{"id":"bd260030-40bb-444a-8ab4-1a1327e5ef07","arxiv_id":"2511.15803","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"An upper limit on large-scale white noise (k_BH ≤ 1.8×10^-13 Mpc^-1 at 99% CL) is converted, via the authors' LOBA formula, into a required small-scale cutoff (≲3 pc^-1) or negative running (α_s ≲ −0.015) of the primordial spectrum.","lead":"Cosmologists searched for a predicted 'white noise' signal — extra power on the very largest cosmic scales, supposedly spilled there by non-linearities working on tiny ripples — and found none. The non-detection becomes a bound on the primordial ripples themselves: they must switch off or steepen before roughly a parsec scale, far below direct observation.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (5) translation of k_BH bound to k_cut/α_s uses A_s=2.1e-10, not the Planck value 2.1e-9; with the correct value, k_cut=3 pc^-1 gives k_BH~4e-12 Mpc^-1, ~20x the 99% bound, so the quoted implications do not follow.","rationale":"I read the paper in good faith: it sets a constraint on large-scale white noise using standard MCMC methods, openly discusses cosmic confusion, and the k_BH upper bound itself may be robust. However, the central claim as presented in the abstract—that this bound forces a spectral cutoff at k_cut≲3 pc^-1 or running α_s≲−0.015—depends on Eq. (5), which is not derived here and, more importantly, is evaluated with the wrong fiducial A_s. The paper uses A_s=2.1×10^-10 in the translation (§II) while consistently stating A_s≈2.1×10^-9 elsewhere. The arithmetic is straightforward: with the correct Planck amplitude, the predicted k_BH at the quoted cutoff is ~20–40 times larger than the 99% bound, meaning the quoted limits are not supported. This is an internal numerical inconsistency, not a matter of external consensus, so it directly undermines the headline conclusion. The reader identified the same weakest assumption (Eq. (5) and the A_s discrepancy), so I agree. The bound on k_BH might survive, but the paper's principal interpretation is false as written; a corrected version, with proper derivation or citation of Eq. (5) and recomputed limits, could be reconsidered. Hence my recommendation is REJECT rather than CONDITIONAL, since the current central claim cannot be accepted without major revision.","tokens_in":6319,"tokens_out":6272,"duration_ms":59589,"concrete_test":"Recompute the cutoff translation using Eq. (5) with the fiducial A_s = 2.1×10^-9 as used in §I and §III (and by Planck), rather than the A_s = 2.1×10^-10 used in §II, keeping k_cut = 3 pc^-1 = 3×10^6 Mpc^-1 and n_s = 0.965. If the resulting k_BH exceeds 1.80×10^-13 Mpc^-1 (it should, by roughly a factor of 20), then the quoted k_cut ≲ 3 pc^-1 and α_s ≲ −0.015 do not follow from the paper's own scaling relation; the paper must be revised to use the correct A_s and recompute the implied small-scale limits.","verdict_should_be":"REJECT","load_bearing_attack":"The paper's central claim in the abstract—that the k_BH upper bound forces k_cut≲3 pc^-1 or α_s≲−0.015—rests entirely on Eq. (5), imported from Paper I without derivation and with the weight function W[k] in Eq. (2) never specified. But even granting Eq. (5), the paper evaluates it inconsistently. §II states 'using the scaling relation above with fiducial values A_s ≈ 2.1×10^-10', whereas §I and the abstract use the Planck value A_s ≈ 2.1×10^-9. Plugging k_cut = 3 pc^-1 = 3×10^6 Mpc^-1, k_0=0.05 Mpc^-1, n_s=0.965 into Eq. (5) with A_s=2.1×10^-9 gives k_BH ≈ A_s^2 (k_cut/k_0)^{2(n_s−1)} k_cut ≈ (4.4×10^-18)(0.286)(3×10^6) ≈ 3.8×10^-12 Mpc^-1, which exceeds the paper's own 99% bound of 1.80×10^-13 Mpc^-1 by about a factor of 20 (and the 95% bound by ~40). With the lower A_s=2.1×10^-10, the same calculation yields ~3.8×10^-14 Mpc^-1, comfortably below the bound, which is the only way the quoted cutoff limit works. Thus the headline implication is an artifact of using a wrong fiducial amplitude. The α_s≲−0.015 limit is derived from the same unsupported Eq. (5) and is likewise not robust. The MCMC bound on k_BH itself may be sound, but the paper's principal interpretation does not follow from its own equations.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper argues that non-linear mode coupling during cosmic evolution inevitably generates large-scale white noise (LSWN), which can dominate the power spectrum at the largest scales. After adding a white-noise component k_BH/k to the primordial curvature power spectrum, the authors constrain its amplitude with CLASS + COBAYA using Planck 2018, ACT DR6 lensing, and DESI DR2 BAO data, obtaining k_BH ≤ 9.94e-14 Mpc^-1 (95% C.L.) and k_BH ≤ 1.80e-13 Mpc^-1 (99% C.L.) in Eq. (6). They then use the LOBA scaling relation, Eq. (5), to translate this bound into statements that the primordial spectrum must be cut off at k_cut ≲ 3 pc^-1 or have running α_s ≲ −0.015. The paper also discusses 'cosmic confusion'—the degeneracy between LSWN and primordial white noise—and frames the result as a probe of small scales far beyond direct CMB reach.","tokens_in":6642,"tokens_out":7901,"duration_ms":75481,"significance":"If the LOBA framework and the numerical translation are correct, the paper proposes a genuinely novel way to constrain the primordial power spectrum at scales ~7 orders of magnitude smaller than the directly observable CMB scales. The MCMC analysis uses a standard, mature pipeline and public data, which is a strength; the explicit upper bounds with confidence levels are clear and falsifiable. However, the paper's headline implications rest on an external scaling relation (from Paper I) that is not derived or fully specified in this manuscript, and there is a numerical inconsistency in the fiducial A_s used to evaluate that relation. The central bound itself may be sound, but the interpretation is not currently supported by the paper's own equations.","major_comments":[{"comment":"The translation of the k_BH bound into k_cut and α_s uses A_s = 2.1e-10 in §II, while the Planck value A_s ≈ 2.1e-9 is quoted earlier in the same section and is the actual fitted amplitude. Substituting A_s = 2.1e-9, n_s = 0.965, and k_cut = 3 pc^-1 = 3e6 Mpc^-1 into Eq. (5) gives k_BH ≈ 3.8e-12 Mpc^-1, which exceeds the 99% bound in Eq. (6) by about a factor of 20 (and the 95% bound by about 40). Thus the derivation as written is invalid; with the correct amplitude the equation implies a different (substantially stronger) k_cut limit. The α_s ≲ −0.015 statement is also obtained from Eq. (5) and inherits this problem. Please correct the arithmetic and the fiducial value, or show that Eq. (5) uses a different normalization.","section":"§II, Eq. (5) and Abstract"},{"comment":"The central LOBA scaling relation, Eq. (5), and the weight function W[k] in Eq. (2) are imported from Paper I without derivation or specification. Since all implications in §II and §III are obtained from Eq. (5), the reader cannot verify the relation, its numerical coefficient, or the conditions under which it holds. The paper should either reproduce the derivation in an appendix, give an explicit form for W[k], or state clearly that this is a result of Paper I and quote the relevant equation. Without this, the headline constraints on k_cut and α_s are not self-contained.","section":"§I.B, Eqs. (2) and (5)"},{"comment":"The paper acknowledges 'cosmic confusion': the observable large-scale power is (P_prim + P_LSWN)|T|^2, so the upper limit on k_BH constrains the sum of primordial white noise and LSWN, not LSWN alone. Nevertheless, the abstract and §IV state that the data 'force' a cutoff or running in the primordial spectrum. This conclusion is only valid under the additional assumption that the Paper I LSWN model is correct and that no primordial white-noise component is present. The conditional nature of this implication should be stated explicitly in the abstract and conclusions, or the interpretation should be framed as a constraint on the combined amplitude.","section":"§I.A and §IV"},{"comment":"The assertion that k_LSWN ≈ sqrt(k_cut k_BH) and that the three scales k_cut, k_LSWN, k_BH 'each differ by a factor of A_s' is not derived and does not obviously follow from Eq. (5) as written. If this relation is used to claim a hierarchy of 'nine orders of magnitude', it needs a derivation or a specific reference to the result in Paper I.","section":"§III"}],"minor_comments":[{"comment":"The phrase 'cutoff at k_cut ≲ 3 pc^-1, corresponding to physical wavelengths greater than about one parsec' is dimensionally inconsistent: if k_cut is a wavenumber, then k_cut ≲ 3 pc^-1 corresponds to wavelengths λ ≳ 0.3 pc, not ≳ 1 pc. Please correct or clarify.","section":"Abstract and §IV"},{"comment":"The notation '(1)Δ²_R[k]' for the primordial component is awkward and ambiguous; consider using a subscript or superscript, e.g., Δ²_{R,prim}[k].","section":"§II, Eq. (3)"},{"comment":"Typo: 'the observed power law power spectrum much be cutoff' should read 'must be cut off'.","section":"§IV"},{"comment":"Minor typos: 'Jean's length' should be 'Jeans length', and 'the Jean's length' should be 'the Jeans length'.","section":"§I.B"},{"comment":"The contours for the 6- and 7-parameter models are said to lie almost exactly on top of each other; since k_BH is the main result, consider showing a 1D posterior for k_BH or a zoomed panel to make the upper bound visible.","section":"Fig. 1"}],"recommendation":"major_revision","confidential_remarks":"The paper depends heavily on two companion papers (Paper I and Paper α) that are not available to the referee. I would recommend requiring the authors to provide the LOBA derivation, the form of W[k], and a self-contained derivation of Eq. (5) before acceptance. The numerical inconsistency in A_s is a load-bearing error that must be fixed, but it appears fixable within the scope of a revision; the central MCMC bound may be sound."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The one thing to know: the MCMC bound on k_BH is probably fine, but the abstract's implications are not. The paper adds a white-noise term k_BH/k to the primordial curvature spectrum in modified CLASS, fits Planck 2018 + ACT DR6 lensing + DESI DR2 BAO with COBAYA, finds a non-detection, and quotes k_BH ≤ 9.9×10^-14 Mpc^-1 (95%) and 1.8×10^-13 (99%). That bound looks robust: k_BH is uncorrelated with the other parameters, the pipeline is mature, and the paper honestly frames the result as a null and explicitly flags the cosmic-confusion degeneracy between generated and primordial white noise.\n\nWhat is genuinely new, conditional on Paper I: a low-ℓ CMB non-detection as a probe of the primordial spectrum at scales orders of magnitude below direct observation, expressed through a clean one-parameter parametrization. That is an interesting idea and a worthwhile target for follow-up.\n\nThe soft spot is load-bearing. The headline k_cut ≲ 3 pc^-1 and α_s ≲ −0.015 are the k_BH bound inverted through Eq. (5), imported from Paper I without derivation and with the weight function W[k] in Eq. (2) never specified. Even granting Eq. (5), §II evaluates it with A_s ≈ 2.1×10^-10, while the same section quotes the Planck amplitude as 2.1×10^-9. With the correct value, k_cut = 3 pc^-1 gives k_BH ≈ 4×10^-12 Mpc^-1, about twenty times the 99% bound. The quoted limit does not follow. Using the right A_s, Eq. (5) yields k_cut ≲ 0.1 pc^-1, a cutoff at tens of parsecs rather than one parsec — still far below direct probes, but roughly a factor of 25 weaker than advertised, and the α_s claim inherits the same problem. I checked the stress-test arithmetic; it holds. (The reader's factor of 40 against the 99% bound is off; the right factor there is about 20.)\n\nMinor issues: no code or data shipped, so the modified CLASS cannot be checked; treating a necessarily non-Gaussian, nonlinearly generated signal as a linear additive white-noise component is an idealization, though a defensible leading-order one; and the §I novelty claim, that generic LSWN has not been previously recognized, is asserted rather than weighed against the existing mode-coupling and backreaction literature. I cannot check Paper I, so I leave that open. The §III statement that the detailed fit confirms the Paper I estimates is also somewhat self-referential, since the same Eq. (5) does the translating on both sides.\n\nWho gets value: people working on small-scale primordial power spectrum constraints, and anyone who wants a textbook example of why you sanity-check fiducial values in derived limits. I would not cite it as it stands, but a corrected version would be citable for the k_BH bound.\n\nRecommendation: send it to referees. Every problem is addressable: fix A_s, recompute the translation, ship the modified CLASS configuration, and give the LOBA derivation or at least a checkable W[k] in this paper or in Paper I. After that, this could be a solid result.","headline":"The k_BH upper bound from the Planck/ACT/DESI fit is probably a sound data statement; the headline k_cut ≲ 3 pc^-1 and α_s ≲ −0.015 implications do not survive the paper's own equations, since Eq. (5) is evaluated with an A_s ten times too small and imported from an unverifiable companion paper.","tokens_in":7364,"tokens_out":15356,"would_cite":false,"duration_ms":134044,"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":"The paper claims that non-linear cosmic mode coupling inevitably produces large-scale white noise, and that its non-detection in current data forces the primordial spectrum to deviate from a pure power law, either by cutting off below about","keywords":["large-scale white noise","primordial power spectrum","CMB low multipoles","spectral index running","small-scale cutoff","non-linear mode coupling","cosmic confusion","LSWN"],"falsifier":"Recompute Eq. (5) with the fiducial amplitude A_s ≈ 2.1×10^-9 (not 2.1×10^-10) and k_cut = 3 pc^-1; if k_BH comes out to ~4×10^-12 Mpc^-1, exceeding the 99% bound by a factor of ~20, then the quoted cutoff limit is not supported by the paper's own equations. Alternatively, a future CMB experiment that detects excess low-multipole power with k_BH around 10^-13 Mpc^-1 would directly contradict the upper bound.","tokens_in":5949,"feed_emoji":"🌌","tokens_out":3171,"duration_ms":33124,"temperature":0.7,"pith_summary":"This paper tries to establish that non-linearities in the evolution of cosmic inhomogeneities inevitably spill power from small to very large scales, producing a white-noise component in the density field. Confronting this prediction with Planck, ACT, and DESI data, it finds no excess power on the largest scales and derives an upper bound on the white-noise amplitude k_BH. The authors then translate this bound into a statement about the primordial power spectrum: if the observed spectrum extends as a pure power law to arbitrarily small scales, the non-linearities would have generated more large-scale noise than observed. Therefore the primordial spectrum must either cut off at k_cut ≲ 3 pc^-1 or run with α_s ≲ −0.015. A sympathetic reader would take this as evidence that the smallest scales of the early universe can be probed indirectly through the largest observable scales.","feed_headline":"New bound forces primordial spectrum to steepen below 3 pc","feed_subtitle":"Non-detection of large-scale white noise in CMB rules out a pure power-law spectrum over ten orders of magnitude.","key_machinery":"The key object is the white-noise wavenumber k_BH, which measures the amplitude of large-scale white noise added to the primordial curvature power spectrum as k_BH/k. Its constraining power comes from the fact that on the largest observable scales (low CMB multipoles) this term grows relative to the nearly scale-invariant primordial part, so the non-detection of excess low-ℓ power directly bounds k_BH. The second key mechanism is the LOBA scaling relation, Eq. (5), imported from the companion paper, which connects k_BH to a small-scale cutoff k_cut in the primordial spectrum. This relation carries the translation from a large-scale bound to small-scale physics, and it is the step where the p","core_discovery":"The central claim is that the late-time large-scale curvature power spectrum takes the form of the primordial spectrum plus a white-noise term, P[h, k] ≈ (P_prim[k] + P_LSWN) |T[t,k]|^2, where the LSWN amplitude is parametrized by a wavenumber k_BH through Δ_R^2(k) = A_s(k/k_0)^(n_s−1) + k_BH/k. Using a modified CLASS Boltzmann code and COBAYA MCMC parameter estimation against Planck 2018 TT/TE/EE, Planck lensing, ACT DR6 lensing, and DESI BAO data, the paper finds k_BH ≤ 1.80×10^-13 Mpc^-1 at 99% C.L. Under the LOBA scaling relation k_BH ∼ A_s^2 (k_cut/k_0)^(2(n_s−1)) k_cut, this non-detection is interpreted as requiring a cutoff at k_cut ≲ 3 pc^-1 or a spectral-index running of α_s ≲ −0.01","pith_inferences":["The small-scale conclusion depends on the LOBA scaling relation, Eq. (5), which is imported without derivation and whose weight function W[k] is never specified; if that relation is modified, the quoted k_cut and α_s limits change even though the k_BH bound itself is independent.","There is an internal inconsistency in the amplitude used for A_s: the paper evaluates Eq. (5) with A_s ≈ 2.1×10^-10 in Section II, while the standard Planck value and the values used elsewhere are 2.1×10^-9. With the correct value and k_cut = 3 pc^-1, Eq. (5) gives k_BH ≈ 4×10^-12 Mpc^-1, roughly 40 times the 99% bound, so the quoted cutoff limit does not follow from the paper's own equations as w","The paper admits 'cosmic confusion'—large-scale white noise generated by non-linearities is formally indistinguishable from a white-noise component intrinsic to the primordial spectrum. Therefore the constraint is strictly a bound on the total white-noise power in the initial conditions plus nonlinear generation, not a standalone proof that small-scale nonlinearities must be suppressed, unless one"],"forward_implications":["If the bound holds, a pure power-law primordial spectrum over more than ~10 orders of magnitude in wavelength is ruled out, forcing either a cutoff near or above 1 comoving parsec or a negative running of the spectral index.","The constraint turns the low-multipole CMB into a direct probe of non-linear processes on scales seven orders of magnitude smaller than any telescope can resolve.","A measurement of α_s at the level of −0.015 or more negative would be a falsifiable confirmation; current Planck uncertainties (α_s = −0.006 ± 0.013) are consistent but do not yet verify the predicted running.","Because any process generating shear in the matter flow contributes to LSWN, the bound represents a minimal constraint; extensions such as phase transitions, gravitational waves, or topological defects would tighten it, making LSWN a generic test of early-universe physics."],"fun_headline_variants":["Quiet cosmos tightens grip on early-universe spectrum","No cosmic hiss: primordial power must bend before 3 pc","White noise silence rewrites primordial spectrum rules","Cosmic static absence pins down early universe physics","Large-scale quiet sets new limits on inflation-era spectrum"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The entire small-scale interpretation rests on the relation, borrowed from the companion paper, that converts a measured white-noise amplitude into a cutoff scale, plus the assumption that the observed large-scale noise is generated solely by small-scale nonlinearities rather than being present in the primordial spectrum from the start.","fun_headline_variants_meta":{"raw":{"variants":["Quiet cosmos tightens grip on early-universe spectrum","No cosmic hiss: primordial power must bend before 3 pc","White noise silence rewrites primordial spectrum rules","Cosmic static absence pins down early universe physics","Large-scale quiet sets new limits on inflation-era spectrum"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000167,"raw_usage":{"total_tokens":1138,"prompt_tokens":834,"completion_tokens":304,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":578,"completion_tokens_details":{"reasoning_tokens":227}},"tokens_in":578,"tokens_out":304,"duration_ms":3591,"temperature":1.0,"reasoning_tokens":227,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T21:20:23.066208+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute Eq. (5) with the fiducial amplitude A_s ≈ 2.1×10^-9 (not 2.1×10^-10) and k_cut = 3 pc^-1; if k_BH comes out to ~4×10^-12 Mpc^-1, exceeding the 99% bound by a factor of ~20, then the quoted cutoff limit is not supported by the paper's own equations. Alternatively, a future CMB experiment that detects excess low-multipole power with k_BH around 10^-13 Mpc^-1 would directly contradict the upper bound.","supporting_citations":[],"review_version":1}