{"id":"afa10d0c-3bd7-42ff-81f5-be2874e56a97","arxiv_id":"1908.02401","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"Freeing the sound horizon and calibrating distances with three gravitational lenses yields H0 = 72 ± 7 km/s/Mpc and H0 r_s = 9895 ± 161 km/s, and r_s = 137 ± 4.5 Mpc when combined with H0LiCOW.","lead":"Cosmologists used distances from gravitational lenses, supernovae, and galaxy clustering to estimate the Hubble constant and the size of the sound horizon without relying on the cosmic microwave background. They find the sound horizon from late-time data is smaller than the CMB-inferred value, pointing to a real discrepancy in our cosmological model.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Headline r_s tension rests on the H0LiCOW H0, whose lens-model systematics are unquantified; the paper's own lens-calibrated H0 has ~10% error and does not by itself exclude the CMB r_s.","rationale":"The reader correctly identifies the lens-distance calibration as the weak link, and I agree that the three lens D_ang are the only absolute calibrators in the paper's own ladder. However, the sharper problem is that the tight 4.5 Mpc error on rs is not obtained from the paper's data alone; it comes from inserting the external H0LiCOW H0 into rs = H0rs / H0. The paper's own D_ang, with ~10% H0 precision, produce an rs uncertainty of ~14 Mpc, which comfortably includes the CMB value. Therefore the claim of a systematically lower rs is not an independent result of the inverse distance ladder; it is a restatement of the H0LiCOW–Planck H0 tension. Both the paper's D_ang and H0LiCOW's H0 depend on the same unquantified systematics (Osipkov-Merritt anisotropy and lensing/dynamical mass equality), and the paper itself notes that more general anisotropy models shift the distances. Because the direction of the known shift (Jee et al., subm.) would move rs even further from the CMB value, the concern is not about resolving the tension but about whether the significance can be trusted. The absence of any model-form systematic in the error budget makes the reported 2.2σ discrepancy unsupported. Given the paper's transparency and the plausibility of the methodology, the CONDITIONAL verdict remains appropriate; the authors should add the systematic or clearly state that the rs value depends on H0LiCOW's assumptions.","tokens_in":10212,"tokens_out":15097,"duration_ms":150940,"concrete_test":"Rerun the paper's MCMC likelihood (Eq. 6) with the three D_ang values and the external H0LiCOW H0 prior shifted by the offset between the Osipkov-Merritt and two-parameter anisotropy determinations of Jee et al. (subm., as cited in Sec. 2.3), propagating the implied systematic into both the lens calibrators and the H0 prior. Then recompute the 68% credible interval for rs. If the central rs shifts by more than 4.5 Mpc, or if 147 Mpc falls inside the shifted interval, the claimed discrepancy with the CMB sound horizon is not robust to the anisotropy-model assumption.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that the sound horizon from low-redshift probes is systematically lower than the CMB value rests on the step rs = H0rs / H0, with H0 taken from H0LiCOW (72.5 ± 2.3 km/s/Mpc). The paper's own data, however, yield H0 = 72 ± 7 km/s/Mpc and H0rs = 9895 ± 161 km/s. Propagating only the paper's own uncertainties gives rs about 137 ± 14 Mpc, which is within 0.7σ of the CMB value (147.05 ± 0.30 Mpc). Thus the inverse distance ladder alone, without the H0LiCOW H0, does not establish a discrepancy; the low rs is essentially imported from H0LiCOW. The paper's Section 2.3 explicitly states that the lens distances change when more general stellar-anisotropy models are used, and cites Jee et al. (subm.) as finding slightly smaller D_ang, which would move H0 upward and rs downward. Yet no systematic term for this model-form uncertainty is included in the quoted errors. Because the H0LiCOW H0 and the three D_ang calibrators share the same lensing/dynamical assumptions, a bias of only ~2–3 km/s in H0 (corresponding to Δrs ≈ 4–5 Mpc) would erase the claimed tension. The paper provides no estimate of such a bias, so the reported 4.5 Mpc error on rs is not the dominant uncertainty and the central claim is not yet supported.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper revisits the H0 and sound-horizon tension using an inverse distance ladder calibrated with angular-diameter distances to three H0LiCOW lenses, combined with JLA Type Ia supernovae and BAO measurements from BOSS, 6dFGS+SDSS-MGS, and WiggleZ, while leaving rs free. The expansion history is parameterized with a fourth-order cosmographic series, making the analysis independent of the Einstein field equations. The authors find H0rs = (9895 ± 161) km/s and H0 = (72 ± 7) km/s/Mpc from the lens-calibrated ladder, and, after combining H0rs with the H0LiCOW time-delay H0 = (72.5 ± 2.3) km/s/Mpc, they obtain rs = (137.0 ± 4.5) Mpc, which they interpret as systematically lower than the CMB-inferred value of about 147 Mpc. The paper also examines robustness to removing low-redshift supernovae and to BAO reconstruction choices.","tokens_in":10543,"tokens_out":4919,"duration_ms":47024,"significance":"If the claimed result were fully supported, it would be important because it would locate the late-time/early-time discrepancy in the absolute distance scale and the sound horizon rather than in the CMB-fixed value of rs, with implications for new physics or systematics in distance calibrations. The paper is transparent about the lens-anisotropy assumption and provides a useful comparison of results from different BAO data combinations. The likelihood treatment is standard, the data choices are clearly described, and the paper explicitly separates the model-independent combination H0rs from the absolute calibration step. However, as discussed in the major comments, the central claim of a tension in rs is not established by the inverse distance ladder alone: the paper's own H0 uncertainty of ±7 km/s/Mpc propagates to a ±14 Mpc uncertainty on rs, which is consistent with the CMB value, and the headline 4.5 Mpc error is achieved only by importing the H0LiCOW H0, whose lens-model systematics are not included in the error budget.","major_comments":[{"comment":"The central claim that low-redshift data yield a sound horizon systematically lower than the CMB value is not supported by the inverse distance ladder alone. Table 2 gives H0rs = (9895 ± 161) km/s and H0 = (72 ± 7) km/s/Mpc from the lens-calibrated ladder; dividing the former by the latter gives rs ≈ 137 ± 14 Mpc, which is within about 0.7σ of the Planck value rs = (147.05 ± 0.30) Mpc. The quoted rs = (137.0 ± 4.5) Mpc is obtained by instead dividing by the external H0LiCOW H0 = (72.5 ± 2.3) km/s/Mpc, whose lens-model assumptions are the same as those entering the three calibrating angular-diameter distances. The manuscript should state this dependence explicitly and present the propagated rs from Table 2 alongside the H0LiCOW-combined value.","section":"§3, Table 2"},{"comment":"The three angular-diameter distances are the sole absolute calibrators and dominate the error budget, but the quoted uncertainties do not include the model-form systematic of the assumed Osipkov-Merritt stellar-anisotropy profile or the assumed equality of lensing and dynamical mass. The paper itself notes that Jee et al. (submitted) obtain slightly smaller D_ang with more general anisotropy families, which would increase H0 and decrease rs. Because the external H0LiCOW H0 used for the headline rs shares these same assumptions, a bias of only 2–3 km/s/Mpc in H0 (corresponding to Δrs ≈ 4–5 Mpc) would erase the claimed tension. A quantitative estimate of this systematic needs to be included before the 4.5 Mpc error can be treated as the dominant uncertainty.","section":"§2.3, Table 1"},{"comment":"The fourth-order cosmographic expansion is fitted to BOSS BAO at z = 0.61 and to a lens at z = 0.745 without any estimate of truncation error. At these redshifts the expansion converges slowly, and the claim that the results are independent of the adopted expansion history requires a demonstration that higher-order terms (or a different model of H(z)) do not shift H0rs and H0 by more than the quoted errors. Please add a quantitative truncation test, for example by comparing fits with fifth- and sixth-order terms or by examining residuals.","section":"§2, Eqs. (1)–(4)"}],"minor_comments":[{"comment":"The reference to 'Barnal et al. (2016)' should be 'Bernal et al. (2016)' in both occurrences.","section":"Introduction and Discussion"},{"comment":"The prior ranges on the model parameters θ = (H0, rs, Ωk, q0, j0, s0, M) are not stated; please specify them, since the text reports uniform priors on rs but not the bounds on the other parameters.","section":"§2.4"},{"comment":"The y-axis label 'cln(1+z)/DM' should be typeset as 'c ln(1+z)/D_M' for clarity.","section":"Figure 1"},{"comment":"The statement that consistency of the 6dFGS DV point with other distance scalings would require H0 = (60 ± 6) km/s/Mpc is presented without derivation; given that this point is included in the fiducial fit, a short explanation of how this number was obtained would help the reader assess its impact.","section":"§4.2"}],"recommendation":"major_revision","confidential_remarks":"The paper is technically straightforward and transparent, but the headline claim is stronger than what the inverse distance ladder alone supports. The combination with H0LiCOW's H0 introduces the same lens-model systematics that dominate the calibrating distances, so the 4.5 Mpc error on rs is likely an underestimate. A major revision that adds a systematic-error term for the lens modeling and reframes the central claim as a consistency test conditioned on the H0LiCOW calibration would be appropriate; alternatively, the editors may wish to treat this as a methods note rather than a definitive claim of new tension."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nThe headline here is that the paper gives a clean, model-independent inverse-distance-ladder measurement of H0rs, but the claimed sound-horizon tension is not actually established by the low-redshift data alone: it appears only after combining their H0rs with the H0LiCOW H0, which shares the same lens-model assumptions as the three angular-diameter distances used for calibration. The paper is transparent about this in the text, but the abstract's phrasing overstates it.\n\nWhat is new is modest but real: a third lens (J1206) added to the earlier two-lens analyses, a robustness check to removing z<0.1 SNe, a distance-ratio consistency test between SNe, BAO and lensing, and a clear statement that the 6dFGS BAO point is internally inconsistent with other scalings, requiring H0 = 60 ± 6 to fit. Their H0rs = 9895 ± 161 km/s is robust across data combinations and agrees with Bernal et al. and Aylor et al. This is worth having as a cross-check.\n\nThe soft spots are the same as the stress-test note, and they matter. First, the r_s = 137 ± 4.5 Mpc is obtained by dividing their H0rs by the H0LiCOW H0, but the D_ang's and the time-delay distances come from the same lens modeling family. A bias of only 2–3 km/s in H0 would erase the tension. Their own lens-calibrated H0 = 72 ± 7 implies r_s ≈ 138 ± 14, fully compatible with Planck. So the 'systematically lower' conclusion is a prior-dependent statement, not an independent late-time measurement. Second, the 6dFGS point is included in the main analysis despite their own evidence that it is an outlier; excluding it shifts H0rs by ~80 km/s. That should be either justified or the analysis run without it. Third, the fourth-order expansion runs to z=0.8 with no truncation-error estimate; probably minor for BAO and SNe but worth a sentence. Fourth, the Osipkov-Merritt anisotropy and mass-equality assumptions in the D_ang are not given a systematic term; Jee et al.'s updated distances would shift the result.\n\nThe paper is honestly written, cites the relevant prior work, and the central H0rs measurement is solid. It just doesn't independently deliver the r_s tension it advertises. A good referee could push for an abstract rewrite and a rerun without 6dFGS. It deserves peer review.","headline":"Useful, honest inverse-distance-ladder analysis, but the advertised sound-horizon tension is largely inherited from the H0LiCOW H0 prior rather than independently established by the low-redshift data.","tokens_in":11150,"tokens_out":3779,"would_cite":true,"duration_ms":38706,"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":"Leaving the sound horizon free, a lens-calibrated low-redshift ladder returns H0 = 72 ± 7 and r_s = 137 ± 4.5 Mpc, below the CMB value.","keywords":["Hubble constant tension","sound horizon","inverse distance ladder","time-delay lenses","baryon acoustic oscillations","Type Ia supernovae","cosmography"],"falsifier":"Obtain spatially-resolved stellar kinematics for the three lens galaxies to determine their velocity-anisotropy profiles without the assumed Osipkov-Merritt form, then recompute the three angular-diameter distances; if the corrected distances move H0 r_s to a CMB-compatible value around 147 Mpc, the claimed low r_s dissolves.","tokens_in":9975,"feed_emoji":"🌌","tokens_out":7781,"duration_ms":71473,"temperature":0.7,"pith_summary":"Measuring the expansion rate H0 from low-redshift data usually requires assuming the sound horizon scale r_s from the cosmic microwave background. This paper removes that assumption. Using angular-diameter distances to three gravitationally lensed quasars to set the absolute scale, supernova and BAO data to trace relative distances, and a fourth-order cosmographic fit independent of any cosmological model, it obtains H0 = 72 ± 7 km/s/Mpc and H0 r_s = 9895 ± 161 km/s. Combined with the lens-based H0 measurement, this gives r_s = 137.0 ± 4.5 Mpc, systematically lower than the CMB-inferred value of about 147 Mpc. If correct, the early-versus-late universe tension is not an artifact of fixing r_s from the CMB; it is a genuine discrepancy in the cosmological model or in the distance calibration.","feed_headline":"Sound horizon from low redshifts: 137 Mpc, not 147","feed_subtitle":"Freeing r_s in the inverse distance ladder still yields a higher H0 and a real tension.","key_machinery":"The machinery is the inverse distance ladder built on a fourth-order polynomial expansion of the expansion history H(z)/H0 in redshift, with free coefficients for deceleration, jerk, snap, and curvature, together with the distance duality relations D_lum = (1+z)^2 D_ang = (1+z) D_M. Supernova and BAO relative distances set the shape of this expansion, while three lens angular-diameter distances fix the absolute scale; because r_s is left as a free parameter, the BAO data constrain the product H0 r_s rather than H0 alone. The lens distances carry about 80 percent of the error budget, so this absolute calibration is the load-bearing part of the argument.","core_discovery":"The paper shows that when r_s is left free and the distance ladder is calibrated by three time-delay lens angular-diameter distances, the low-redshift data independently prefer H0 = (72 ± 7) km/s/Mpc and H0 r_s = (9895 ± 161) km/s. Combining the latter with the lens-based H0 = 72.$5^{{+2.1}}$_{-2.3} km/s/Mpc yields r_s = (137.0 ± 4.5) Mpc, roughly 10 Mpc below the CMB-inferred value of about 147 Mpc. Because the analysis uses a cosmographic expansion and distance duality rather than a specific dark-energy model or a Cepheid calibration, the authors conclude that the H0/r_s tension reflects either new physics beyond standard cosmology or systematic errors in the low-redshift distance calibration, not the choice of r_s prior.","pith_inferences":["If future spatially-resolved lens kinematics remove the mass-anisotropy degeneracy and shift the lens distances upward, as the two-parameter anisotropy reassessment suggests, the inferred H0 would rise and the tension with the CMB would strengthen rather than dissolve.","The same distance-ratio test shown in the paper could be applied to gravitational-wave standard sirens, turning catalog-level data into a redshift-resolved check for distance-dependent systematics.","A robust low r_s from this ladder would favor early-universe solutions such as extra relativistic species or a smaller recombination scale, while a systematics explanation would point to anisotropic stellar distributions in the lens galaxies.","The product H0 r_s ≈ 9895 km/s, being independent of absolute calibration, is the sharpest number in the paper; improving BAO shape measurements could pin it down even before lens distances improve."],"forward_implications":["The early-to-late universe tension persists even when r_s is not pinned to the CMB, so it cannot be dismissed as a prior artifact.","Percent-level low-redshift H0 measurements, for example from future time-delay lens samples of ten to forty systems, would discriminate between r_s around 137 Mpc and around 147 Mpc.","The analysis is independent of the assumed dark-energy model because the fourth-order cosmographic expansion and distance duality are the only geometry assumptions.","Removing supernovae with z < 0.1 changes the results negligibly, so low-redshift supernova systematics and local peculiar velocities are not driving the outcome.","The low-redshift 6dFGS BAO distance is inconsistent with other distance scalings unless H0 is around 60 km/s/Mpc, which may explain the lower H0 seen in earlier inverse-ladder analyses."],"supporting_citations":[{"why":"Supplies two of the three lens angular-diameter distances (RXJ1131 and B1608) that set the absolute calibration scale.","marker":"Jee et al. (2015)"},{"why":"Supplies the third lens distance (J1206) and the lens-based H0 used to convert H0 r_s into r_s.","marker":"Birrer et al. (2019)"},{"why":"Supplies the JLA supernova distance moduli that propagate relative distances across the redshift range.","marker":"Betoule et al. (2014)"},{"why":"Supplies the BOSS consensus BAO distances and H(z) r_s in three redshift bins, the dominant BAO constraint.","marker":"Alam et al. (2017)"},{"why":"Supplies the low-redshift volume-averaged BAO distance whose inconsistency pulls H0 r_s downward.","marker":"Carter et al. (2018)"},{"why":"Supplies the inverse-distance-ladder formalism and the fourth-order expansion reused here.","marker":"Macaulay et al. (2018)"},{"why":"Earlier free-r_s inference giving a comparable r_s around 137 Mpc, which the paper's result confirms.","marker":"Bernal et al. (2016)"},{"why":"Earlier BAO-and-lensing r_s inference that serves as a comparison target for the H0 r_s measurement.","marker":"Aylor et al. (2018)"}],"fun_headline_variants":["Low-redshift r_s = 137 Mpc, 10 below CMB value","H0=72, r_s=137: low-redshift tension with CMB persists","Lens-calibrated ladder: r_s=137 Mpc, H0=72 km/s/Mpc","Freeing r_s yields H0=72 and r_s=137, still at odds with CMB","Time-delay lenses set r_s at 137 Mpc, 10 less than CMB"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The three lens angular-diameter distances are unbiased absolute calibrators, which requires the assumed stellar-orbit anisotropy in each lens to be correct and lensing mass to equal dynamical mass; these distances dominate the error budget.","fun_headline_variants_meta":{"raw":{"variants":["Low-redshift r_s = 137 Mpc, 10 below CMB value","H0=72, r_s=137: low-redshift tension with CMB persists","Lens-calibrated ladder: r_s=137 Mpc, H0=72 km/s/Mpc","Freeing r_s yields H0=72 and r_s=137, still at odds with CMB","Time-delay lenses set r_s at 137 Mpc, 10 less than CMB"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00074,"raw_usage":{"total_tokens":3331,"prompt_tokens":1003,"completion_tokens":2328,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":619,"completion_tokens_details":{"reasoning_tokens":2205}},"tokens_in":619,"tokens_out":2328,"duration_ms":17331,"temperature":1.0,"reasoning_tokens":2205,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T14:45:50.164910+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Obtain spatially-resolved stellar kinematics for the three lens galaxies to determine their velocity-anisotropy profiles without the assumed Osipkov-Merritt form, then recompute the three angular-diameter distances; if the corrected distances move H0 r_s to a CMB-compatible value around 147 Mpc, the claimed low r_s dissolves.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies two of the three lens angular-diameter distances (RXJ1131 and B1608) that set the absolute calibration scale."},{"cited_title":"L., Verde, L., & Riess, A","cited_arxiv_id":null,"evidence_quote":"Earlier free-r_s inference giving a comparable r_s around 137 Mpc, which the paper's result confirms."}],"review_version":1}