper itself notes NSBH mergers produce sGRBs and that long-duration merger GRBs exist, so the all-BNS assumption is not innocent. More importantly, there is no sensitivity analysis: no error bars, no variation of jet structure, no discussion of what NSBH contributions would do. And the predicted ~10/yr lensed GRBs sits uncomfortably with the null results from 11 years of Fermi GBM lensed-GRB searches (Ahlgren & Larsson 2020; Chen et al. 2022), which the paper cites but does not compare against. A few sentences of discussion would have tempered the claim or explained why those searches would not see these systems.\n\nThat said, the central thesis—that multi-messenger lensing is a promising future probe—does not depend on those specific numbers. The qualitative case is well supported by independent literature.\n\nVerdict: worth engaging. It is a solid review for a theme issue, and the preliminary estimates are useful signposts, but the rate section needs a caveat or a pointer to the future paper with the full sensitivity analysis. I would send it to a referee, mainly to check the rate claims against known searches and to ensure the in-prep results are labelled clearly. For the right reader, it is a useful entry point to the field.","headline":"A well-written review of multi-messenger strong lensing that makes its case on broad literature, but the quantitative rate estimates are preliminary and need uncertainty quantification against existing null searches.","tokens_in":22103,"tokens_out":5893,"would_cite":true,"duration_ms":52758,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Strong lensing of gravitational waves and their electromagnetic counterparts will open a new multi-messenger window on cosmology, gravity, and compact-object physics.","keywords":["gravitational lensing","gravitational waves","multi-messenger astronomy","gamma-ray bursts","fast radio bursts","kilonovae","Hubble constant","modified gravity"],"falsifier":"Run the scenario-1 calculation for one year at the assumed sensitivities: detecting no lensed short-GRB pair with matching light curves and time delays would rule out the roughly $10\\,{\\rm yr}^{-1}$ forecast, while finding the predicted number would support it. For the gravity test, a single strongly lensed GW+EM source with $\\Delta t_{\\rm GW}\\neq\\Delta t_{\\rm EM}$ in the geometric-optics regime (lens mass well above $10^5\\,M_\\odot$) would falsify the premise that equal delays are guaranteed by general relativity.","tokens_in":21117,"feed_emoji":"🔭","tokens_out":10915,"duration_ms":104042,"temperature":0.7,"pith_summary":"This review sets out to establish that strong gravitational lensing, applied jointly to gravitational-wave signals and their electromagnetic counterparts, is a practical and powerful multi-messenger tool rather than a rare curiosity. The core idea is that a lensed compact-binary merger repeats the same event with the same time-delay pattern in both the GW channel and the gamma-ray burst, kilonova, or fast radio burst channel, so the two messengers act as cross-checks on each other. The paper claims this enables tests of the speed and propagation of gravitational waves, sub-percent-level cosmological distance measurements, and early access to kilonova emission that would otherwise wait for third-generation detectors. Its most concrete forecasts are roughly ten detectable lensed short-GRB systems per year and about one GRB-lensed companion for every thirteen lensed GW events at design sensitivity, together with a false-alarm probability near $10^{-8}$ for associating a lensed FRB with a lensed GW pair. The authors argue that enabling this science requires rapid follow-up, cross-matching of lens catalogs with GW sky regions, and shared tools and databases.","feed_headline":"Lensed gravitational waves could expose ~10 gamma-ray bursts a year","feed_subtitle":"Matching repeated time delays across messengers tests gravity, sharpens H0, and recovers faint counterparts.","key_machinery":"The load-bearing object is the strongly lensed multi-messenger event: a compact-binary merger whose GW signal and its electromagnetic counterpart are both multiply imaged by a foreground galaxy. The governing identity is the equality of arrival-time delays across messengers, $\\Delta t_{\\rm GW}=\\Delta t_{\\rm EM}$ in the geometric-optics regime, with the delay set by the Fermat potential difference $\\Delta\\psi$ (the lensing quantity that controls arrival-time differences); this identity turns a time-delay measurement in one band into a prediction in the other. The paper's calculations also rest on a detection probability $P_{\\rm det}(\\theta,D_L)$ for short GRBs that is unity for on-axis jets within the core angle and falls off as a Gaussian in off-axis angle, and on network signal-to-noise thresholds (SNR greater than 6 or 8) for GW detectability, with wave-optics modulation allowed for low-mass lenses. Microlensing by stars in the lens galaxy is treated as a separate frequency-dependent distortion: wave-optics effects for GWs versus geometric-optics magnification for optical emission, which the paper proposes to use jointly to constrain the microlens population.","core_discovery":"The paper's central claim is that multi-messenger strong lensing turns the rare event of a lensed compact-binary merger into a high-precision laboratory. When a GW source with an electromagnetic counterpart is strongly lensed, the multiple GW arrivals and the multiple EM images share the same geometric and Shapiro time delays, so the difference $\\Delta t_{\\rm GW}-\\Delta t_{\\rm EM}$ isolates any messenger-dependent propagation effect without knowing the intrinsic emission delay. The same repeated-image structure lets a lensed FRB be associated with a lensed GW at false-alarm probability $\\sim 10^{-8}$, and lets sub-threshold GW images be recovered by searching a few seconds around a detected lensed GRB. The paper's quantitative estimates, from simulations reported here, are that combining gamma-ray monitors with a 50% sky duty cycle and a three-detector GW network at design sensitivity yields about $10\\,{\\rm yr}^{-1}$ detectable lensed GRB systems, and that starting from detectable lensed GW events gives about one associated lensed GRB per thirteen GW lenses. The authors further argue that lensed binary neutron star mergers, although rarer than lensed binary black hole mergers, are the more promising targets for modified-gravity and kilonova studies because they are more magnified, sit at higher redshift, and have detectable electromagnetic counterparts.","pith_inferences":["If the roughly ten-per-year lensed-GRB estimate holds, the first joint GW and GRB lensing seasons will simultaneously constrain the binary neutron star merger rate, the jet opening angle, and the short-GRB luminosity function, since all three enter the detection probability.","The time-delay matching strategy does not depend on the specific messenger: the same logic would apply to lensed neutrinos or other future signals, provided multiple images are resolved and arrival times can be measured.","The paper's idealized finding that double-image lenses have smaller Fermat-potential uncertainties than quads suggests that follow-up resources for lensed GW and GRB events should be weighted toward doubles; realistic-noise simulations would sharpen or overturn that targeting rule.","A null result in the first two years of joint gamma-ray and GW lens searches would itself constrain jet models, because the predicted rate rests on GRB 170817A-like luminosity and aligned-jet assumptions."],"forward_implications":["A combined year of design-sensitivity GW data plus gamma-ray data should find roughly ten lensed short-GRB systems, and about one in every thirteen lensed GW events should have a detectable lensed GRB counterpart in a two-second time window.","Lensed FRBs can be matched to lensed GW events at false-alarm probability near $10^{-8}$, which can identify counterparts even when one signal is sub-threshold or affected by wave-optics modulation.","A strongly lensed GW+EM source with measured $\\Delta t_{\\rm GW}$ and $\\Delta t_{\\rm EM}$ constrains the speed of gravitational waves without needing to know the intrinsic delay between the merger and its electromagnetic flash.","Lensed binary neutron star mergers at high redshift can deliver early-warning time-delay predictions on hour-to-day timescales, allowing kilonova observations within days and tighter constraints on ejecta properties and the neutron-star equation of state before third-generation detectors arrive.","Millisecond-precision time delays from lensed GW and FRB systems could carry $H_0$ constraints to sub-percent precision, complementing the few-percent-level results from lensed quasars."],"supporting_citations":[{"why":"Proposed that lensed GW time delays combined with EM data give far superior cosmological constraints, motivating the paper's sub-percent H0 discussion.","marker":"[45]"},{"why":"Introduced the strong-lensing method for testing the speed of gravitational waves over cosmological distances.","marker":"[51]"},{"why":"Independently showed how comparing time delays of lensed GW and EM signals constrains GW speed, forming the basis of Sec. 2(b)(i).","marker":"[52]"},{"why":"Provides the three modified-GW-propagation model parametrizations whose low- versus high-redshift contrast the paper uses to argue lensed sources are better gravity probes.","marker":"[55]"},{"why":"Predicts rates, selection, and localization of lensed GWs, used to argue lensed BNSs are high-redshift and electromagnetic-followable.","marker":"[56]"},{"why":"Supplies lensed BNS and NSBH time-delay predictions and early-warning fractions, used for kilonova follow-up scheduling.","marker":"[57]"},{"why":"Sets out the lensed FRB-GW association method, including false-alarm probabilities and the wave-optics posterior used in Fig. 3.","marker":"[88]"},{"why":"The source for the on-axis and off-axis GRB detectability formula used in the rate estimates.","marker":"[102]"},{"why":"Provides the joint GW-GRB luminosity function and detection-rate model used as input to the lensed GRB simulation.","marker":"[105]"},{"why":"The authors' own simulation that produces the scenario-2 rate of one lensed GRB per thirteen GW lenses.","marker":"[108]"}],"fun_headline_variants":["Lensed GWs may reveal 10 gamma-ray bursts yearly","Multi-messenger lensing: find GRBs, test gravity","Lensed mergers: ~10 GRBs per year for gravity tests","GW lensing ties GRBs, FRBs, and kilonovae","Gravitational lensing links messengers to test physics"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The predicted rates assume that every detectable short gamma-ray burst comes from a binary neutron-star merger, shines as brightly as GRB 170817A, and has its jet aligned with the binary's orbital inclination; if many short bursts instead come from neutron-star-black-hole mergers or have dimmer, broader jets, the forecast of about ten lensed GRB systems per year and one GRB companion per thirteen GW lenses shrinks.","fun_headline_variants_meta":{"raw":{"variants":["Lensed GWs may reveal 10 gamma-ray bursts yearly","Multi-messenger lensing: find GRBs, test gravity","Lensed mergers: ~10 GRBs per year for gravity tests","GW lensing ties GRBs, FRBs, and kilonovae","Gravitational lensing links messengers to test physics"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000573,"raw_usage":{"total_tokens":2709,"prompt_tokens":947,"completion_tokens":1762,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":563,"completion_tokens_details":{"reasoning_tokens":1673}},"tokens_in":563,"tokens_out":1762,"duration_ms":12929,"temperature":1.0,"reasoning_tokens":1673,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-09T11:49:24.313585+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the scenario-1 calculation for one year at the assumed sensitivities: detecting no lensed short-GRB pair with matching light curves and time delays would rule out the roughly $10\\,{\\rm yr}^{-1}$ forecast, while finding the predicted number would support it. For the gravity test, a single strongly lensed GW+EM source with $\\Delta t_{\\rm GW}\\neq\\Delta t_{\\rm EM}$ in the geometric-optics regime (lens mass well above $10^5\\,M_\\odot$) would falsify the premise that equal delays are guaranteed by general relativity.","supporting_citations":[{"cited_title":"2024 How well can modified gravitational wave propagation be constrained with strong lensing?","cited_arxiv_id":null,"evidence_quote":"Provides the three modified-GW-propagation model parametrizations whose low- versus high-redshift contrast the paper uses to argue lensed sources are better gravity probes."},{"cited_title":"2017 ARRIVAL TIME DIFFERENCES BETWEEN GRAVITATIONAL WAVES AND ELECTROMAGNETIC SIGNALS DUE TO GRAVITATIONAL LENSING","cited_arxiv_id":null,"evidence_quote":"Predicts rates, selection, and localization of lensed GWs, used to argue lensed BNSs are high-redshift and electromagnetic-followable."},{"cited_title":"2023 Associating fast radio bursts with compact binary mergers via gravitational lensing","cited_arxiv_id":null,"evidence_quote":"Sets out the lensed FRB-GW association method, including false-alarm probabilities and the wave-optics posterior used in Fig. 3."},{"cited_title":"2016 Perspectives on Gamma-Ray Burst 19royalsocietypublishing.org/journal/rsta Phil","cited_arxiv_id":null,"evidence_quote":"The source for the on-axis and off-axis GRB detectability formula used in the rate estimates."}],"review_version":1}