{"id":"6d97748b-2776-400d-a396-22b9a223e21d","arxiv_id":"2501.03065","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":3.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"A thesis that develops non-Gaussian PBH abundance computations, argues that broad power spectra are dominated by the broadest compaction profiles (threshold 2/5), and uses LVK and PTA data to constrain PBH models.","lead":"This PhD thesis compiles the author's published research on primordial black holes (PBHs), focusing on how non-Gaussianities affect PBH abundance calculations and how gravitational wave data from pulsar timing arrays and LIGO/Virgo can constrain PBH models. A central observation is that for broad curvature power spectra, the PBH formation threshold is set by the broadest compaction profiles, not the average one.","discovery_kind":"review","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 'always 2/5' threshold is an extrapolation: Eq. (3.43) is assumed valid for non-Gaussian broad profiles, but this is untested; a numerical relativity check of the actual dominant profiles is required.","rationale":"The reader's weakest assumption already identifies the same load-bearing point: the universal 2/5 threshold rests on the empirical fit Eq. (3.43) and on a Gaussian statistical analysis that is assumed to extend to non-Gaussian fields. My stress-test sharpens this into a precise testable condition: the profiles that dominate the abundance in the non-Gaussian case are not the same as the profiles for which Eq. (3.43) was calibrated, so the threshold must be re-measured for those profiles. Since the thesis is already CONDITIONAL and the concern reinforces the existing verdict rather than overturning it, I recommend no change to the reader's verdict. The proposed numerical relativity check is the decisive experiment: it directly tests whether the central 'always 2/5' claim holds for the non-Gaussian broad spectra that the thesis itself emphasizes as the realistic case.","tokens_in":57728,"tokens_out":5917,"duration_ms":59812,"concrete_test":"Perform numerical-relativity collapse simulations for the specific non-Gaussian profiles used in Sec. 3.3.3, e.g. ζ=-μ ln(1-ζ_G/μ) with μ=5/2 and a log-normal power spectrum with Δ=1 and k_* r_m=2. For each simulated profile, measure the critical compaction C_c from the threshold amplitude and compute q from Eq. (3.42). Check whether the q→0 branch that dominates the abundance has C_c=2/5 within the numerical uncertainty (say 5%). If C_c deviates from 2/5 for these profiles, the 'always 2/5' statement in the Sec. 3.3 Summary fails for non-Gaussian broad spectra, and the abundance and constraint calculations built on it must be revised.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim, stated in Sec. 3.3 Summary as 'The corresponding threshold is, therefore, always 2/5', requires two independent conditions: (i) for non-peaked power spectra the PBH abundance is dominated by compaction profiles with peak curvature q close to 0, and (ii) the true critical threshold for those q→0 profiles is C_th(0)=2/5. Condition (i) is demonstrated analytically only under Gaussian statistics (Eq. 3.91) and numerically for one USR example (Fig. 3.16); condition (ii) is assumed by carrying the empirical fit Eq. (3.43) into the non-Gaussian computation of Eq. (3.105). But Eq. (3.43) was calibrated on a restricted family of compaction profiles, and the non-Gaussian map ζ=F(ζ_G) changes the relation between the linear compaction C_G, the peak curvature q, and the full compaction C (Eqs. 3.49, 3.104). A profile with q→0 in the non-Gaussian field is therefore not guaranteed to have the same threshold as the q→0 profile used to extract 2/5. The thesis itself notes in Sec. 3.2.1 (footnote 6) that primordial NG can shift δ_c by a few percent for |f_NL|<O(5), yet Sec. 3.3.3 keeps C_th(q) unchanged. Because β depends exponentially on the threshold, even a 10% shift in C_th changes the amplitude A required for a fixed abundance by O(1) and propagates into all derived abundance and constraint results. The universal claim is thus an extrapolation beyond the tested domain rather than an established result.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This PhD thesis develops a comprehensive framework for computing the primordial black hole (PBH) abundance from inflationary curvature perturbations, with emphasis on primordial non-Gaussianities, threshold statistics on the compaction function, and the dependence of the collapse threshold on the compaction profile. It derives a master formula for the abundance with arbitrary local non-Gaussianity (Eq. 3.58), generalizes it to the PBH mass function (Eq. 3.68), and proposes in Sec. 3.3 that for non-peaked power spectra the abundance is dominated by the broadest compaction profiles, with a claimed universal threshold C_th = 2/5. The thesis then applies these tools to update LVK O3 and PTA constraints, discusses scalar-induced gravitational waves, and analyzes single-field ultra slow-roll and curvaton production models. The abstract and conclusions present PBHs as potential dark matter candidates and as a possible source of the PTA signal.","tokens_in":58101,"tokens_out":6809,"duration_ms":65470,"significance":"If the 'always 2/5' claim survives scrutiny, it is an important result: abundance predictions for broad power spectra would shift by orders of magnitude relative to average-profile prescriptions, with direct consequences for PBH-dark-matter and PTA interpretations. The manuscript is strong in presenting exact resummation-based formulas, in carefully assessing the convergence of perturbative expansions, and in spelling out applied constraints from LVK and PTA data. It also gives credit to the underlying numerical relativity inputs. However, the universal-threshold claim rests on an empirical fit to C_th(q) that has not been validated for the non-Gaussian profiles used in Sec. 3.3.3, and several phenomenological 'predictions' are obtained only after tuning the amplitude A to a target abundance. The core idea is promising, but at present the evidence is not yet at the level required for the strongest version of the claim.","major_comments":[{"comment":"The central claim that the threshold is 'always 2/5' for non-peaked power spectra is an extrapolation beyond the calibrated domain of Eq. (3.43). The numerical fit C_th(q) was calibrated on a restricted family of compaction profiles in Refs. [263,265]; the non-Gaussian map ζ = F(ζ_G) changes the relation between C_G, q, and C (Eqs. 3.49 and 3.104), so a profile with q → 0 in the non-Gaussian field is not guaranteed to have the same threshold as the q → 0 profile used to extract 2/5. The manuscript itself notes in Sec. 3.2.1 (footnote 6) that primordial non-Gaussianity can shift δ_c by a few percent for |f_NL| < O(5), yet Sec. 3.3.3 keeps C_th(q) unchanged while using strongly non-Gaussian examples (µ* = 5/2, r_dec = 0.1). Because β depends exponentially on the threshold, even a 10% shift in C_th changes the amplitude A required for a fixed abundance by O(1) and propagates into all derived abundance and constraint results. A dedicated numerical relativity check of the dominant non-Gaussian profiles, or a clearly stated restriction of the universal claim to Gaussian curvature perturbations, is needed before the 'always 2/5' statement can be accepted.","section":"Sec. 3.2.2, Eq. (3.58); Sec. 3.2.3, Eq. (3.68)"},{"comment":"Several phenomenological conclusions are obtained by fixing the amplitude A to match a reference abundance (e.g., β ≃ 10^-16 in Fig. 3.8, or f_PBH = 1 in Fig. 3.11) and then interpreting the resulting mass function as a prediction. This is a consistency constraint rather than a parameter-free prediction: because β depends exponentially on A and C_th, a different threshold choice is reabsorbed by an O(1) change in A, as the thesis itself acknowledges around Figs. 3.5 and 3.8. The text should state more explicitly in each application which results are robust to this tuning and which are only illustrative; otherwise the distinction between 'prediction' and 'fit' is blurred in the abstract and in Chapter 5.","section":"Sec. 3.2.2, Eq. (3.58); Sec. 3.2.3, Eq. (3.68)"},{"comment":"The manuscript uses two different thresholds for the same broad-power-spectrum case: C_th = 0.56 from the average-profile prescription (Eq. 3.45) and C_th = 2/5 from the broad-profile prescription (Section 3.3). The comparison in Fig. 3.17 is performed for a log-normal spectrum with Δ = 1 and fixed q = 0.5 and shows a ratio β/β_0 of order one, but this is a single benchmark. Because the abundance is exponentially sensitive to the threshold, a systematic scan in Δ, µ* (or r_dec), and q is needed to establish that the two prescriptions agree within the stated accuracy, or to justify replacing the 0.56 threshold by 2/5.","section":"Sec. 3.2.1, Eq. (3.45); Sec. 3.3.4, Fig. 3.17"}],"minor_comments":[{"comment":"The figure references 'fig.2.10' should read 'fig.3.10' in the three places where they appear in the text.","section":"Sec. 3.2.2"},{"comment":"The heading 'Classification of the costraints' contains a typo; it should be 'constraints'.","section":"Sec. 4.1"},{"comment":"The formula for C_th(q) is typeset in a way that is ambiguous: the incomplete gamma function should be written with explicit parentheses, e.g., Γ(5/(2q)) − Γ(5/(2q), 1/q), to avoid confusion.","section":"Eq. (3.43)"},{"comment":"The symbol γ is overloaded: γ_m in Eq. (3.27), the critical-collapse exponent γ in Eq. (3.30), and the correlation coefficient γ in Eq. (3.78). Distinct symbols or a short nomenclature table would improve readability.","section":"Throughout, especially Eqs. (3.27), (3.30), (3.78)"},{"comment":"The thesis interleaves textbook review material with original computations, and it would benefit from an explicit statement in each chapter separating the author's own results from previously published work with which the thesis is in dialogue.","section":"General structure"}],"recommendation":"major_revision","confidential_remarks":"This is a PhD thesis by publication, and most technical chapters have already passed peer review as separate papers. The main risk I see is that the novel universal-threshold claim in Sec. 3.3 has not yet been tested in numerical relativity for the non-Gaussian profiles used there; I would ask the editor to require either a validation of that claim or a clearly tempered statement. The rest of the thesis is a comprehensive and useful synthesis, and the applied constraints are competently presented, but the strongest advertised conclusion should not outrun its evidence."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Read this thesis if you want a single place to see the author's framework for PBH abundances with non-Gaussianities, from threshold statistics on the compaction function to updated LVK/PTA constraints. The main new claim is that for non-peaked power spectra the abundance is dominated by the broadest compaction profiles, so the threshold is always 2/5. That claim is plausible but not proven; it rests on an extrapolation of an empirical fitting function.\n\nThe thesis does a lot well. The perturbative expansion of local non-Gaussianities and its breakdown for broad spectra is treated carefully and convincingly. The master formula for the abundance (Eq. 3.58) is a useful synthesis, and the mass-function computations around the QCD peak are concrete. The constraint chapters are competently done; the inclusion of the three-body binary formation channel in the LVK analysis is a genuine update, and the PTA constraints are handled with appropriate care. The author is also honest about the fact that the amplitude A is tuned to match reference abundances, so many 'predictions' are actually fits.\n\nThe soft spot is the 'always 2/5' threshold. It depends on Eq. (3.43), a numerical fit calibrated on a restricted family of compaction profiles. In the non-Gaussian extension (Sec. 3.3.3), the same fit is used without checking that the non-linear map zeta=F(zeta_G) preserves the relation between the peak curvature of the linear compaction and the true threshold. The thesis itself notes (footnote 6) that primordial non-Gaussianities can shift delta_c by a few percent for |f_NL| < O(5), but then uses the same C_th(q) anyway. Since beta depends exponentially on the threshold, even a 10% shift in C_th changes the required amplitude A by O(1), which propagates into all derived abundances. The 'always' in 'always 2/5' is thus an extrapolation, not an established result. The thesis does show that for broad spectra the abundance is dominated by small q profiles, but the universal value needs a numerical check.\n\nWho is it for? People actively computing PBH abundances from broad power spectra and interpreting LVK/PTA signals. They will find the framework useful, but should treat the 2/5 claim as an approximation to be tested against full numerical relativity (or at least against the non-Gaussian profiles explicitly).\n\nMy recommendation: send it to peer review. The framework and constraints are useful, and the central claim is significant enough to warrant scrutiny. But the referee should insist on either a numerical relativity check or a clear caveat that the universal threshold holds only in the Gaussian limit for the fitted family.","headline":"A systematic compilation of PBH abundance methods; the 'always 2/5' threshold for broad spectra is an extrapolation that needs testing, not a settled result.","tokens_in":58631,"tokens_out":4118,"would_cite":false,"duration_ms":40574,"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":"Broadest profiles set the critical compaction threshold at 2/5","keywords":["Primordial black holes","Critical collapse","Compaction function","Threshold statistics","Broad power spectrum","Non-Gaussianities","Gravitational waves","Dark matter"],"falsifier":"Numerical relativity simulations of collapse starting from a set of broad, non-peaked initial profiles with the same compaction maximum but different peak curvatures should find the critical compaction threshold equal to $2/5$ in every case; a spread in thresholds, or values clearly different from $2/5$, would falsify the universal-threshold claim.","tokens_in":57488,"feed_emoji":"🕳️","tokens_out":7252,"duration_ms":105189,"temperature":0.7,"pith_summary":"This thesis tries to establish a sharper rule for when an overdensity in the early universe collapses into a primordial black hole. It argues that, for the broad and non-peaked power spectra that realistic inflationary models tend to produce, the critical threshold is set not by the statistically average compaction profile but by the broadest profiles. The threshold then takes a universal value, 2/5, independent of the shape of the power spectrum. If this is right, standard abundance computations that use average profiles need revision, and the change matters for how much dark matter PBHs can explain and for the gravitational-wave backgrounds associated with their formation.","feed_headline":"Broadest profiles set the critical compaction threshold at 2/5","feed_subtitle":"If right, primordial black hole abundance predictions for broad power spectra must be revised.","key_machinery":"The load-bearing object is the compaction function $C(r)$, twice the local mass excess over the areal radius, which on superhorizon scales reads $C(r)=-2\\Phi r\\,\\zeta'(r)[1+\\tfrac{r}{2}\\zeta'(r)]$. Collapse occurs when its maximum exceeds a threshold $C_{\\rm th}$ that depends on the peak curvature $q=-\\tfrac{r_m^2 C''(r_m)}{4C(r_m)}$, with $C_{\\rm th}(q)$ running from $2/3$ for spiky profiles to $2/5$ for broad ones. The abundance calculation is carried by the joint Gaussian probability of the compaction and the curvature perturbation, with a correlation parameter $\\gamma$ that is near unity for peaked spectra and small for broad spectra. Minimizing the effective squared threshold in $q$ pushes the dominant contribution to $q=0$ once $\\gamma$ falls below a critical value, which is the mechanism that makes $2/5$ universal. The volume-averaged compaction, $\\bar{C}(R_m)=\\frac{3}{R_m^3}\\int_0^{R_m} dx\\,x^2 C(x)$, has threshold $2/5$ for both spiky and broad profiles, providing the profile-independent extension.","core_discovery":"The paper's central claim is that the relevant critical threshold for primordial black hole formation from critical collapse is the one corresponding to the broadest compaction profiles whenever the curvature power spectrum is not sharply peaked. Concretely, the threshold function $C_{\\rm th}(q)$, which grows from $2/5$ to $2/3$ as the curvature at the compaction peak increases, enters the abundance integral through an effective threshold; for broad spectra, parametrized by a small correlation parameter $\\gamma$, the effective threshold is minimized at $q=0$, forcing $C_{\\rm th}=2/5$. The same conclusion holds in the non-Gaussian case for the logarithmic USR-type relation. For very peaked spectra, by contrast, the average profile remains the right choice. The thesis also shows that the volume average of the compaction function has a profile-independent threshold of $2/5$, a step toward an observable with no shape dependence.","pith_inferences":["If the $2/5$ threshold is universal for broad spectra, published PBH constraints that were derived with average-profile thresholds may need to be re-derived; the direction and size of the shift will depend on each model's spectrum width.","The volume-averaged compaction route suggests a practical test: compute the one-point statistics of $\\bar C(R_m)$ directly from the curvature power spectrum and compare PBH abundances against threshold-statistics results; numerical simulations can then settle whether $2/5$ is truly independent of profile.","Because the broadest profiles are rare, the claim implies that PBH formation selects atypical fluctuations; if confirmed, this would also affect predictions for the clustering and spin distribution of PBHs, since the collapsing profiles are not the average ones."],"forward_implications":["For any non-peaked power spectrum, PBH abundance should be computed with the $2/5$ threshold rather than the average-profile threshold; this typically lowers the predicted abundance at a fixed amplitude.","Peaked spectra remain governed by the average profile, so the universal threshold applies only once the spectrum is sufficiently broad.","The result extends to the non-Gaussian case for positive, log-type non-Gaussianity, so the $2/5$ rule survives beyond Gaussian statistics.","Because thresholds enter abundances exponentially, small threshold changes translate into large abundance changes, and retuning the power-spectrum amplitude to compensate changes other predictions such as the induced gravitational-wave signal.","A profile-independent observable, the volume average of the compaction, can be used with threshold $2/5$; its statistics reduce to computing connected cumulants of the volume-averaged compaction."],"supporting_citations":[{"why":"This reference supplies the result that the abundance is dominated by the broadest compaction profiles for non-peaked spectra, which is the basis of Section 3.3.","marker":"[6]"},{"why":"This reference introduces the compaction function as the collapse criterion and provides the threshold behavior that the thesis builds on.","marker":"[263]"},{"why":"This reference gives the numerical fit $C_{\\rm th}(q)$ used to set the $q\\to 0$ threshold at $2/5$.","marker":"[265]"},{"why":"This reference provides the smoothing scale $r_m$ and the threshold values for log-normal and broad power spectra used throughout the abundance computations.","marker":"[254]"},{"why":"This reference develops the threshold-statistics master formula for the PBH mass fraction with non-Gaussianities that Section 3.2 extends.","marker":"[1]"},{"why":"This reference supplies the two-dimensional Gaussian probability for the compaction and curvature perturbation and the high-peak limit used in the analysis.","marker":"[264]"},{"why":"This reference provides the logarithmic USR-type non-Gaussian relation used in the worked examples of the broad-profile argument.","marker":"[247]"}],"fun_headline_variants":["PBH threshold pinned to 2/5 for broad spectra","Broad spectra set PBH threshold at 2/5","Why broad profiles dictate PBH formation threshold","Critical compaction threshold drops to 2/5 for wide spectra","Cosmic whispers: PBH threshold fixed by broadest profiles"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The universal $2/5$ threshold holds if the numerically fitted threshold function $C_{\\rm th}(q)$ is accurate for every profile shape and if the minimum of the effective threshold really sits at $q=0$ for broad, non-Gaussian spectra; if either fails, the universal value does not follow.","fun_headline_variants_meta":{"raw":{"variants":["PBH threshold pinned to 2/5 for broad spectra","Broad spectra set PBH threshold at 2/5","Why broad profiles dictate PBH formation threshold","Critical compaction threshold drops to 2/5 for wide spectra","Cosmic whispers: PBH threshold fixed by broadest profiles"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000294,"raw_usage":{"total_tokens":1733,"prompt_tokens":987,"completion_tokens":746,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":603,"completion_tokens_details":{"reasoning_tokens":665}},"tokens_in":603,"tokens_out":746,"duration_ms":7031,"temperature":1.0,"reasoning_tokens":665,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T21:56:36.878734+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Numerical relativity simulations of collapse starting from a set of broad, non-peaked initial profiles with the same compaction maximum but different peak curvatures should find the critical compaction threshold equal to $2/5$ in every case; a spread in thresholds, or values clearly different from $2/5$, would falsify the universal-threshold claim.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"This reference develops the threshold-statistics master formula for the PBH mass fraction with non-Gaussianities that Section 3.2 extends."}],"review_version":1}