{"id":"8c335ef7-dbcb-4be1-9dea-17c83b1a00bc","arxiv_id":"2509.09797","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"The angular size of a dust wormhole's shadow in a closed Friedmann universe first decreases, then increases with observation time, following a power-law relation in the wormhole size.","lead":"Scientists calculated the shadow an observer would see from a wormhole made of dust inside a closed, expanding universe. The shadow's size first shrinks as slow light rays arrive, then grows as cosmic expansion dominates, giving a distinctive time-varying signature.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Small-eta approximation is pushed beyond its validity: Fig. 5 observation times exceed the throat lifetime (tau > 2 pi b) and the power law uses L_min at the throat where eta >> 0.1.","rationale":"The reader's weakest_assumption correctly identified the small-eta approximation with tau0=0 as a limitation, but framed it as an acknowledged incompleteness affecting only later epochs or different formation times. The stress-test reveals a stronger, internal problem: the reported figures themselves violate the approximation's validity. Fig. 5 plots observation times tau_obs/b between 25 and 40, whereas the exact elliptic LTB solution (Eq. 5) gives a throat collapse at tau=2 pi b ~ 6.28 b; the small-eta metric (7) is a Taylor expansion around eta=0 that incorrectly predicts unbounded growth r ~ tau^(2/3) and misses the recollapse entirely. The same issue invalidates the power-law derivation: Eq. (36) uses L_min, whose turning point is at the throat R_t=0, where eta is largest and the small-eta condition fails most severely. The paper's own Section 5 acknowledges eta increases near the throat, but does not connect this to the plotted curves or the scaling law. If the exact computation shows the throat is already singular at the plotted times, then the non-monotonic shadow and the chi_*^(1+2k/3) scaling are not reliable predictions of the model as stated. A simple analytical check of the throat radius at the relevant observation times settles the matter, which is why this concern is load-bearing and why the conditional acceptance suggested by the reader is not justified without major revision or rederivation in the full LTB solution.","tokens_in":9963,"tokens_out":37841,"duration_ms":249646,"concrete_test":"Evaluate the exact LTB throat radius r(0,tau) from Eq. (5) at the observation times used in Fig. 5 (tau_obs/b=25-40) and for the eta_obs=1.1 configuration of Fig. 6; because r(0,tau)=2b sin^2(eta/2) with tau=b(eta-sin eta), it vanishes for tau >= 2 pi b ~ 6.28 b, which would show that the wormhole throat no longer exists in the plotted range and that the small-eta geodesics (16)-(20) are inapplicable.","verdict_should_be":"REJECT","load_bearing_attack":"The central claims—the non-monotonic shadow in Fig. 5 and the scaling law (38)—are produced by the small-eta expansion of Section 3.2, but they are evaluated outside the domain of that expansion. For the throat R=0, Eqs. (5) with tau0=0 give tau=b(eta-sin eta), so the exact throat recollapses at tau=2 pi b ~ 6.28 b; the small-eta formulas (7), valid for eta << 1, describe only tau << b and never recollapse. Fig. 5 plots tau_obs/b from 25 to 40, and Fig. 4 uses tau_obs/b ~ 38, i.e., 4-6 times the throat lifetime. At those epochs the throat's local parameter is eta ~ (6 tau/b)^(1/3) ~ 5-6, so the stated validity bound eta <= 0.1 is exceeded by orders of magnitude; the geodesic equations (16)-(20) and the turning-point condition (23) do not describe the actual geometry. The scaling (38) is no safer: it substitutes L_min from Eq. (36), whose turning point is at R_t=0 (the throat), the place where eta is maximal and the approximation fails most severely. Section 5 admits that eta grows near the throat, but does not apply this caveat to Fig. 5 or Eq. (38). Thus the paper's two headline results are not established by its own approximations; they may be artifacts of extrapolating a leading-order expansion into a regime where the wormhole has already collapsed.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies gravitational lensing by time-dependent Lemaître-Tolman-Bondi (LTB) dust wormholes that are matched to a closed Friedmann dust-filled universe. The authors derive null geodesic equations in the LTB metric within a small-η approximation, match the wormhole region to the Friedmann cosmology via the conditions of Ref. [14], and define a time-dependent shadow as the set of directions from which photons have not yet reached the observer by a given observation time. The central results are a claimed non-monotonic dependence of the shadow angular size on observation time, caused at early times by the gradual arrival of smaller-angular-momentum photons and at later times by the cosmological expansion, and a scaling law d_sh ∼ χ_*^{1+2k/3} for the shadow size as a function of the wormhole boundary coordinate χ_*. The paper is presented as an initial-stage analysis, with the limitations of the small-η approximation and the choice τ_0(R)=0 acknowledged in the conclusion.","tokens_in":10354,"tokens_out":15177,"duration_ms":134740,"significance":"If the results were established, this would be a useful contribution to the observational phenomenology of dynamic wormholes, providing one of the first treatments of a time-dependent wormhole shadow in a cosmological setting. The paper contains a careful derivation of the geodesic equations in the small-η regime, explicit matching conditions, and numerical plots of photon paths and shadow sizes. However, the two headline claims are derived and plotted in regimes where the small-η approximation is not valid, and the paper's own conclusion admits that the analysis covers only the initial stage. Because the non-monotonic shadow and the power-law scaling are consequences of extrapolating the approximation into regimes where the throat has either collapsed or has η significantly larger than 0.1, the significance is currently conditional on a substantial revision that addresses the validity domain.","major_comments":[{"comment":"The small-η approximation is stated in Section 2 (after Eq. (7)) to be valid for η≤0.1, which at the throat R=0 corresponds to τ/b≈η^3/6≤1.7×10^-4, while the exact LTB throat, from Eq. (5) with h=1 and F=2b, recollapses at τ=2πb≈6.28b. However, Figs. 4 and 5 display observation times τ_obs/b≈27, 38, and 40, which are both orders of magnitude beyond the η≤0.1 validity bound and later than the throat recollapse. At those epochs the configuration is no longer a wormhole, so the claimed non-monotonic shadow is not a property of the physical model under study. The authors need to restrict the plots to times before the throat recollapses and to epochs where η≤0.1 along the entire photon path, or to solve the geodesic equations in the exact LTB metric.","section":"§4.3, Figs. 4–5"},{"comment":"The shadow boundary at late observation times is controlled by photons whose angular momentum tends to L_min, which have a turning point at the throat R_t=0 according to Eq. (23). At R=0 the parameter η is maximal: for L=L_min the integrand in Eq. (20) diverges at the turning point, so the affine parameter and the coordinate time τ grow without bound, and the small-η assumption fails precisely at the location where the scaling d_sh∼χ_*^{1+2k/3} is evaluated. Section 5 acknowledges that η increases near the throat, but this caveat is not applied to Eq. (38) or to Fig. 5. The power law is therefore not established; a full treatment of the geodesics or a rigorous error bound that covers the photon ensemble defining the shadow boundary is required.","section":"§4.3, Eqs. (36)–(38)"},{"comment":"Figure 5 reports τ_obs/b ranging from about 25 to 40 for χ_*≈0.015, but using the matching relation b=a0 sin^{3+2k}χ_* and the observer parameters (χ_obs=1, η_obs=1.1) that are used for Table 1 gives τ_obs/b≈1.4×10^5, not the plotted range. The paper does not state the η_obs values corresponding to Fig. 5; if the plotted range actually corresponds to smaller η_obs, then the claimed non-monotonic dependence is not being presented for the same observer configuration as the rest of the paper. This inconsistency must be clarified and reconciled.","section":"§4.3, Fig. 5 vs. Table 1"}],"minor_comments":[{"comment":"The heading contains a typo: 'pohoton motion' should be 'photon motion'.","section":"§3, heading"},{"comment":"The symbol L is used both for the Lagrangian and for the conserved angular momentum; please use a different symbol for one of them to avoid confusion.","section":"§3.1, Eq. (12)"},{"comment":"The expression for α_sh should be derived step by step; as written the factors (1−cos η_obs)^2 in the numerator and denominator are not transparent and the overall dimensions are unclear.","section":"§4.3, Eq. (34)"},{"comment":"The 'black line' in Fig. 6 should specify whether it is the analytic expression (38) with a fixed normalization or a numerical fit, and the adopted proportionality constant should be given.","section":"§4.3, Fig. 6"},{"comment":"The description of Ref. [18] is somewhat dismissive; a neutral formulation would be more appropriate for a journal report.","section":"§1, Introduction"}],"recommendation":"major_revision","confidential_remarks":"The paper is part of a coherent research program and the self-citation to Ref. [14] is appropriate. The decisive issue is the validity of the small-η extrapolation; if the authors cannot provide a validity check or redo the shadow calculation in the exact LTB metric, the central claims may not survive review. I recommend major revision rather than rejection because the setup is plausible and the required fix is identifiable, but it is substantial."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague —\n\nThis is a real extension of the authors' earlier LTB-wormhole program. For the first time they compute photon deflection and a 'shadow' for a dynamic, dust-sourced wormhole embedded in a closed Friedmann universe, and they get two concrete qualitative results: the shadow size initially decreases with observation time as low-angular-momentum rays arrive, then increases as cosmic expansion wins; and the shadow scales as d_sh ~ chi_*^{1+2k/3}. The geodesic derivation in Sec. 3 is clean, with explicit error estimates around 10^-3 for eta <= 0.1, and the matching to the Friedmann model follows their earlier paper. The citations are appropriate, with the main load-bearing reference being their own [14], which is legitimate here since they are extending that program.\n\nThe soft spots are in the domain of the approximation and in the presentation. Everything rests on eta small and tau0 = 0, i.e., a wormhole born with the universe and probed by photons that cross it almost immediately. The authors acknowledge this in Sec. 5, but the abstract and Sec. 4 state the results more broadly. The 'shadow' itself is defined by the minimum-angular-momentum photon that reaches the observer by the observation time; that is a nonstandard, time-dependent definition, and it needs a clear statement and a sanity check against, say, a static-wormhole shadow in the same formalism.\n\nThe stress-test note's recollapse argument does not, on reading, land. The photons in the wormhole region have small eta by construction; the throat's eta at the observer's proper time is not what enters the geodesic equations. The real problem is the plotting range in Fig. 5. For chi_* ~ 0.015, one has b/a0 ~ 1.5e-6, so tau_obs/b = 25-40 corresponds to eta_obs ~ 0.06-0.08. A light ray from a wormhole at comoving distance ~1 from the observer cannot arrive until eta_obs ~ 1. So the plotted times are before the wormhole is observable; the shadow is undefined there. This needs reconciliation or a different x-axis. Also, the scaling (38) is a consequence of the chosen F(R) and the matching, not an independent prediction; calling the dots in Fig. 6 a numerical confirmation overstates what is essentially a curve of the same model.\n\nThis paper is for people working on observational signatures of wormholes and exotic compact objects. It deserves a serious referee; the math is careful and the idea is legitimately new. With a sharper boundary on the domain and a corrected observation-time axis, it can be a useful contribution.","headline":"Careful first lensing study of dynamic LTB wormholes, with a time-dependent shadow and a scaling law, but the plotted observation-time range in Fig. 5 appears to be before the wormhole is causally visible, so the headline results need re-scoping.","tokens_in":10868,"tokens_out":22089,"would_cite":false,"duration_ms":445708,"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":"This paper shows that the shadow of a dynamic wormhole in an expanding universe first shrinks and then grows, and that its angular size obeys a specific power law in the wormhole's size.","keywords":["gravitational lensing","wormhole shadow","Lemaitre-Tolman-Bondi solution","Friedmann universe","null geodesics","dynamic wormhole","cosmic expansion","dust cosmology"],"falsifier":"Integrate null geodesics numerically in the exact LTB metric for the same F(R)=2b(1+$R^{2}$)^k and h(R)=1/(1+$R^{2}$) without expanding in eta, place an observer at chi_obs=1, and measure the shadow angular diameter at several observation times. If the curve is monotone rather than shrink-then-grow, or if the d_sh versus chi_* data at fixed observation time deviate from the chi_*^{1+2k/3} slope, the paper's central claim is refuted.","tokens_in":9781,"feed_emoji":"🌀","tokens_out":5209,"duration_ms":49559,"temperature":0.7,"pith_summary":"The paper studies gravitational lensing by a wormhole built from the Lemaitre-Tolman-Bondi dust solution and embedded in a closed dust-filled Friedmann universe. It claims that the shadow a distant observer sees has an angular size that is non-monotonic in observation time: at early times the shadow shrinks as photons with smaller angular momentum gradually arrive, and at later times it grows because cosmic expansion dominates. It also derives a power law d_sh ~ chi_*^{1+2k/3} connecting the shadow angular size to the wormhole boundary coordinate and the density-profile exponent. If correct, evolving wormholes would have a distinctive time-dependent lensing signature that static wormhole models do not possess. The authors present this as a first-stage result under a small-eta approximation with tau_0(R)=0, so the detailed conclusions are restricted to wormholes born with the universe and observed in their early evolution.","feed_headline":"A wormhole's shadow shrinks, then grows, with cosmic time","feed_subtitle":"Angular size first drops as slow photons arrive, then rises as cosmic expansion stretches the sky—a signature static wormholes lack.","key_machinery":"The central object is an LTB wormhole matched to a closed dust-filled Friedmann universe through the choices F(R)=2b(1+$R^{2}$)^k and h(R)=1/(1+$R^{2}$), with matching conditions at a boundary chi_* linking the wormhole coordinate R_* to the cosmological coordinate chi_*. The argument runs through the small-eta approximation r ~ (3/2)^{2/3} $F^{{1/3}}$ $tau^{{2/3}}$, which reduces photon motion to turning points at F(R_t)=(500/243)(L/C)^3. The shadow radius is then obtained from the standard coordinate formula for image angles, with L_sh replaced by the minimum angular momentum L_min ~ $\\sqrt$(K) chi_*^{1+2k/3}, yielding the power-law angular size.","core_discovery":"In the small-eta regime, the boundary of the wormhole shadow on the observer's sky is set by the smallest photon angular momentum L_sh that has reached the observer by the observation time tau_obs. Early in the observation, this boundary moves inward because lower-L photons keep arriving, so the shadow shrinks; later, the expansion of the Friedmann universe stretches the image and the shadow grows. Analytically, the shadow diameter obeys d_sh ~ chi_*^{1+2k/3}, where chi_* is the coordinate boundary of the wormhole region and k is the exponent in the mass-distribution function F(R)=2b(1+$R^{2}$)^k, and the paper reports that numerical ray tracing confirms this power law. The authors emphasize that the analysis covers only the beginning of the wormhole's evolution, when it appears together with the universe, and that late-forming wormholes require dropping the small-eta and tau_0=0 assumptions.","pith_inferences":["Beyond the paper, a full numerical integration of null geodesics in the exact LTB metric without the small-eta cutoff could test whether the two-phase shrink-then-grow shadow persists for photons that pass near the throat, where eta grows large.","As an extension, if the non-monotonic signature survives for wormholes formed at later cosmic times, it would offer a way to distinguish LTB wormholes from static wormholes and ordinary lenses, whose shadows do not shrink then grow.","One testable extension is to scan other density profiles F(R): if the shadow size continues to follow a power law in chi_* with an exponent set by the profile, shadow scaling would become a probe of the radial mass distribution rather than a special property of the chosen model.","A further editorial inference is that the late-time growth phase might be observable as a population of lensing objects whose shadows enlarge at a rate tracking cosmic expansion, a signature that could be sought in time-domain surveys."],"forward_implications":["An observer watching a young LTB wormhole should see its shadow shrink as lower-angular-momentum photons keep arriving, then grow as cosmic expansion dominates.","Because the shadow size scales as chi_*^{1+2k/3}, a measured angular size would constrain the combination of wormhole-region size and dust-density exponent.","The shadow boundary is time-dependent rather than set by closed photon orbits, so dynamic wormholes have no single static shadow radius and any observational report must specify the observation time.","The results apply to wormholes born simultaneously with the universe; later-forming wormholes or late-time observations require an extension beyond the small-eta, tau_0=0 regime, as the paper itself notes.","The dust-density deficit around wormhole regions may connect such objects to observed cosmic voids, suggesting a possible observational target beyond direct shadow imaging."],"supporting_citations":[{"why":"Provides the LTB wormhole model, the matching conditions to a closed Friedmann universe, and the earlier traversability analysis that this paper extends to lensing.","marker":"[14]"},{"why":"Establishes the elliptic-branch LTB wormhole and the throat conditions used here.","marker":"[13]"},{"why":"Supplies the parametric LTB solution in terms of eta that underlies the small-eta expansion.","marker":"[24]"},{"why":"Defines the Lemaitre form of the LTB dust solution used as the starting geometry.","marker":"[15]"},{"why":"Gives Tolman's formulation of the inhomogeneous dust cosmology on which the wormhole model is built.","marker":"[16]"},{"why":"Provides Bondi's analysis of spherically symmetric dust models that fixes the dynamical framework.","marker":"[17]"},{"why":"Supplies the coordinate formula that converts photon arrival directions into image angular coordinates for the shadow radius.","marker":"[25]"}],"fun_headline_variants":["Wormhole shadow: down then up with cosmic time","LTB wormhole shadow: shrink then stretch","Cosmic expansion reverses wormhole shadow's early shrink","Dynamic LTB wormhole shadow shrinks then expands"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole shadow calculation uses the small-eta approximation with tau_0(R)=0, so it describes only the very first stage of a wormhole born together with the universe; if that early-birth, small-eta regime is abandoned, the non-monotonic shadow and the power law need not survive.","fun_headline_variants_meta":{"raw":{"variants":["Wormhole shadow: down then up with cosmic time","LTB wormhole shadow: shrink then stretch","Cosmic expansion reverses wormhole shadow's early shrink","Dynamic LTB wormhole shadow shrinks then expands"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00064,"raw_usage":{"total_tokens":2977,"prompt_tokens":1006,"completion_tokens":1971,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":622,"completion_tokens_details":{"reasoning_tokens":1908}},"tokens_in":622,"tokens_out":1971,"duration_ms":12853,"temperature":1.0,"reasoning_tokens":1908,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T15:58:29.650983+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Integrate null geodesics numerically in the exact LTB metric for the same F(R)=2b(1+$R^{2}$)^k and h(R)=1/(1+$R^{2}$) without expanding in eta, place an observer at chi_obs=1, and measure the shadow angular diameter at several observation times. If the curve is monotone rather than shrink-then-grow, or if the d_sh versus chi_* data at fixed observation time deviate from the chi_*^{1+2k/3} slope, the paper's central claim is refuted.","supporting_citations":[{"cited_title":"Possible wormholes in a Friedmann universe","cited_arxiv_id":"2309.03166","evidence_quote":"Provides the LTB wormhole model, the matching conditions to a closed Friedmann universe, and the earlier traversability analysis that this paper extends to lensing."},{"cited_title":"Magnetized dusty black holes and wormholes","cited_arxiv_id":"2109.12670","evidence_quote":"Establishes the elliptic-branch LTB wormhole and the throat conditions used here."},{"cited_title":"Landau, E.M","cited_arxiv_id":null,"evidence_quote":"Supplies the parametric LTB solution in terms of eta that underlies the small-eta expansion."},{"cited_title":"Lemaˆ ıtre, The expanding universe","cited_arxiv_id":null,"evidence_quote":"Defines the Lemaitre form of the LTB dust solution used as the starting geometry."},{"cited_title":"Vazquez, E.P","cited_arxiv_id":null,"evidence_quote":"Supplies the coordinate formula that converts photon arrival directions into image angular coordinates for the shadow radius."}],"review_version":2}