{"id":"d0e28d4c-c84d-48f6-a67c-6e6adfc3a28a","arxiv_id":"2502.02571","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Sharp primordial features survive nonlinear structure formation as localised bumps or dips in the matter power spectrum, while their oscillatory patterns are erased, leaving an oscillatory imprint in the halo mass function.","lead":"The authors use N-body simulations to show that sharp features in the primordial power spectrum from inflation leave a surviving localised bump or dip in the nonlinear matter power spectrum, even though their oscillations are washed out. The result opens a path to probing inflationary physics with small-scale structure, while warning that such signals look similar to warm dark matter effects.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Surviving feature is a monotonic ~10% tilt at the resolution edge, not a localized bump; position-recovery claim is untested even for the single kf.","rationale":"The central claim requires that the post-nonlinear signature be a localized feature whose amplitude and position encode the primordial feature amplitude and scale. The reader correctly flagged the lack of kf variation and convergence tests. My stress-test sharpens this: the single kf = 2 Mpc^-1 run does not even exhibit a localized peak in the presented z=0 ratio; the text says the deviation reaches ~±10% at the smallest accessible scales, implying a monotonic rise toward the resolution limit. A feature that is still rising at the edge of the simulated range has no measured position, so the 'position recovers kf' part of the abstract is not supported by the current data. This is not an internal inconsistency, but an overreach relative to what Fig. 6 and Sec. IIIB1 establish. It is also consequential because a monotonic tilt is degenerate with running of the spectral index or with the WDM-like suppression discussed in Sec. IIIB3, weakening the claimed ability to recover kf. The survival of a primordial feature in the nonlinear power spectrum is nevertheless qualitatively demonstrated, so a conditional accept remains appropriate; the condition should include demonstrating an in-range peak and kf scaling.","tokens_in":24258,"tokens_out":8904,"duration_ms":88070,"concrete_test":"From the existing z=0 snapshots (sim-1, sim-2, sim-3, ΛCDM), compute the ratio P/P_ΛCDM and check whether d ln(P/P_ΛCDM)/d ln k changes sign (i.e., the ratio has a local maximum) within the resolved range. If no local maximum exists, the 'localized bump' and its position are not measured, and the recoverability claim should be restated as a broadband tilt. If a peak does exist, run at least one additional simulation with a different kf (e.g., 8 Mpc^-1) and verify that the peak position scales with kf.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Sec. IIIB1 describes the z=0 ratio as 'a characteristic enhancement/decrease in power above k = 2Mpc−1, reaching up to ∼±10% at the smallest scales accessible'. This indicates the residual is still growing at the resolution limit rather than peaking at a scale tied to kf. The abstract's claim that the signature is a 'localised power enhancement or decrease' whose 'position can in principle be used to recover the scale' therefore lacks a demonstrated positional marker: in the presented simulations the effect is a monotonic tilt toward small scales, and no in-range peak is reported. Because only kf = 2 Mpc^-1 is simulated, the scaling of any putative peak with kf is also untested. This matters because if the residual is a broad tilt, it is degenerate with spectral-index running and with the WDM-like suppressions the authors themselves fit in Sec. IIIB3, so the recoverability part of the central claim is not established.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper investigates whether sharp features in the primordial power spectrum—motivated by UV-complete inflationary models—survive the nonlinear gravitational evolution that shapes the late-time matter distribution. The authors build a unified template for sharp features from time-dependent slow-roll parameter or sound-speed variations, derive it via in-in perturbation theory in App. A, constrain its parameters with Planck 2018 TTTEEE+lensing data, and then run 1024^3 N-body simulations with kf=2 Mpc^-1 and |δA|=0.2 for three feature models plus a featureless benchmark, all started at z=32 with 2LPT initial conditions. They report that oscillatory patterns are damped by nonlinearities, while a characteristic enhancement or suppression of roughly ±10% persists at z=0 at the smallest resolved scales, together with an oscillatory pattern in the z=1 halo mass function. They also compare with the Planck-favoured AL-anomaly template and discuss degeneracies with warm dark matter. The central claim is that the surviving power-spectrum signature is a localized bump whose amplitude and position can in principle recover the primordial feature scale.","tokens_in":24428,"tokens_out":8023,"duration_ms":74902,"significance":"If established, this result would open a new window for constraining inflationary physics at small scales and would sharpen the known degeneracies between primordial features and non-cold dark matter. The paper has real strengths: the in-in derivation in App. A is standard and internally consistent; the initial-condition power at z=32 is validated against the linear spectrum at the 2% level; the comparison with Halofit and with a separate AL-anomaly simulation is instructive; and the authors are candid about the preliminary nature of the study. At the same time, the quantitative support for the abstract's recoverability claim is currently weak: the z=0 residuals in Fig. 6 are a monotonic tilt at the resolution edge rather than a localized in-range peak, only one feature scale and one random seed are used, and no error bars or convergence tests are presented. The central claim is defensible as a proof of concept only if these gaps are addressed or the claims are substantially toned down.","major_comments":[{"comment":"The abstract and conclusion state that the surviving signature is a 'localised power enhancement or decrease' whose position can be used to recover the primordial feature scale. The simulations do not show any localized, in-range peak: at z=0 the residuals in Fig. 6 grow monotonically toward the smallest resolved scales, reaching about ±10% at the numerical edge, and no extremum is reported at a scale tied to kf=2 Mpc^-1. This is a broad tilt, degenerate with spectral-index running and with the WDM-like suppression fitted in Sec. IIIB3, so the position-recovery claim is not demonstrated. Because only kf=2 Mpc^-1 is simulated and no resolution or convergence study is presented, the scaling of any putative peak with kf is also untested. I recommend either softening the claims to match the demonstrated monotonic tilt, or running additional simulations with different kf values and larger dynamic range to establish whether a peak actually forms.","section":"Abstract; Sec. IIIB1, Fig. 6"},{"comment":"No error bars, covariance estimates, or seed-variation tests are provided for the matter power-spectrum ratios or the halo mass function ratios. All feature runs share a single random seed, so the noise from nonlinear mode coupling is unquantified; at z=0 the ±10% residuals could be partly sample variance or resolution artifacts, and the high-mass bins in Fig. 7 contain few halos. A convergence test varying box size, particle number, and random seed, together with an estimate of the ratio covariance, is needed before the quantitative survival amplitude can be considered robust.","section":"Sec. IIIB, Tables II-III, Figs. 6-7"},{"comment":"The N-body runs are initialized from the ad hoc Gaussian wave-packet template (14), not from the power spectra of the concrete UV-complete models computed in Sec. IIA. The fidelity of (14) to those models is established only qualitatively from Figs. 1-2, and the mapping between template parameters and UV-model parameters in Table III is presented without derivation or validation. The paper should either test at least one concrete model spectrum in the N-body code or explicitly restrict the conclusions to the template family, since the claim that the results apply to UV-complete inflationary models rests on this unvalidated equivalence.","section":"Sec. IIB2; Sec. IIIB; Table III"}],"minor_comments":[{"comment":"The display of Eq. (10) in the main text is typeset ambiguously, with a trailing 'sin(2kτ)' that appears to hang at the end of the brace; the derivation in App. A is clear, but the equation should be typeset consistently.","section":"Eq. (10)"},{"comment":"The relationship between the Dirac-delta templates (13) and the Gaussian envelope template (14) is not explained; in particular, Eq. (14) replaces the 1/(k/kf)^2 decay of the slow-roll template with a Gaussian envelope, and the text should state explicitly that this is a phenomenological fit rather than a limit of Eq. (13).","section":"Sec. IIB2"},{"comment":"The sentence 'the shaded gray region corresponds to the the scales simulated' contains a duplicated article; this is a minor typo.","section":"Sec. IIIB1"},{"comment":"The scaling argument δA Δk/kf is introduced with no derivation and then immediately shown to fail against the simulations; it would be helpful to state the assumptions under which it is derived so the reader can see why it is not expected to hold.","section":"Sec. IIIB1"},{"comment":"The conclusions repeat the 'localised power enhancement or decrease' phrasing; if the abstract is revised per the first major comment, the conclusions should be revised consistently to avoid overstating the demonstrated result.","section":"Sec. IV"}],"recommendation":"major_revision","confidential_remarks":"The manuscript fits the journal's scope and the authors' presentation is generally clear. My main concern is that the headline claim about recovering the primordial scale from a localized bump is ahead of the evidence presented; I would urge the editor to require either the additional simulations and error analysis described in the major comments or a commensurate softening of the abstract and conclusions. No issues with citation practice or novelty disclosure arose."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a genuinely useful proof of principle, but read the abstract as a hope, not a result. The dedicated N-body propagation of a sharp-feature template is new, and I buy the qualitative story: oscillations get washed out, a broad suppression/enhancement survives to z=0, and Halofit is not reliable for these spectra. The in-in derivation in App. A is standard and clean, the initial conditions check out at the 2% level, and the paper is honest about degeneracies with WDM, DAO, and modified gravity.\n\nThe soft spot is real and it is in the main claim. The text of Sec. IIIB1 describes the z=0 ratio as an enhancement/decrease above k = 2 Mpc−1 reaching ±10% at the smallest scales accessible. That is a monotonic tilt growing toward the resolution limit, not a localized bump peaking at a scale tied to kf. The abstract and conclusions claim the position can be used to recover the feature scale; nothing in the presented simulations demonstrates that, because no in-range peak is reported and only kf = 2 Mpc−1 is simulated. The stress-test note has this right.\n\nThe quantitative support is also thinner than the text implies: one random seed, no convergence test, no power-spectrum error bars or covariance. The HMF comparison is at least honest about Poisson errors, but the power-spectrum ratios carry no uncertainty. For a paper whose central quantitative claim is a surviving ~10% feature, that is a real gap.\n\nWhat I liked: taking the template from concrete UV models, checking Planck constraints first, using paired simulations with the same seed, and explicitly showing that the naive integrated-power scaling fails. The Halofit failure at z=0 is a useful caution for the community. The paper also flags its own limitations, including the degeneracy with WDM and the unresolved question of primordial non-Gaussianities.\n\nBottom line: worth a serious referee, but the abstract and conclusions need to be brought in line with the actual shape of the simulated signal, and the simulations need variance estimates and at least one additional kf before the position-recovery claim is credible. I would send this to review with a request for major revision.","headline":"Useful proof-of-principle N-body study, but the abstract overclaims: the surviving signal is a monotonic tilt at the resolution edge, not a localized bump whose position recovers kf.","tokens_in":24989,"tokens_out":2509,"would_cite":true,"duration_ms":24934,"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":"Sharp features from inflation leave surviving bumps in the nonlinear matter power spectrum.","keywords":["primordial power spectrum","sharp features","inflation","N-body simulations","nonlinear structure formation","matter power spectrum","halo mass function","cosmological tensions"],"falsifier":"Repeat the same initial-condition pipeline for several feature scales, say $k_f = 0.5$, $2$, and $5\\,\\mathrm{Mpc}^{-1}$, with multiple independent random seeds and at least two resolutions: if the location or amplitude of the $z=0$ bump does not track $k_f$ and $\\delta A$, or if the bump vanishes once cosmic variance is averaged, the paper's central claim is refuted.","tokens_in":24000,"feed_emoji":"🌌","tokens_out":12265,"duration_ms":109404,"temperature":0.7,"pith_summary":"Sudden violations of slow-roll inflation produce sharp features in the primordial power spectrum, and this paper asks whether those features can survive the strongly nonlinear gravitational evolution that builds cosmic structure. Using N-body simulations seeded with a Gaussian wave-packet feature at $k_f = 2\\,\\mathrm{Mpc}^{-1}$ and $|\\delta A|=0.2$, the authors find that the oscillatory ringing is erased by mode coupling, but a localised enhancement or deficit of roughly ten percent remains in the matter power spectrum at $z=0$, alongside an oscillatory signature in the halo mass function. The sign and position of the surviving bump track the amplitude and scale of the primordial feature, so nonlinear structure could in principle be used to recover the inflationary feature's parameters. Because CMB data allow such features at small scales, the result turns small-scale structure formation into a plausible new probe of inflation, while also warning that the effect is degenerate with exotic dark-matter scenarios and that current nonlinear emulators miss it.","feed_headline":"Sharp inflation signals survive as bumps in matter power spectrum","feed_subtitle":"Nonlinear evolution erases the ringing but leaves a localised bump tied to the primordial scale.","key_machinery":"The load-bearing object is the three-parameter Gaussian wave-packet template for the primordial power-spectrum correction, $$\\delta P_\\zeta(k) = \\delta A \\, $e^{{-(k-k_f)^2/(2\\Delta_k^2)}}$ \\sin(2k/k_f),$$ which the paper derives from a unified effective description in which a sharp feature is a transient bump in either the slow-roll parameter or the sound speed of curvature fluctuations. This single template reproduces the power spectra of a single-field step potential and of a multi-field turn, and it is what gets fed into the initial conditions of the simulations. The nonlinear stage is carried by matched $1024^3$-particle runs sharing one random seed, evolved from redshift 32 to $z=0$ with a standard Tree-PM N-body code; the comparison between feature and featureless runs isolates the surviving signal.","core_discovery":"On the paper's own terms, the discovery is that a sharp primordial feature of the wave-packet form $$\\delta P_\\zeta(k) = \\delta A \\exp\\left[-\\frac{(k-k_f)^2}{2\\$Delta_k^{2}$}\\right] \\sin\\left(2k/k_f\\right),$$ with $\\delta A = \\pm 0.2$ and $k_f = 2\\,\\mathrm{Mpc}^{-1}$, does not get completely erased by nonlinear structure formation. After evolving $1024^3$ particles to $z=0$, the oscillatory ringing has been damped away by mode coupling, but a localised enhancement or deficit of roughly ten percent in the matter power spectrum survives at scales above the feature scale, with a sign that follows $\\delta A$ and a position set by $k_f$. The same simulations produce a roughly ten percent oscillation in the halo mass function as a function of halo mass. The paper reads these residuals as proof of principle that the scale, amplitude, and sign of a primordial sharp feature can in principle be recovered from small-scale nonlinear structure, while cautioning that the signals resemble those of non-cold dark matter and therefore require joint probes.","pith_inferences":["If the bump's position truly tracks $k_f$ for a range of scales, the nonlinear matter power spectrum becomes a ruler for inflationary feature scales down to galactic scales, something the paper gestures at but does not demonstrate for other $k_f$.","The similarity to warm dark matter suggests a concrete discriminator: fit the power spectrum and the halo mass function jointly, since primordial features lack the characteristic low-mass cutoff of warm dark matter halos; the paper notes this possibility but does not quantify it.","Because the naive scaling of the bump with $\\delta A \\Delta_k/k_f$ fails, a one-loop effective-field-theory calculation for the wave-packet template would give a first-principles prediction for the bump amplitude and width that could be tested against the simulations.","A multi-seed, multi-resolution extension would put error bars on the roughly ten percent residuals; until then, the statistical significance of the surviving bump remains an open question."],"forward_implications":["Oscillatory, resonant features in the primordial spectrum are washed out by nonlinear mode coupling by $z=0$, so only the localised bump or dip is observable.","A measured bump in the nonlinear matter power spectrum can in principle recover the scale $k_f$ and the sign of the primordial feature amplitude $\\delta A$.","CMB constraints leave the $k_f \\gtrsim 1\\,\\mathrm{Mpc}^{-1}$ region open to features as large as order one, so the simulated configurations are not excluded.","The $z=3$ suppression in the negative-amplitude runs is comparable to the power deficit hinted by Lyman-$\\alpha$ forest data, making primordial features a candidate explanation for that tension.","Nonlinear emulators trained only on featureless simulations fail to reproduce the $z=0$ response, so reconstructing primordial features from data will require simulations or emulators that include them in initial conditions."],"supporting_citations":[{"why":"Supplies the CMB data and baseline cosmology used to constrain the feature parameters; the simulated amplitudes are chosen to stay below those constraints.","marker":"[5]"},{"why":"Step-potential model in single-field inflation whose numerically solved spectrum motivates the sharp-feature template.","marker":"[23]"},{"why":"Early model of a sudden slow-roll violation that provides the physical mechanism behind the sharp features studied here.","marker":"[108]"},{"why":"Kinetic-turn model in multi-field inflation that motivates the speed-of-sound feature template and the boost in primordial power.","marker":"[119]"},{"why":"Supplies the in-in integral that turns a transient slow-roll or sound-speed feature into the power-spectrum correction used for template building.","marker":"[16]"},{"why":"The nonlinear emulator used as a comparison; its failure for sharp-feature runs motivates the call for feature-aware emulators.","marker":"[131]"},{"why":"The N-body code used for the simulations; the paper's central z=0 results are produced with it.","marker":"[142]"},{"why":"Earlier dark-acoustic-oscillation simulations showing oscillations washed out while the feature scale survives, which the paper extends to primordial features and the halo mass function.","marker":"[145]"},{"why":"Provides the template for the phenomenological feature favoured by CMB data and the comparison results used in the case-study simulation.","marker":"[52]"}],"fun_headline_variants":["Ringing erased, but sharp inflation bump survives","Sharp feature leaves local bump despite nonlinear washout","Inflation feature bump survives, ringing does not","Nonlinear evolution preserves localized feature bumps","Sharp primordial bumps persist, ringing fades"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument depends on the simulated Gaussian wave-packet shape, with the feature scale tied to its oscillation frequency and a 20 percent amplitude, being what real inflation models produce; the authors test only one feature scale, one random seed, and no resolution or convergence study.","fun_headline_variants_meta":{"raw":{"variants":["Ringing erased, but sharp inflation bump survives","Sharp feature leaves local bump despite nonlinear washout","Inflation feature bump survives, ringing does not","Nonlinear evolution preserves localized feature bumps","Sharp primordial bumps persist, ringing fades"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00059,"raw_usage":{"total_tokens":2805,"prompt_tokens":1019,"completion_tokens":1786,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":635,"completion_tokens_details":{"reasoning_tokens":1718}},"tokens_in":635,"tokens_out":1786,"duration_ms":13201,"temperature":1.0,"reasoning_tokens":1718,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-09T11:42:03.077483+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Repeat the same initial-condition pipeline for several feature scales, say $k_f = 0.5$, $2$, and $5\\,\\mathrm{Mpc}^{-1}$, with multiple independent random seeds and at least two resolutions: if the location or amplitude of the $z=0$ bump does not track $k_f$ and $\\delta A$, or if the bump vanishes once cosmic variance is averaged, the paper's central claim is refuted.","supporting_citations":[],"review_version":1}