{"id":"b58cf399-69a6-4aa4-ab20-067c61c1b369","arxiv_id":"2608.09457","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":8.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"The paper computes μT, μE, yT and yE cross-power spectra for CMB spectral distortion anisotropies from acoustic damping with local-type non-Gaussianity, using full mode-coupling geometry and transport, finding new small-scale damping and y-distortion features.","lead":"This paper calculates the small spatial variations in the cosmic microwave background spectrum caused by sound-wave damping in the early universe, including the effect of primordial non-Gaussianity. It gives more accurate predictions for correlations between spectral distortions and temperature and polarization, which future CMB experiments could use to test inflation.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The enhanced-small-scale-power claim rests on an incomplete third-order propagation estimate that the authors explicitly flag; omitted O(R^3) terms could contaminate the A_p versus f_NL separation.","rationale":"The reader's verdict (CONDITIONAL) already rests on the incompleteness of the third-order propagation estimate, and I agree. The paper is careful to flag this: the opening note preceding Section 5.2 says 'we do not attempt a complete calculation at this order,' and Section 5.2 repeats that a rigorous treatment 'requires an expansion to third order in perturbations, which is beyond the scope of this paper.' The abstract, however, states without this caveat that for enhanced small-scale power, anisotropies generated by propagation of the distorted average spectrum 'can become comparable to those from anisotropic dissipation' and that their different angular dependences and parameter scalings 'principally allow' A_p and f_NL to be constrained separately. That claim depends on the propagation template being the dominant O(R^3) effect. Without a computation or a bound on the remaining O(R^3) source terms—for example, products of first-order with second-order temperature and velocity fields in the Liouville and Thomson collision terms—the two-template decomposition is an assumption rather than a derived result. The proposed check, a full third-order calculation using the existing formalism of Ota & Bartolo (2019), would settle whether the omitted terms are subdominant. This concern does not invalidate the core second-order source derivation or the standard small-scale predictions, so the conditional verdict remains appropriate.","tokens_in":41671,"tokens_out":6631,"duration_ms":69430,"concrete_test":"Compute the complete O(R^3) distortion–temperature cross-spectra for Model I using the third-order Boltzmann formalism of Ota & Bartolo (2019, ref [54]), including the terms Θ^(1)[∂ηΘ^(2)+γ̂·∇Θ^(2)] and the f_NL^2 average-distortion propagation, and compare the full result with the paper's 'propagation + anisotropic dissipation' template sum over ℓ ∈ [10, 2000] for f_NL = 1 and 10. If the full result differs from the template sum by more than about 10% in the multipole bins used for parameter separation, the separate-constraint claim is not established; if the difference is smaller, the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that for enhanced small-scale power, propagation of the average distortion produces anisotropies comparable to anisotropic dissipation, with different angular dependences and parameter scalings allowing A_p and f_NL to be constrained separately, relies on a partial third-order calculation. Section 5.2 computes the propagation template by inserting the isotropic average distortion (an O(R^2) object) into the first-order (O(R)) FH transport equations, yielding an O(R^3) contribution of the specific form ⟨R R⟩ × μ̄. A complete O(R^3) treatment would additionally include direct third-order sources from the Liouville and Thomson collision terms proportional to products of first-order and second-order temperature/velocity fields, as well as primordial third-order correlators with different transfer functions. The paper states in the introductory note and in Section 5.2 that it does not attempt this complete calculation and that the result should be regarded as an estimate. Without an estimate or bound on the omitted terms, the assertion that the two templates capture the leading-order effects is unsupported. If an omitted term has comparable amplitude and overlapping multipole dependence, the claimed separation of A_p and f_NL would be degraded, because the observable power spectra would mix the templates in a way not represented by the paper's two-parameter model.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper develops a calculation of CMB spectral distortion anisotropies (μT, μE, yT, yE cross-power spectra) arising from acoustic damping in the presence of local-type primordial non-Gaussianity. The authors derive the second-order blackbody-mixing source from the Liouville and Thomson collision terms in a gauge-invariant form, project it onto angular multipoles in Fourier space, and insert the resulting effective anisotropic heating rates into the frequency-hierarchy (FH) implementation in CosmoTherm. For a nearly scale-invariant primordial spectrum they compare with earlier work, identify improved small-scale damping and y-distortion behaviour, and test tight-coupling and monopole-source approximations. For an illustrative enhanced small-scale power model they separate the signal into a propagation template, scaling as A_p, and an anisotropic-dissipation template, scaling as A_p f_NL, and argue that the different angular dependences allow A_p and f_NL to be constrained separately.","tokens_in":41956,"tokens_out":4433,"duration_ms":51315,"significance":"If the results hold, this is the most complete treatment to date of spectral distortion anisotropies from acoustic damping: it includes the full mode-coupling triangle geometry, frequency-dependent transport, and continuous spectral evolution through the FH method, and it is implemented in a public code (CosmoTherm). The standard-ΛCDM predictions for μT/μE/yT/yE are plausible and the comparison with previous calculations is useful. The paper's most important new phenomenological claim, however, concerns the enhanced small-scale power scenario, where the separation of A_p and f_NL rests on a partial third-order propagation calculation that the authors themselves label an estimate. Because that scenario is explicitly presented as a path to constraining A_p and f_NL separately, the incompleteness of the third-order treatment is load-bearing rather than cosmetic.","major_comments":[{"comment":"The propagation response of the average distortion is computed by inserting the isotropic average distortion into the linear FH equations, which is formally an O(R^3) subset of the full third-order problem. The paper explicitly states that it 'do[es] not attempt a complete calculation at this order' and that the results 'should be regarded as an estimate.' A complete O(R^3) treatment would also include direct third-order Liouville and Thomson sources and primordial third-order correlators with different transfer functions and statistical properties. The abstract and Section 5.2 nevertheless use this estimate to claim that propagation anisotropies can be comparable to anisotropic dissipation and that A_p and f_NL can be constrained separately (Figs. 8 and 9). This claim is unsupported unless the authors either supply a quantitative bound or estimate of the omitted O(R^3) terms, or explicitly reframe the enhanced-small-scale-power results as an illustration rather than a prediction. Without such a bound, an omitted term with comparable amplitude and similar multipole dependence would mix the two templates and degrade the claimed parameter separation.","section":"§5.2 and introductory note (p.3)"},{"comment":"The statement that the shown Model I signals 'should be within reach of Planck, ACT and SPT' is not supported by any noise, foreground, or Fisher-forecast calculation in the manuscript. The plotted power spectra are signal-only predictions; detectability of the A_p versus f_NL separation depends on covariance, cosmic variance, foreground contamination, and the interplay with the average-distortion constraint. Since the central new phenomenological message is that the two templates can be distinguished, a quantitative forecast (or at least a clear statement that this is only an order-of-magnitude expectation) is needed before the claim can be assessed.","section":"§5.2, Fig. 9"}],"minor_comments":[{"comment":"The caption shows 'R2017 x 5/6' and 'GK2012 x 1/8' but does not explain the meaning of these scaling factors; please state in the caption or text whether they are normalization corrections applied to the previous results and why they are included.","section":"Fig. 4 caption"},{"comment":"The inequality in Eq. (3.4) is labelled with a footnote saying that a factor of order unity to a few should be inserted; as written, the expression is therefore not a strict bound. Please replace the inequality by an explicit estimate with a stated uncertainty range.","section":"Eq. (3.4) and footnote 6"},{"comment":"The transfer-function database uses ℓmax=10 and neglects polarization terms in the source term, with a statement that this affects heating rates around recombination by 5–10%. Since the paper emphasizes that y-distortion signals are sensitive to source details, please briefly state whether this 5–10% uncertainty propagates into the final yT/yE spectra and whether it is included in the claimed accuracy of the comparisons.","section":"§4.1"},{"comment":"The sentence 'As a note in preparation of Sect. 5.2, where we consider an simple model...' contains a grammatical error ('an simple') and the note interrupts the introduction; consider moving this caveat to Section 5.2 itself.","section":"Introduction, note before §5.2"}],"recommendation":"major_revision","confidential_remarks":"The paper is a strong technical contribution and the standard-ΛCDM part of the calculation appears sound. The main concern is that the headline enhanced-small-scale-power claim rests on an explicitly incomplete third-order treatment; this needs either a completeness bound or a downgrade of the claim. The self-citation pattern is heavy but appropriate given the FH/CosmoTherm lineage. The manuscript fits JCAP's scope."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know. First, the source-term derivation in Section 2 is the real contribution: writing the blackbody-mixing source in terms of the gauge-invariant Theta_g and showing the explicit dependence on the angle between the two dissipating modes is new and correct as far as I can tell. Second, the enhanced-small-scale-power section is an honestly-flagged partial estimate, not a finished prediction - the abstract oversells it. The paper does well. It goes beyond the back-to-back squeezed approximations used in earlier work, evaluates the effective heating rates with the full triangle geometry, and pushes them through the FH transfer functions to get muT/muE/yT/yE. The standard-LambdaCDM results look plausible: they reproduce previous large-scale calculations, add the expected extra damping, and the tests of tight-coupling and monopole-only sourcing give a useful sense of where approximations hold. The comparison with Ravenni et al. and Ganc & Komatsu is honest and informative. The soft spot is exactly where the stress-test put it, and the authors deserve credit for flagging it themselves. The propagation response for enhanced small-scale power is a partial O(R^3) calculation: inserting the averaged distortion into the first-order transport equations. The introductory note and Section 5.2 say this is not a complete third-order treatment and that the result 'should be regarded as an estimate.' That caveat is easy to miss in the abstract, which states that the different angular dependences and parameter scalings 'principally allow' A_p and f_NL to be constrained separately. The stress-test concern is legitimate: without a bound on the omitted direct third-order terms, the claimed separation of templates is not established. But this is a limitation of the illustrative section, not a flaw in the core derivation. A referee should ask the authors to soften the abstract and to provide any crude estimate of the size of the omitted terms. No code or data are provided, so independent reproduction is harder, but the FH framework is documented in prior papers. Self-citation here is appropriate; the relevant earlier work is theirs. Bottom line: this deserves a serious referee. The core derivation and the standard-spectrum predictions are worth publishing. The enhanced-power part should be framed as an illustration with an explicit caveat, and the referee should push for that framing to be consistent between abstract and body.","headline":"Solid new derivation of the distortion source with full mode-coupling geometry; the enhanced small-scale power claim is an explicitly partial estimate, so read that part as illustrative.","tokens_in":715,"tokens_out":1044,"would_cite":true,"duration_ms":33470,"reading_group":"yes","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 computes CMB spectral-distortion anisotropies from acoustic damping with local-type primordial non-Gaussianity, and finds that for enhanced small-scale power the propagation of the average distortion adds a signal comparable to…","keywords":["CMB spectral distortions","primordial non-Gaussianity","acoustic damping","spectral distortion anisotropies","frequency hierarchy","local-type non-Gaussianity","small-scale power spectrum","Boltzmann transfer functions"],"falsifier":"Evaluate the full third-order contribution to the $\\mu T$ correlation in the enhanced small-scale model; if the omitted terms alter the angular pattern or the $\\propto A_p$ scaling beyond the quoted uncertainty, the claimed parameter separation fails. A separate check is the large-scale $y T$ amplitude, where the new transport treatment differs visibly from older estimates and multifrequency CMB data could discriminate the two.","tokens_in":41476,"feed_emoji":"🌌","tokens_out":7635,"duration_ms":69040,"temperature":0.7,"pith_summary":"This paper aims to put predictions for CMB spectral-distortion anisotropies from acoustic damping on a common footing with the full Boltzmann transport of the distorted photon spectrum. It derives the second-order blackbody-mixing source explicitly, including velocity-dependent scattering, and computes the $\\mu T$, $\\mu E$, $y T$, and $y E$ cross-power spectra for local-type primordial non-Gaussianity using the frequency-hierarchy treatment. For a nearly scale-invariant primordial spectrum, the results agree broadly with earlier estimates on large angular scales but show additional small-scale damping and modified $y$-distortion correlations. For enhanced small-scale curvature power, the paper finds that anisotropies generated as the average distorted spectrum propagates through the perturbed universe become comparable to those from anisotropic dissipation, with different angular dependences and scalings ($\\propto A_p$ versus $\\propto A_p f_{NL}$) that in principle allow the small-scale amplitude $A_p$ and $f_{NL}$ to be constrained separately.","feed_headline":"CMB distortion maps could pin down f_NL and small-scale power","feed_subtitle":"New calculation separates the two parameters by their angular signatures in spectral-distortion anisotropies.","key_machinery":"The carrier of the calculation is the frequency-hierarchy treatment: the spectral dimension is expanded in frequency-space basis functions derived from thermalization, and the coefficients are promoted to angular multipoles, so Comptonization, double Compton and bremsstrahlung, Thomson scattering, free streaming and photon diffusion are followed in one system. On the source side, the paper builds effective anisotropic heating rates $s_{\\ell 0}(\\eta,k)$ from first-order photon and baryon transfer functions together with the primordial bispectrum; the mode-coupling kernel $\\hat{M}_\\ell$ encodes the full triangle geometry. On the transfer side, the distortion hierarchy has no restoring force: in tight coupling the monopole and dipole of a distortion do not exchange energy, so sourced modes are overdamped and then damp with a modified diffusion scale rather than oscillating. This combination is what lets the paper separate the direct anisotropic-dissipation signal from the propagation signal.","core_discovery":"The paper's central claim is that treating spectral evolution and photon transport together changes the predicted distortion cross-spectra, and that in enhanced small-scale power scenarios it creates a separate, previously missed signal. The source is written compactly as $S^{\\rm mix}=\\Theta_g[\\Theta_g-\\Theta_{g,0}-\\frac{1}{10}\\Theta_{g,2}]-\\frac{1}{2}(\\Theta_g^2-[\\Theta_g^2]_0-\\frac{1}{10}[\\Theta_g^2]_2)$ with $\\Theta_g=\\Theta+\\Psi-V$, so that all blackbody-mixing terms are determined by one gauge-independent temperature variable. In Fourier space the source depends on the full triangle formed by the observable mode and the two dissipating modes, $s_{\\ell 0}(\\eta,k)\\propto\\int dk_1\\,dk_2\\,B(k,k_1,k_2)\\, \\hat{M}_\\ell(\\eta,k_1,k_2,\\chi_1,\\chi_2)$, a geometry that earlier treatments dropped by taking the dissipating modes exactly back-to-back. Distortion perturbations are overdamped rather than acoustic; their damping scale is $\\sqrt{8/15}\\,k_D$, which explains the faster small-scale falloff of $\\mu T$ and $y T$. In the enhanced-power model, the propagation template scales as $\\propto A_p$ and the anisotropic-dissipation template as $\\propto A_p f_{NL}$, so the two parameters are not locked into a single product.","pith_inferences":["Because the propagation and anisotropic-dissipation templates also have different redshift windows, the same decomposition could be used to constrain the scale dependence of the small-scale power, for example by shifting $k_p$ in the model; this is an extension the paper leaves to future forecasts.","The triangle-angle dependence of $\\hat{M}_\\ell$ should matter more for non-local bispectrum shapes, so the full geometry may help distinguish local from equilateral or folded non-Gaussianity.","A natural next test is to compute the $\\mu\\mu$, $yy$ and $y\\mu$ auto- and cross-spectra for the same models; the paper notes these are subleading, but they carry independent spectro-spatial information if measured."],"forward_implications":["For a nearly scale-invariant primordial spectrum, the refined $\\mu T$ and $\\mu E$ spectra closely follow previous estimates at $\\ell\\lesssim 400$ but then damp faster, so small-scale anisotropy measurements need the full transport treatment.","The $yT$ and $yE$ spectra are more sensitive to the source evolution; tight-coupling and monopole-only approximations are adequate for $\\mu$-distortion spectra but not for precision $y$-distortion predictions.","If the small-scale power spectrum is enhanced, the total $\\mu T$ signal is a sum of an $\\propto A_p$ propagation template and an $\\propto A_p f_{NL}$ anisotropic-dissipation template, whose different $\\ell$-dependences can break the degeneracy between $A_p$ and $f_{NL}$.","Distortion anisotropies are overdamped rather than acoustic, giving an extra damping factor that cannot be reproduced by attaching ordinary temperature transfer functions to a local heating modulation."],"supporting_citations":[{"why":"Supplies the standard blackbody-mixing source from dissipation of acoustic modes and the average heating rate it implies.","marker":"[17]"},{"why":"Establishes the evolution and overdamped damping of distortion anisotropies that the paper refines.","marker":"[22]"},{"why":"Provides the frequency-hierarchy basis and generalized Boltzmann hierarchy used for the spectro-spatial evolution.","marker":"[24, 25, 27, 41]"},{"why":"Earlier $\\mu T$ estimate for local-type non-Gaussianity that the paper compares against.","marker":"[32]"},{"why":"Previous numerical $\\mu T$ and $yT$ power spectra used as a comparison baseline.","marker":"[62]"},{"why":"Introduced the distortion-anisotropy window on primordial non-Gaussianity that this calculation puts on a more complete footing.","marker":"[55]"},{"why":"Earlier derivation of monopole, dipole and quadrupole mixing sources, extended here to full triangle geometry.","marker":"[51]"}],"fun_headline_variants":["CMB distortion maps disentangle f_NL and small-scale power","New propagation signal separates CMB distortion parameters","New CMB distortion signal breaks f_NL-small-scale degeneracy","Angular signatures separate f_NL and small-scale power in CMB distortions"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the propagation response, computed as a partial third-order treatment, captures the leading-order effect, so that if omitted third-order terms are not small the claimed separate constraints on $A_p$ and $f_{NL}$ would be weakened.","fun_headline_variants_meta":{"raw":{"variants":["CMB distortion maps disentangle f_NL and small-scale power","New propagation signal separates CMB distortion parameters","New CMB distortion signal breaks f_NL-small-scale degeneracy","Angular signatures separate f_NL and small-scale power in CMB distortions"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000901,"raw_usage":{"total_tokens":3984,"prompt_tokens":1154,"completion_tokens":2830,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":770,"completion_tokens_details":{"reasoning_tokens":2758}},"tokens_in":770,"tokens_out":2830,"duration_ms":19796,"temperature":1.0,"reasoning_tokens":2758,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T17:04:50.994743+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Evaluate the full third-order contribution to the $\\mu T$ correlation in the enhanced small-scale model; if the omitted terms alter the angular pattern or the $\\propto A_p$ scaling beyond the quoted uncertainty, the claimed parameter separation fails. A separate check is the large-scale $y T$ amplitude, where the new transport treatment differs visibly from older estimates and multifrequency CMB data could discriminate the two.","supporting_citations":[{"cited_title":"Chluba, R","cited_arxiv_id":null,"evidence_quote":"Supplies the standard blackbody-mixing source from dissipation of acoustic modes and the average heating rate it implies."},{"cited_title":"Amin, and Marc Kamionkowski","cited_arxiv_id":null,"evidence_quote":"Establishes the evolution and overdamped damping of distortion anisotropies that the paper refines."},{"cited_title":"Ganc and E","cited_arxiv_id":null,"evidence_quote":"Earlier $\\mu T$ estimate for local-type non-Gaussianity that the paper compares against."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Previous numerical $\\mu T$ and $yT$ power spectra used as a comparison baseline."},{"cited_title":"Pajer and M","cited_arxiv_id":null,"evidence_quote":"Introduced the distortion-anisotropy window on primordial non-Gaussianity that this calculation puts on a more complete footing."},{"cited_title":"CMB spectral distortions as solutions to the Boltzmann equations.Journal of Cosmology and Astroparticle Physics, 2017(1):037, January 2017","cited_arxiv_id":null,"evidence_quote":"Earlier derivation of monopole, dipole and quadrupole mixing sources, extended here to full triangle geometry."}],"review_version":1}