{"id":"6fb2444e-de6c-488e-b27f-248c1b710d81","arxiv_id":"2412.07532","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"Redshift drift forecasts that include spatial curvature show curvature sensitivity comparable to matter density and an open/closed asymmetry, with the first joint standard-plus-differential drift constraints for the ELT Golden Sample.","lead":"A forecasting study of redshift drift measurements for the SKA and ELT finds that sensitivity to spatial curvature is comparable to sensitivity to matter density, especially at low redshift, and stronger than sensitivity to the dark energy equation of state. It also provides the first joint forecast combining standard and differential redshift drift measurements for the ELT Golden Sample.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The joint drift FoM gain—the paper's main novelty—relies on zi/zr=0.15, but the Golden Sample Lyα forest only allows zi/zr≳0.7, so the gain is not observationally realizable.","rationale":"The reader's verdict focuses on the unverified uncertainty ratio between differential and standard drift. That is a valid concern, but a more fundamental problem precedes it: the joint forecast's best-case geometry is not observable. The differential technique is explicitly tied to the Lyα forest (Section 4), and for the Golden Sample quasars (z≈3–5) the forest only contains absorbers with zi/zr≳0.7. The paper's Table 5 and Figure 9 advertise a ~15% FoM gain at zi/zr=0.15, a configuration that would place Lyα absorption in the unobservable UV for ground-based ANDES. At the physical ratios, the differential drift is nearly degenerate with the standard drift, so the gain should be minimal. Recomputing the forecast with realistic zi/zr is a straightforward analytical check. This concern is independent of the uncertainty ratio; it invalidates the central novelty even under the most optimistic ratio assumption. The sensitivity-to-curvature claims (Sections 2–3) are mathematically sound and not affected. I therefore recommend CONDITIONAL acceptance, conditional on the joint forecast being redone for observable intervening redshifts, or the paper being revised to present the joint result only as a conceptual illustration. The reader's identified assumption, while real, is not the single most load-bearing one.","tokens_in":13665,"tokens_out":21121,"duration_ms":200728,"concrete_test":"Using the public FRIDDA code (or an independent Fisher calculation), recompute the Golden Sample joint FoM with the same fiducial models and priors, but restrict the differential drift to intervening redshifts actually accessible in the Lyα forest, e.g., zi = max(0.75(1+z_r)−1, 0) and zi/zr = 0.7 for all seven quasars (or the per-quasar minimum). If the FoM gain over standard drift plus priors drops below about 5% (instead of the reported 15%), the paper's main novelty claim is not observationally supported.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The paper's stated main novelty (Section 5) is the joint standard plus differential redshift drift forecast for the ANDES Golden Sample, with a maximal FoM gain of about 15% over standard drift plus priors (Table 5). This gain is obtained for zi/zr = 0.15 and equal velocity uncertainties. However, the differential technique as described in Section 4 relies on the Lyα forest. For a quasar at z_r in the Golden Sample (3.0 ≤ z_r ≤ 4.8), the Lyα forest spans rest wavelengths 91.2–121.6 nm, so an intervening absorber at zi has Lyα at 121.6(1+zi) nm. The lowest accessible zi (set by the Lyman limit of the quasar) is zi_min = 0.75(1+z_r)−1, giving zi_min ≈ 2.0 for z_r=3.0 and ≈3.35 for z_r=4.8, i.e., zi/zr ≈ 0.67–0.70. The assumed range zi/zr ∈ [0.15, 0.85] includes values for which the absorber's Lyα would be at 180–250 nm, unobservable from the ground. The paper's own Figure 9 shows the gain is largest at zi/zr≈0.15–0.25 and falls off rapidly, so at the physically allowed zi/zr≳0.7 the differential drift adds little information. Thus the quantitative joint-forecast claim is not realizable for the Golden Sample as observed by ANDES. The uncertainty-ratio concern identified in the reader's report is secondary; even a ratio of unity does not rescue the gain at inaccessible geometries.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript presents Fisher-matrix forecasts for standard and differential redshift drift measurements, allowing for a non-flat w0CDM background with free curvature Ωk. It derives analytic sensitivity coefficients from the Friedmann equation, reports that the sensitivity of the drift to curvature is comparable to that to matter and asymmetric between open and closed universes, and then produces forecasts for SKA and for the ELT ANDES Golden Sample. The paper's stated main novelty is a joint standard-plus-differential drift analysis for the Golden Sample (Section 5), which claims an additional up-to-15% figure-of-merit gain in the four-dimensional parameter space (Table 5).","tokens_in":14069,"tokens_out":12450,"duration_ms":120071,"significance":"The standard-drift forecasts with curvature are a useful and clearly presented extension of previous work, and the analytic sensitivity discussion is transparent and cross-checked with an independent code. The public availability of the Fisher code (FRIDDA) strengthens reproducibility. The open/closed asymmetry in sensitivities is an interesting qualitative result. However, the quantitative joint-measurement claim relies on observing geometries (zi/zr as low as 0.15) that are physically inaccessible for the Lyα-forest-based differential technique on the Golden Sample, which substantially limits the practical significance of the headline 15% gain.","major_comments":[{"comment":"The assumed range zi/zr ∈ [0.15,0.85] and the 'best case' zi/zr = 0.15 used to quote the maximal FoM gain in Table 5 are not physically realizable for the differential redshift drift technique as described in Section 4, which relies on the Lyman-α forest. For a Golden Sample quasar at zr, the lowest-redshift intervening absorber whose Lyα line falls in the observed spectrum is set by the blue cutoff of the forest; with a conservative 400 nm atmospheric/instrument cutoff for ANDES, zi_min ≈ 2.29, giving zi/zr ≈ 0.76 for the lowest-redshift quasar (zr = 3.0), and the ratio is only slightly lower (≈0.67) even if the Lyman limit at 91.2 nm is used. At the accessible ratios zi/zr ≳ 0.7, Figure 9 shows that the differential drift adds only a few percent to the FoM, so the reported 'additional 15%' is not observationally realizable. The authors should recompute the joint forecast for physically allowed geometries, or explicitly demonstrate an alternative absorption-line strategy that reaches low zi, and adjust the claims in Section 5 and the abstract accordingly.","section":"Section 5, Table 5 and Figure 9"}],"minor_comments":[{"comment":"The caption reads 'rounded off the the nearest integer'; this should be 'rounded off to the nearest integer'.","section":"Table 5 caption"},{"comment":"It would aid the reader if the physically allowed range of zi/zr (roughly ≳0.7) were marked on the figure, so that the falloff of the gain at accessible geometries is immediately visible.","section":"Figure 9"},{"comment":"The text states that the definitions differ by a minus sign from [7,20] to recover the standard drift when zi = 0; it would be helpful to note explicitly that this sign choice also affects the sign of the plotted sensitivity coefficients, so that readers comparing with earlier work are not confused.","section":"Section 4, Eq. (10)-(12)"},{"comment":"The indirect measurement S_v(zi,0) = S_v(zr,0) − S_v(zr,zi) is correctly described as non-independent, but the text could state that its uncertainty is the quadrature sum of the two direct measurements, which is relevant for the proposed SKA consistency test.","section":"Section 6, Eq. (13)"}],"recommendation":"major_revision","confidential_remarks":"The standard redshift-drift analysis (Sections 2-3) is solid and publishable in principle. The main barrier is the unrealistic observing geometry assumed for the differential-drift joint forecast, which is presented as the paper's main novelty. If the authors restrict the forecast to allowed zi/zr, or provide a concrete alternate observing method reaching low zi, the quantitative claim would need to be substantially revised; otherwise the differential-drift section should be presented as a purely conceptual exploration. I recommend major revision rather than rejection because the issue is fixable in scope."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper's curvature sensitivity analysis is genuinely useful and well executed. The quantitative inclusion of Omega_k in standard redshift drift forecasts, the open/closed asymmetry, and the analytic derivative discussion are all solid, and the code is public and cross-checked. If you only care about whether curvature will matter for SKA and ELT planning, that part is reliable. The problem is the paper's stated main novelty: the joint standard plus differential redshift drift forecast for the ANDES Golden Sample. The claimed FoM gain of about 15% is computed at zi/zr = 0.15, but that geometry is not observable in the Golden Sample. For a quasar at zr between 3.0 and 4.8, the Ly-alpha forest only extends down to the Lyman limit, which sets zi_min = 0.75(1+zr)-1, i.e. zi/zr in about 0.67-0.70. At those ratios, Figure 9 shows the differential drift adds almost nothing. The reader's concern about the unverified noise ratio is secondary; even equal uncertainties don't rescue the inaccessible geometry. The paper itself recommends zi in 0.75-1.25, which is below the forest limit for these quasars, so this is not an internal inconsistency the authors caught. I checked the stress-test note and it holds up. The threshold calculation is right, and the paper's own figure confirms the gain is concentrated at low zi/zr. The standard drift forecasts with curvature, the sensitivity ranking, and the asymmetry are worth publishing. The joint forecast section should be either restricted to physically accessible geometries or explicitly reframed as a conceptual illustration with no quantitative claim for the Golden Sample. This deserves a serious referee, not a desk reject, because the useful half is solid and the flawed half is instructive. But I would not cite it as it stands, and I wouldn't bring it to reading group without flagging the geometry problem first.","headline":"Solid curvature-sensitivity analysis, but the headline joint differential-drift forecast rests on an observationally inaccessible part of parameter space.","tokens_in":546,"tokens_out":948,"would_cite":false,"duration_ms":48571,"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":"Redshift drift measurements are more sensitive to spatial curvature than earlier flat-universe forecasts assumed, and joint standard plus differential drift measurements can add roughly 15% to the ELT Golden Sample's constraining power.","keywords":["redshift drift","Sandage test","spatial curvature","Fisher matrix forecasts","differential redshift drift","ELT ANDES Golden Sample","SKA","w0CDM"],"falsifier":"Measure, via end-to-end simulations of the differential drift reduction on the seven ANDES Golden Sample quasars, the achieved spectroscopic velocity uncertainty relative to the standard drift at intervening redshifts near $z_i/z_r\\approx0.15$–$0.25$; if the typical ratio is $\\gtrsim2$, the claimed $\\sim15\\%$ four-dimensional figure-of-merit gain from joint measurements does not materialize.","tokens_in":13486,"feed_emoji":"🔭","tokens_out":8374,"duration_ms":76865,"temperature":0.7,"pith_summary":"Redshift drift—the slow change in an object's redshift as the universe expands—is the most model-independent cosmological probe planned for the next generation of telescopes. This paper relaxes the usual flat-universe assumption in forecasts for the SKA and the ELT's ANDES Golden Sample, and finds that the drift's sensitivity to spatial curvature is comparable to its sensitivity to matter density, especially at low redshifts, and larger than its sensitivity to the dark energy equation of state. The sensitivity is also asymmetric in the sign of curvature, so closed and open universes with the same $|\\Omega_k|$ are not equally easy to constrain. For the Golden Sample, the paper provides the first forecasts of jointly measuring the standard and differential redshift drift along the same line of sight, reporting a best-case gain of about 15% in the four-parameter figure of merit. That gain is fragile: if the differential drift's velocity uncertainty is more than about twice the standard drift's, most of the improvement disappears.","feed_headline":"Differential redshift drift adds 15% to forecast power","feed_subtitle":"Joint ELT drift measurements sharpen curved-universe constraints, but only if differential velocity errors stay comparable.","key_machinery":"The carrying object is the dimensionless redshift drift $S_z = h[1+z-E(z)]$, with the corresponding spectroscopic velocity $S_v = (cH_0\\Delta t)[1-E(z)/(1+z)]$, evaluated in a curved $w_0$CDM background. The forecast machinery is the Fisher matrix $F_{ij}=\\sum_a (\\partial f_a/\\partial p_i)(1/\\sigma_a^2)(\\partial f_a/\\partial p_j)$, whose inverse gives parameter covariances and whose determinant's inverse $n$th root defines the global figure of merit. The differential drift is modeled as the difference $S_z(z_r,z_i)=h[(z_r-z_i)-(E(z_r)-E(z_i))]$, and the paper's central comparison is between the theoretical sensitivity coefficients $\\partial S/\\partial p_i$ for the four parameters and across fiducial values $\\Omega_k = -0.1, 0, +0.1$.","core_discovery":"On the paper's own terms, the central discovery is that spatial curvature is not a peripheral nuisance in redshift drift cosmology: it is a first-class parameter with sensitivity comparable to matter and greater than the dark energy equation of state. Working in a $w_0$CDM model with $E^2(z)=\\Omega_k(1+z)^2+\\Omega_m(1+z)^3+(1-\\Omega_m-\\Omega_k)(1+z)^{3(1+w_0)}$, the authors show that the drift's sensitivity coefficients to $\\Omega_k$ and $\\Omega_m$ behave similarly at low redshifts, and that the sensitivity to curvature is larger for closed than for open universes of the same $|\\Omega_k|$. They then forecast, for the first time, joint standard and differential drift measurements on the seven Golden Sample quasars: with an intervening-to-reference redshift ratio around 0.15 and equal velocity uncertainties, the joint measurement improves the four-dimensional figure of merit by about 15% over standard drift plus priors, and the same data yield an indirect low-redshift measurement $S_v(z_i,0)=S_v(z_r,0)-S_v(z_r,z_i)$ that bridges the ELT and SKA redshift ranges.","pith_inferences":["The authors do not pursue model selection, but the sign asymmetry implies that a single well-placed low-redshift drift detection could discriminate closed from open universes more cleanly than Gaussian parameter contours suggest.","Their fixed-ratio assumption treats all seven quasars identically; allowing each line of sight its own intervening redshift would likely redistribute, and possibly increase, the reported joint gain.","Because the differential measurement uses absorption features already in the same spectra, the joint analysis is best read as a data-analysis upgrade to an already planned observation rather than a new observing program.","The assumed proportionality between differential and standard velocity uncertainties could be tested with existing high-resolution spectrograph data before the ELT era, giving an early empirical check on the forecast's main condition."],"forward_implications":["SKA and ELT/ANDES redshift drift forecasts that assume flatness will overstate their constraining power, particularly for $\\Omega_m$, because the strong $\\Omega_m$–$\\Omega_k$ anticorrelation weakens matter constraints when curvature is freed.","A future drift detection at $z\\approx1$ carries information about the sign of curvature: closed universes give a larger positive-drift window than open universes with the same $|\\Omega_k|$, so the same measurement has different discriminating power in the two cases.","Joint standard and differential drift measurements on the Golden Sample add roughly 15% to the four-parameter figure of merit at no extra telescope time, provided the differential drift velocity uncertainty is comparable to the standard one and the intervening redshift is low, $z_i/z_r\\approx0.15$–$0.25$.","Because $S_v(z_i,0)=S_v(z_r,0)-S_v(z_r,z_i)$, Golden Sample measurements can synthesize a prediction for low-redshift drift that the SKA can test directly; a mismatch, absent systematics, would indicate a breakdown of the cosmological principle.","If the differential drift velocity uncertainty is a factor of two worse than the standard drift's, most of the joint-measurement gain disappears, so the main observing-strategy requirement is to keep the two uncertainties comparable."],"supporting_citations":[{"why":"defines the redshift drift observable that the paper forecasts.","marker":"[1]"},{"why":"establishes the ELT route for high-redshift drift measurements and the Lyman-α forest method.","marker":"[2]"},{"why":"proposes the differential redshift drift technique that the paper models and forecasts.","marker":"[7]"},{"why":"supplies the SKA low-redshift measurement program and its assumed velocity uncertainties.","marker":"[8]"},{"why":"provides the standard small-curvature constraints that motivate testing non-flat universes.","marker":"[15]"},{"why":"presents the disputed closed-universe evidence that motivates including Ω_k as a free parameter.","marker":"[16]"},{"why":"defines the seven-quasar ANDES Golden Sample used for the ELT forecasts and joint measurements.","marker":"[17]"},{"why":"provides the Fisher forecast code that the paper extends to include curvature.","marker":"[19]"},{"why":"gives the earlier exploration of differential redshift drift characteristics that the joint forecast builds on.","marker":"[20]"}],"fun_headline_variants":["Curvature rivals matter in redshift drift sensitivity","Open and closed universes skew drift sensitivity","Joint drift probes boost forecast power 15%"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The joint-forecast gain assumes the differential redshift drift's per-target spectroscopic velocity uncertainty is proportional to the standard drift's—equal, twice, or four times worse—and the actual ratio has not been measured; if it is worse than about two, Figure 9 shows that most of the differential drift's figure-of-merit gain disappears.","fun_headline_variants_meta":{"raw":{"variants":["Curvature rivals matter in redshift drift sensitivity","Open and closed universes skew drift sensitivity","Joint drift probes boost forecast power 15%"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000312,"raw_usage":{"total_tokens":1789,"prompt_tokens":971,"completion_tokens":818,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":587,"completion_tokens_details":{"reasoning_tokens":772}},"tokens_in":587,"tokens_out":818,"duration_ms":8900,"temperature":1.0,"reasoning_tokens":772,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T18:44:50.006131+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure, via end-to-end simulations of the differential drift reduction on the seven ANDES Golden Sample quasars, the achieved spectroscopic velocity uncertainty relative to the standard drift at intervening redshifts near $z_i/z_r\\approx0.15$–$0.25$; if the typical ratio is $\\gtrsim2$, the claimed $\\sim15\\%$ four-dimensional figure-of-merit gain from joint measurements does not materialize.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"provides the Fisher forecast code that the paper extends to include curvature."},{"cited_title":"Sandage, The Change of Redshift and Apparent Luminosity of Galaxies due to the Deceleration of Selected Expanding Universes., Astrophys","cited_arxiv_id":null,"evidence_quote":"defines the redshift drift observable that the paper forecasts."},{"cited_title":"Liske, et al., Cosmic dynamics in the era of Ex- tremely Large Telescopes, Mon","cited_arxiv_id":null,"evidence_quote":"establishes the ELT route for high-redshift drift measurements and the Lyman-α forest method."},{"cited_title":"Cooke, The ACCELERATION programme: I","cited_arxiv_id":null,"evidence_quote":"proposes the differential redshift drift technique that the paper models and forecasts."},{"cited_title":"Kl ¨ockner, D","cited_arxiv_id":null,"evidence_quote":"supplies the SKA low-redshift measurement program and its assumed velocity uncertainties."},{"cited_title":"Aghanim, et al., Planck 2018 results","cited_arxiv_id":null,"evidence_quote":"provides the standard small-curvature constraints that motivate testing non-flat universes."},{"cited_title":"Di Valentino, A","cited_arxiv_id":null,"evidence_quote":"presents the disputed closed-universe evidence that motivates including Ω_k as a free parameter."},{"cited_title":"Cristiani, et al., Spectroscopy of QUBRICS quasar candidates: 1672 new redshifts and a golden sample for the Sandage test of the redshift drift, Mon","cited_arxiv_id":null,"evidence_quote":"defines the seven-quasar ANDES Golden Sample used for the ELT forecasts and joint measurements."},{"cited_title":"Esteves, C","cited_arxiv_id":null,"evidence_quote":"gives the earlier exploration of differential redshift drift characteristics that the joint forecast builds on."}],"review_version":1}