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All documents · Literature audits (23 September)

Literature verification & novelty report — PBH formation in a matter-dominated / oscillating-scalar era

EN 2026-09-23 · 33.1 KB · Markdown

Verification date: 2026-09-23. Everything below was taken from fetched text (arXiv abstract pages, arXiv HTML/PDF full texts converted locally with pdftotext, GitHub API, INSPIRE API, arXiv API). Quotes are verbatim; my own arithmetic is labelled as such.

Part 1 — Ledger of observational / cosmological inputs

# Item STATUS Key verbatim evidence Source
1 Carr et al. 2026, arXiv:2601.06024 VERIFIED-WITH-CORRECTION Title: "Primordial black holes: constraints, potential evidence and prospects" (Carr, Iovino, Perna, Vaskonen, Veermäe; v1 9 Jan 2026, v2 1 Apr 2026). Sec. V: the window (≈10⁻¹⁷–10⁻¹⁰ M⊙) "remains the only unconstrained region in the PBH mass spectrum. These PBHs are too heavy to evaporate, and the optical ML searches are insensitive due to wave-optics and finite-source-size effects"; closing: "The asteroid-mass window currently lacks robust observational constraints, making it an interesting target for future searches." Near 10¹⁹–10²⁰ g it lists and then discounts: (i) WD ignition [Graham+2015]: "From the observed survival of WDs, it was inferred that PBHs with masses 10^19–10^20 g cannot make up the bulk of the local DM" but "...fail to produce self-sustaining ignition"; (ii) dwarf-galaxy star destruction [351–354, incl. Esser et al. 2025 = arXiv:2503.03352]: "An alternative approach considers the potential destruction of main-sequence stars in dwarf galaxies, which are known to be DM dominated. However, although realistic accretion modelling yields consumption times comparable to the simple Bondi time for compact stars [355], recent work indicates that the lifetimes of main-sequence stars are much longer than the Bondi time and remain largely unaffected by asteroid-mass PBHs embedded in their cores [356]" ([356] = Bellinger et al. 2023, arXiv:2312.06782); (iii) NS in globular clusters: "sensitive to the density of DM in globular clusters, which remains highly uncertain"; (iv) femtolensing: "does not hold". Correction: the review never states "f_PBH = 1 is allowed"; it says the window "lacks robust observational constraints". It cites Esser et al. 2025 but does not treat it as robust. Gottlieb et al. 2026 is not cited (v2 predates it). https://arxiv.org/abs/2601.06024 ; https://arxiv.org/html/2601.06024v2
2 Gorton & Green 2024, arXiv:2403.03839 VERIFIED Title: "How open is the asteroid-mass primordial black hole window?" Abstract: "We find that for current constraints the asteroid-mass window narrows, but remains open (i.e. all of the DM can be in the form of PBHs) unless the PBH MF is wider than expected. Future evaporation and microlensing constraints may together exclude all of the DM being in PBHs, depending on the width of the PBH MF and also the shape of its low and high mass tails." (Abstract only; the conclusions section was not separately fetched.) https://arxiv.org/abs/2403.03839
3 Esser et al. 2025, arXiv:2503.03352 VERIFIED Title: "Constraints on asteroid-mass primordial black holes in dwarf galaxies using Hubble Space Telescope photometry" (A&A 698, A290). "In the ultra-faint dwarf galaxy Triangulum II, PBHs around 10^19g are excluded at the 2σ (3σ) level from constituting more than ~55% (~78%) of the dark matter, while the possibility that PBHs represent the entirety of the DM is excluded at the 3.7σ level." https://arxiv.org/abs/2503.03352
4 Gottlieb et al. 2026, arXiv:2606.02700 VERIFIED-WITH-CORRECTION Title: "The Life and Death of Stars That Capture Primordial Black Holes" (Gottlieb, Cantiello, Norton, Van Tilburg, Kleban; 1 Jun 2026). Abstract: "PBHs in the asteroid mass window (10^17−10^23 g) remain viable dark matter candidates and can be captured by stars... We find that the fate of these systems bifurcates: PBHs that form an accretion disk before consuming the host drive explosive disruption, whereas PBHs captured too late or growing too slowly consume the star quietly." It does claim the Esser limits should be weakened — Sec. 10.3: "our analysis of the capture process indicates that stellar capture of light PBHs—those in the mass window where they may constitute all of the DM—is a rare occurrence. It requires a binary companion that is sufficiently massive and close to the host star... Therefore, we suspect that distortions of stellar mass functions are always small, and that PBH constraints based on stellar populations (Esser et al. 2025) should be significantly weakened." Correction to the brief's framing: the mechanism is capture inefficiency (two-body capture "negligibly rare"; three-body capture via planetary companions, M_crit ∼ 10²² g for inspiral within a MS lifetime), not survival via slow accretion. On accretion: "For MBH=10^−16 M⊙, the Bondi growth time at solar-core conditions tB≈10^10 yr (MBH/10^−16 M⊙)^−1" and "critical initial PBH mass M₀∼10^−16 M⊙ for a solar-type star to reach a main-sequence endpoint within a Hubble time" — so a 10¹⁹ g PBH (5×10⁻¹⁵ M⊙) consumes a solar-type star in ∼2×10⁸ yr; accretion efficiency "η ∼ 10^−2, below the thin-disk value assumed in earlier work". Their capture critique: "It has been suggested that the time-dependent gravitational potential during star formation can enhance PBH capture through adiabatic contraction (Capela et al. 2013, 2014; Esser & Tinyakov 2023). However, these analyses assume an initial position-independent Maxwellian velocity distribution, rather than a phase-space distribution that depends on the gravitational potential of the protostellar cloud." https://arxiv.org/abs/2606.02700 ; PDF text (Sec. 2, 3, 10.3)
5 De la Torre Luque et al. evaporation constraints + "March 2026 erratum" VERIFIED-WITH-CORRECTION Paper: De la Torre Luque, Koechler, Balaji, "Refining Galactic primordial black hole evaporation constraints", arXiv:2406.11949 (v1 17 Jun 2024; v2 25 Mar 2026, comments "13 pages, 9 figures, erratum version at the end"), PRD 110, 123022 (2024). Erratum: PRD 112, 109904 (25 Nov 2025) — so the erratum is Nov 2025 in PRD; March 2026 is only the arXiv v2 posting. Erratum text: "We correct the results obtained using the diffuse X-ray emission from Xmm-Newton, in light of new results from Ref. [63], that demonstrated that the dataset employed was misevaluated. We also update our calculation of the 511 keV emission from evaporating PBHs, which leads to slightly more conservative constraints as well."; "the exposure-weighted average solid angle is 3.463 × 10^−5 sr, while the geometric angle is 0.156 sr, which is more than 4 orders of magnitude higher"; "This correction weakens the PBH fraction limits at low PBH masses, while the effect is not appreciable at high PBH masses, around ∼ 10^17 g."; "The conclusions of our papers remain unchanged, although the XMM-Newton constraints on fPBH weakened substantially. The 511 keV constraint was corrected and remains one of the leading existing constraints, while the Voyager-1 constraint required no revision." Corrected numerical f_PBH bounds at 10¹⁵–10¹⁶ g are NOT stated in the text — only in corrected Figs. S3/S4 ("95% confidence limits"). The erratum figure legends use normalisations "MPBH = 10^15 g, fPBH = 2.9×10^−12; 10^16 g, fPBH = 1.9×10^−9; 10^17 g, fPBH = 1.6×10^−6" (XMM, Fig. S1) and "10^15 g fPBH=3×10^−8; 10^16 g fPBH=6.5×10^−6; 10^17 g fPBH=1.1×10^−3" (511 keV, Fig. S2), but nothing says these equal the limits — do not cite them as bounds. The (unchanged) main text still says "PBHs can constitute a significant fraction of the DM only in the gap between 10^18−10^21 g". Related: De la Torre Luque, Balaji, Silk ApJL 973, L6 (2024) [arXiv:2312.04907] also carries an erratum (ApJL 991, L29 (2025)). https://arxiv.org/abs/2406.11949 ; https://journals.aps.org/prd/abstract/10.1103/msry-jczm
6 ACT DR6 n_s VERIFIED-WITH-CORRECTION Louis et al., arXiv:2503.14452, "The Atacama Cosmology Telescope: DR6 Power Spectra, Likelihoods and ΛCDM Parameters". Abstract: "a spectral index of n_s=0.974±0.003" for P-ACT-LB. Table 5 row (verbatim): "ns ... 0.9666 ± 0.0077 0.9651 ± 0.0044
7 Poltergeist status & ΔN_eff VERIFIED-WITH-CORRECTION (see notes below) Enhancement is still claimed for sudden transitions but only within a linear-theory UV cutoff; gradual transitions give no enhancement; the newest work (May 2026) shows PBH-reheating poltergeist signals are suppressed by the critical-collapse mass tail. Details and quotes in Note 7. see Note 7
8 Ω_GW h² ≈ 10⁻⁵ P_ζ² and LISA 10⁻¹²–10⁻¹³ VERIFIED (with nuance) Kohri & Terada 2018 (arXiv:1804.08577, PRD 97, 123532), monochromatic source Eq. (28)–(29): "Pζ(k) = Aζ δ(log k/k∗)"; "ΩGW(η,k) = (3A²ζ/64) ((4−k̃²)/4)² k̃²(3k̃²−2)² [π²(3k̃²−2)²Θ(2√3−3k̃) + (4 + (3k̃²−2) log 1−4/(3k̃²)
9 f_GW ≈ 2.6×10⁻² Hz (γ 10¹⁹ g/M · T_RH/10⁵ GeV)^{1/3} VERIFIED (coefficient reproduced) My derivation (Note 9) gives 2.60×10⁻² Hz with g* = 106.75; structure (∝ (γ/M)^{1/3} T_RH^{1/3}) is exactly right. Standard k–T anchor: Saikawa & Shirai 2018, Eq. (2.15): "f = k/(2πa0) = Hhc ahc/(2π a0) ≈ 2.65 Hz (g∗s,fin/3.931)^{1/3}(g∗ρ,hc/106.75)^{1/2}(g∗s,hc/106.75)^{−1/3}(Thc/10^8 GeV)". Caveat: Domènech's review Eq. (2.32), "krh = 1.2 × 10^12 Mpc^−1 (Trh/5×10^4 GeV)(g∗/106.75)^{1/2}(g∗s/106.75)^{−1/3}", has a ∼1.4× larger normalisation; with it the coefficient would be ≈3.6×10⁻² Hz. https://arxiv.org/abs/1803.01038 ; https://arxiv.org/abs/2109.01398

Note 7 — Poltergeist mechanism: current status (quotes)

  • Inomata, Kohri, Nakama, Terada 2019a, arXiv:1904.12879 (PRD 100, 043532): enhancement "even if the scalar perturbations on small scales are not enhanced relative to those on large scales"; arXiv v4 (2023): "an error in numerical calculation corrected", conclusions unchanged. https://arxiv.org/abs/1904.12879
  • Inomata et al. 2019b (gradual transition), arXiv:1904.12878 (JCAP 10 (2019) 071): "the presence of an early matter-dominated era does not necessarily enhance the induced gravitational waves" (potential decays during a Hubble-time transition). https://arxiv.org/abs/1904.12878
  • Inomata, Kawasaki, Mukaida, Terada, Yanagida 2020, arXiv:2003.10455 (PRD 101, 123533): PBH-evaporation "sudden reheating" enhancement; "β ≳ 10⁻⁵ - 10⁻⁸ for O(10³ - 10⁵) g PBHs can be constrained ... if the width of the mass function is smaller than about a hundredth of the mass." https://arxiv.org/abs/2003.10455
  • Review: Inomata, Kohri, Terada, arXiv:2511.07266 (10 Nov 2025), "The poltergeist mechanism -- Enhancement of scalar-induced gravitational waves with early matter-dominated era". Enhancement is still claimed for sudden transitions; the nonlinear cutoff is explicit: "|δ| ∼ (1/10)(kη)² Pζ^{1/2}" (Eq. 115); "kNL ∼ √10 ηR^{−1} Pζ^{−1/4} ∼ 470/ηR" (Eq. 116, for Pζ = 2.1×10⁻⁹); "Once the density perturbations become larger than one, the perturbation theory breaks down"; "If the density perturbation becomes larger than unity ... we cannot obtain any reliable results after that on the perturbation evolution without the nonlinear (or nonperturbative) calculation method." Peak scaling (for Pζ = A_s Θ(k_max−k)): "ΩGW(ηc,k)/A_s² ≃ ... 7 × 10^−7 x_R^7 (x_max,R^{5/6} ≲ x_R ≲ x_max,R)", i.e. "proportional to (kmax ηR)^7". N_eff: Fig. 9 caption: "The shaded region is excluded by the constraints on the dark radiation Neff from big bang nucleosynthesis and Planck data." Conclusions: "Another important future direction is understanding the GW spectrum in the presence of nonlinear density perturbations. While our current treatment is conservative, the introduction of the UV cutoff scale is artificial and affects the spectral shape." https://arxiv.org/abs/2511.07266
  • Pearce, Pearce, White, Balázs, arXiv:2311.12340 (JCAP 06 (2024)): "If matter domination ends gradually, a cancellation results in an extremely suppressed signal, while in the limit of an instantaneous transition, there is a resonant-like enhancement"; "the red curve (corresponding to β=50/ηR) is already suppressed by roughly three orders of magnitude compared to the rapid limit." No N_eff bound is derived in that paper (only "provided that it ended before nucleosynthesis"); I found no paper titled "the poltergeist bound". https://arxiv.org/abs/2311.12340
  • Domènech & Tränkle, arXiv:2409.12125 (PRD 111, 063528 (2025)), "From formation to evaporation: Induced gravitational wave probes of the primordial black hole reheating scenario". https://arxiv.org/abs/2409.12125
  • Gouttenoire, Leister, Schwaller, arXiv:2605.21477 (20 May 2026), "Opening the Window of Ultra-Light PBHs by Exorcising the Poltergeist": "Standard monochromatic treatments predict nearly simultaneous evaporation, abrupt reheating, and a large Poltergeist scalar-induced gravitational wave signal"; with the critical-collapse tail ψ_f(M) ∝ M^{3.78}: "For a monochromatic mass function, the signal, dominated by the Poltergeist component, can violate ΔNeff<0.34. Instead, with the Choptuik infrared tail of the PBH mass distribution, the BBN bound and the reach by GW observatories are entirely relaxed." (PBH-reheating context, not an oscillating scalar.) https://arxiv.org/abs/2605.21477
  • ΔN_eff for P_ζ ∼ 10⁻³ (my arithmetic, not a quote): Eq. (116) gives k_NL η_R ≈ √10·(10⁻³)^{−1/4} ≈ 18, i.e. modes only ∼18× inside the horizon at reheating are already nonlinear during the eMD era. Using the review's fit with x_max,R = 18: Ω_GW(η_c)/A_s² ≈ 7×10⁻⁷·18⁷ ≈ 4×10² ⇒ Ω_GW(η_c) ≈ 4×10⁻⁴ ⇒ Ω_GW,0 h² ≈ 1.6×10⁻⁵ × 4×10⁻⁴ ≈ 7×10⁻⁹, far below the N_eff integral bound (Bartolo et al. Eq. 3.23: "∫ d(ln f) ΩGW ≤ ΩR,0 (7/8)(4/11)^{4/3}(Neff − 3.046)", ≈ 1.7×10⁻⁶ in h²Ω for ΔN_eff = 0.3). Without the cutoff (k_max η_R ∼ few hundred) the same fit exceeds Ω = 1, which is unphysical — the point the review makes is that linear theory is inapplicable there. So: the "10⁻³ violates ΔN_eff" claim is not supported once the nonlinear cutoff is imposed; the honest statement is that the linear poltergeist calculation is not applicable for P_ζ ∼ 10⁻³ and no reliable prediction exists (the review calls a nonlinear treatment "an important future direction").

Note 9 — Frequency–mass–T_RH relation (my calculation)

Assumptions: mode enters horizon during MD (k = a_k H_k, H ∝ a^{−3/2}), instantaneous reheating at T_RH, g* = g*s = 106.75, M_H = 4π M_pl² / H (reduced M_pl = 2.435×10¹⁸ GeV), M_PBH = γ M_H.

  1. k = a_k H_k = a_RH H_RH (a_RH/a_k)^{1/2} = a_RH H_RH (H_k/H_RH)^{1/3} ⇒ f = f_RH (M_H,RH γ/M)^{1/3}.
  2. f_RH: H(T) = √(π²g*/90) T²/M_pl; a/a₀ = (3.91/gs)^{1/3} T₀/T ⇒ f = 2.65×10⁻⁸ Hz (T/GeV) (g/106.75)^{1/2}(106.75/g*s)^{1/3} — identical to Saikawa–Shirai Eq. (2.15) (2.65 Hz at 10⁸ GeV). At T_RH = 10⁵ GeV: f_RH = 2.65×10⁻³ Hz.
  3. M_H,RH = M_Pl³/(2·1.66 √g* T_RH²) = 9.45×10²¹ g at 10⁵ GeV.
  4. f = 2.65×10⁻³ Hz × (9.45×10²¹ g γ/M)^{1/3} = 2.65×10⁻³ × (945)^{1/3} (γ 10¹⁹ g/M)^{1/3} = 2.60×10⁻² Hz (γ 10¹⁹ g/M)^{1/3}; T-dependence: f ∝ T_RH × T_RH^{−2/3} = T_RH^{1/3}. ✔ Coefficient and exponents match the brief.

Part 2 — Annotated bibliography / novelty check (2024-01 → 2026-09)

10. Spherically symmetric Einstein–Vlasov / collisionless PBH-formation and thresholds

Searches that returned nothing relevant (explicit negative results):

  • arXiv API all:"Einstein-Vlasov" AND all:primordial → totalResults 0.
  • arXiv API all:Vlasov AND all:"primordial black hole" → 1 hit (2103.03595, DM accretion, irrelevant).
  • INSPIRE t vlasov and t primordial → 0; INSPIRE free text vlasov primordial black hole, date>2023 → 0.
  • INSPIRE t collisionless and t "primordial black" → 0.
  • arXiv API all:collisionless AND all:"primordial black hole" → 6 total, only 2 since 2024: 2609.14218 (below) and 2606.20964 (DM accretion onto BH seeds, irrelevant).
  • arXiv "velocity dispersion" AND "primordial black hole" AND matter (2024+): only 2507.18312 (below) relevant.

Conclusion: no spherically symmetric Einstein–Vlasov PBH-formation or threshold paper exists in 2024-01–2026-09. The only full-GR collisionless PBH-formation work is 3D:

arXiv Authors / date Result Threshold?
2609.14218 Yoo, Escrivà, Harada, Kohri — 13 Sep 2026, "Simulation of PBH formation in a matter-dominated universe" (29 pp) "fully nonlinear numerical relativity" (BSSN, code not named, 80³ grid); triaxial curvature perturbation with ellipticity; matter = dust fluid and "particle-in-cell (PIC) simulation in full numerical relativity for PBH formation" (δ-functions "replaced by the uniform support function"). Dust: "numerical computation crashes associated with the appearance of a singularity ... unless the singularity is hidden well inside the apparent horizon"; "to observe the horizon formation before calculations crash, the initial amplitude must be larger than the previous analytic estimation by a factor of 2." Particles: "calculations do not crash ... the threshold of black hole formation is significantly smaller than the previous analytic estimation by an order of magnitude"; e=0.2: "threshold of PBH formation is at around μ∼0.045". Velocity dispersion is discussed ("This halo would be supported by the effective pressure generated by the velocity dispersion of the particles"); Harada+2023 is cited. Spherical (e=0) dust runs are done "as a test bed" and checked against LTB. Conclusion: "our results forcefully suggest that there is a large theoretical uncertainty in the PBH formation criterion during a matter-dominated epoch." Yes, μ_th for dust (≈2× Harada+2016 hoop estimate) and for particles (≈10× below it). https://arxiv.org/abs/2609.14218
2211.13950 Harada, Kohri, Sasaki, Terada, Yoo — JCAP 02 (2023) 038 (pre-window, the standard reference) Analytic (timescale comparison): "δ̃_th ∝ σ₀^{2/5} for σ₀≪1". Yes (analytic δ_th). https://arxiv.org/abs/2211.13950
2507.18312 Ebrahimian, Abolhasani, Mirbabayi — 24 Jul 2025 (rev. 25 Mar 2026), "Primordial black hole formation in matter domination" Analytic, includes peak-shape distribution: "the effective threshold is larger, ζ_th ~ ζ_rms^{1/10}. And this model requires ζ_rms~10^{-1} ... PBH formation during Matter Domination is barely more efficient than Radiation Domination"; spin a_rms ~ ζ_rms^{7/4}. Yes (analytic ζ_th). https://arxiv.org/abs/2507.18312
2508.10070 Ye, Gong, Harada, Kang, Kohri, Saito, Yoo — 13 Aug 2025 Peak theory + Zel'dovich + hoop-conjecture criterion; mass function & spin. Criterion only (hoop), no simulation. https://arxiv.org/abs/2508.10070
2409.00435 Saito, Harada, Koga, Yoo — 31 Aug 2024 Spins in MD via Zel'dovich + peak theory; "set the threshold value of the amplitude of the fluctuation through the under-extremal condition ā_*<1". Threshold from spin, analytic. https://arxiv.org/abs/2409.00435
2605.04487 Escrivà, Harada, Kohri, Terada, Yoo — 6 May 2026 "semirelativistic N-body framework"; GW from nonspherical collapse (quadrupole); Zel'dovich-deformed sphere in EdS; averaged over Doroshkevich/BBKS. No threshold; not full GR. https://arxiv.org/abs/2605.04487
2403.02878 de Jong — PhD thesis (Lim), Mar 2024 3+1 NR of MD PBH formation (direct vs accretion collapse; spin efficiency O(10%)); consolidates 2021–2023 papers. Hoop-based criterion; no Vlasov. https://arxiv.org/abs/2403.02878

11. Oscillating scalar field / early MD in NR or lattice (2024–2026)

  • Padilla, Milligan, Mulryne, Hidalgo, arXiv:2509.10431 — JCAP 04 (2026) 049 (confirmed at iopscience 10.1088/1475-7516/2026/04/049). What it computes: 1D spherical Misner–Sharp ("fully relativistic nonlinear numerical simulations in spherical symmetry, based on the Misner–Sharp formalism"), quartic potential only ("V(ψ)=λ_{2n}/2n ψ^{2n}", n=2) vs radiation; superhorizon Shibata–Sasaki ICs in an FLRW background with effective w. Thresholds: "p_th^rad=0.0270895", "p_th^sf=0.0271205", "C_max,th≃0.5"; critical exponents "γ=0.3474±0.004" (rad) vs "γ=0.3401±0.0071" (SF), "differ by about 2σ". Not 3D, not Schrödinger–Poisson, not full 3+1 GR; code not public. https://arxiv.org/abs/2509.10431
  • Milligan, Padilla, Mulryne, Hidalgo, arXiv:2504.02600 — JCAP 10 (2025) 025. Same Misner–Sharp code (scalar + perfect fluid). Quartic: "κth=0.1725 ... C_th=0.50 and δ_th=0.45, just as in the radiation dominated universe." Quadratic (oscillating, MD-like): only an upper bound "C_th≤0.2, δ_th≤0.077" over κ∈[0.06,0.2]; "these configurations still collapse into PBHs even for perturbation amplitudes smaller than those predicted by Newtonian estimates"; central soliton profile "with a slope of R^−1.78"; "numerical limitations prevent us from evolving a wide range of initial conditions to determine a precise threshold". No public code. https://arxiv.org/abs/2504.02600
  • Escrivà et al. 2605.04487 — see table above (semirelativistic N-body, GW only).
  • Padilla, Harada, Milligan, Mulryne, arXiv:2604.21520 (23 Apr 2026), "Cosmological discrete self-similarity in PBH formation": massless scalar field collapse in FLRW, |p−p_c|∼10⁻⁸, log-periodic mass scaling. https://arxiv.org/abs/2604.21520
  • Padilla, Harada, Iizuka, arXiv:2608.21834 (22 Aug 2026): DSS imprints on mass functions (kination era, m_{n+1}/m_n ≈ 5.6). https://arxiv.org/abs/2608.21834
  • Milligan, Padilla, Mulryne, arXiv:2608.23367 (24 Aug 2026): Higgs-like spectator in the radiation era, spherical NR (wormhole throat/child universe). https://arxiv.org/abs/2608.23367
  • Cheng, Giannadakis, Heurtier, Lim, arXiv:2507.19166 — JCAP 07 (2026) 048: full NR of scalar inhomogeneities during kination, PBH formation as reheating. https://arxiv.org/abs/2507.19166
  • Baumgarte, Clough, Gerhardinger, Giblin, Miller, arXiv:2606.30641 (29 Jun 2026): 3+1 BSSN, periodic box, radiation era, "threshold, 0.77<δ_c<0.83". https://arxiv.org/abs/2606.30641
  • Baumgarte, Clough, Giblin, arXiv:2509.26470: non-existence/non-uniqueness of Hamiltonian-constraint solutions for cosmological PBH initial data. https://arxiv.org/abs/2509.26470
  • Ning, Cai, Wang, Yoo, arXiv:2608.13206 (13 Aug 2026): GRChombo + flux-conservative hydro, RD, "0.79578 < μ_c < 0.79580", γ ≃ 0.3559. https://arxiv.org/abs/2608.13206
  • Escrivà, arXiv:2609.03051 (2 Sep 2026): 3+1 NR, RD, collective/multiple PBH formation (K_form,c≈0.56). https://arxiv.org/abs/2609.03051
  • Redondo-Yuste & Aurrekoetxea, arXiv:2607.27343 (29 Jul 2026): scalar collapse near threshold, asymptotically flat. https://arxiv.org/abs/2607.27343
  • Escrivà 2504.05813 (Phys. Dark Univ. 50 (2025) 102177) and 2504.05814: Misner–Sharp fluid, type-II fluctuations (RD).
  • Negative author sweeps (INSPIRE/arXiv, 2024–2026): Eggemeier & Niemeyer — no PBH/early-MD paper since 2311.08780; Eggemeier only 2402.18221 (axion miniclusters). Hernández-Aguayo — none. Ureña-López — none on PBHs. "Kou" — nothing relevant found. de Jong — thesis only. Aurrekoetxea — no MD-PBH paper (GRTresna 2501.13046, 2607.27343). Clough — 2509.26470, 2606.30641 (RD). Lim — 2507.19166 (kination). Hidalgo — only the two scalar-field papers above. arXiv "Schrodinger-Poisson" AND "primordial black hole" → 0; "oscillating scalar field" AND "primordial black hole" (2024+) → only 2504.02600.

Novelty verdict: a spherically symmetric Einstein–Vlasov (kinetic, velocity-dispersion-resolving) PBH threshold in an expanding MD background has not been published. The closest competitor is Yoo et al. 2609.14218 (3D PIC, low resolution 80³, threshold "an order of magnitude" below Harada+2016), which a 1D Vlasov code could sharpen and cross-check.

12. Full-GR codes with collisionless particles

Code GR treatment Particles Public? Could do 3D collisionless PBH run?
COSMOS (Yoo et al.) Full 3+1 (SACRA-derived, BSSN), fixed mesh refinement, OpenMP No — README: "Perfect fluid with linear equation of states & massless scalar field"; JOSS paper (arXiv:2606.02053, JOSS 11(121) 9570) lists only these. The PIC module of 2609.14218 is not in the public release and the paper does not name the code. Yes: https://github.com/cmyoo/cosmos (README: BSD 3-Clause) Not with the public version.
GRAMSES (Barrera-Hinojosa & Li, arXiv:1905.08890, JCAP 01 (2020) 007) Constrained ADM, CMC + minimal distortion; "The current version of GRAMSES neglects the latter [tensor DOF] by using the conformal flatness approximation" Yes (N-body, AMR) No public release found (only RAMSES is public). No: conformally flat, no horizon formation.
gevolution (Adamek et al., arXiv:1604.06065) "a weak field expansion of General Relativity" (Poisson gauge, all six metric DOF) Yes Yes: https://github.com/gevolution-code/gevolution-1.2 (MIT) No (weak field).
Magnall, Price, Lasky, Macpherson 2023, arXiv:2307.15194 (PRD 108, 103534) Full GR: Einstein Toolkit/McLachlan BSSN coupled to Phantom SPH via thorn "phantomnr"; dust = pressureless SPH particles; "evolution of non-linear perturbations of the metric past shell-crossing" SPH particles (single-fluid, not multi-stream Vlasov) Paper: "We plan to make our code publicly available." Repo exists: https://github.com/spencermagnall/phantomNR (Fortran, no license file, last push 2023-09-20) Partly: full GR + dust particles, but SPH is not collisionless (no multi-streaming).
CosmoGRaPH (Mertens, Giblin, Starkman) Full GR BSSN Yes: components/ contains bssn, dust_fluid, particles, phase_space_sheet, scalar, Lambda, static; used in Giblin, Mertens, Starkman, Tian, PRD 99, 023527 (2019): "the accuracy of linearized gravity in the presence of collisionless matter and a cosmological constant utilizing fully general relativistic simulations". README caveat: "(Perfect fluid | Particle) Hydrodynamics Code ... But we'll see about the 'particle' part." Yes: https://github.com/cwru-pat/cosmograph (MIT) Best public candidate for a full-GR collisionless 3D run; designed for cosmological boxes, horizon-finding/AMR for PBH collapse not verified.
Daverio, Dirian, Mitsou (arXiv:1904.07841, JCAP 10 (2019) 065) Full GR BSSN + N-body Yes No public code found. —
East, Wojtak, Pretorius (arXiv:1908.05683, PRD 100, 103533) "full solutions of the Einstein-Vlasov (N-body) equations" Yes Not public. —
GRChombo / GRTeclyn Full GR No matter-particle module: GRChombo Source/ = AMRInterpolator, ApparentHorizonFinder, BlackHoles, BoxUtils, CCZ4, Cosmology, GRChomboCore, InitialConditions, Matter, TaggingCriteria, simd, utils. GRTeclyn's ParticleInterpolator/ holds interpolation/extraction utilities (SphericalExtraction, WeylExtraction, …), not matter. Yes (GRTLCollaboration) No.
Einstein Toolkit particle thorn — None found for collisionless matter (only via phantomNR above). — —

13. Public 1D scalar-field GR codes (second EKG code)

  • OllinSphere-BiB (Alcubierre), https://github.com/malcubi/OllinSphere-BiB — Fortran 90, MPI, box-in-box refinement; no license (GitHub API license: null; root contains only Makefile, README, doc, fakempi, gnuplot, ollingraph, par, prl, src, tools). Verified from parameter files:
    • Massive real scalar: par/scalar_massive.par: mattertype = scalar, scalarpotential = phi2, scalar_mass = 1.0, slicing = 1+log.
    • Cosmological (expanding) background: cosmic_run = .true. in deSitter.par (lambda_cosmo = 3.0, "during the evolution we must have a=psi**2", variables cosmobg_a, cosmobg_H, ...) and in scalarDM.par / scalarDM_pert.par: "Cosmological spacetime with scalar field dark matter, zero cosmological constant ... evolves the background plus a perturbation", scalarpotential = phi2, scalar_mass = 1.0, scalar_bg_phi0 = 0.001, scalar_bg_pert = .true., Gaussian perturbation, slicing = cosmocf-1+log, ahfind = .true.. Also complexDM_pert.par; src/matter/cosmo_massintegral.f90.
    • Horizon-penetrating slicing: 1+log with Gammadriver shift (scalarcollapse.par: shift = Gammadriver1), trumpet/puncture examples.
    • Dust: dust.par (mattertype = dust, dust_method = limiter, idata = dustshell, AH finder); perfect fluid (fluid.par); also Proca, Dirac, complex scalar, TOV.
    • Manual: doc/usermanual.pdf (not fetched). This is the best public second EKG cosmological code.
  • SFcollapse1D / NRPyCritCol (Werneck et al., CQG 38 (2021) 245005, arXiv:2106.06553; https://github.com/leowerneck/SFcollapse1D): "gravitational collapse of massless, spherically symmetric scalar fields" — massless only, asymptotically flat.
  • Escrivà: SPriBHoS (MIT) and SPriBHoS-II (BSD-3) at https://github.com/albert-escriva — Misner–Sharp perfect fluid pseudospectral, not scalar field.
  • Milligan/Padilla/Hidalgo Misner–Sharp scalar+fluid code: not public (no URL in 2504.02600 or 2509.10431). Musco's code: not public. Bloomfield et al. 2015 code, "MS-code", "SphericalCollapse": not found (GitHub API Misner-Sharp → 1 unrelated 2015 repo; "primordial black hole" "scalar field" → 0; "primordial black hole" formation spherical → only SPriBHoS/-II; Klein-Gordon collapse spherical relativity → 0).

Corrections the brief should absorb (summary)

  1. n_s (P-ACT-LB) = 0.9743 ± 0.0034, not 0.9744 (P-ACT-LB2: 0.9752 ± 0.0030).
  2. De la Torre Luque erratum is PRD 112, 109904 (Nov 2025); arXiv v2 with erratum is Mar 2026; corrected bounds are only in figures — quote none.
  3. Gottlieb et al. 2026 weakens Esser-type limits via capture inefficiency, not slow-accretion survival; a 10¹⁹ g PBH still eats a solar-type star in ∼2×10⁸ yr by their scaling.
  4. Carr et al. 2026 say the window "lacks robust observational constraints" and discount the dwarf-galaxy limit via Bellinger et al. 2023; they do not assert f_PBH = 1.
  5. Poltergeist: enhancement claimed only for sudden transitions and only below k_NL; for P_ζ ∼ 10⁻³ linear theory fails at kη_R ≈ 18, so neither the "big enhancement" nor the "ΔN_eff violation" can be asserted; cite 2511.07266 and 2605.21477.
  6. Novelty: no 1D Einstein–Vlasov PBH threshold exists; the direct competitor is Yoo et al. arXiv:2609.14218 (13 Sep 2026, 3D PIC, 80³), which finds thresholds an order of magnitude below Harada+2016 — the brief should cite and position against it.

Local text extracts used for quotes are in /tmp/claude-0/-root-PBH/a34e6be4-0ee0-4598-bfd0-88626255d779/scratchpad/ (e.g. 2406.11949v2.txt, 2601.06024v2.txt, 2606.02700v1.txt, webfetch-1790190716408-p940gw.txt = ACT DR6, webfetch-1790190721358-n6b1d1.txt = poltergeist review, webfetch-1790190724191-kyub3g.txt = Kohri–Terada).