Primordial Black Holes are 5D

Alek Bedroya; Dieter L\"ust; Luis A. Anchordoqui

REVIEW 3 major objections 4 minor 2 cited by

Primordial Black Holes are 5D

T0 review · 3 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Within the dark-dimension scenario, quantum gravity constraints force phase-transition and cosmic-string primordial black holes to form as five-dimensional objects, barring exotic low-energy physics.

desk verdict Provocative but conditional: the 'all PBHs are 5D' claim rests on a kination argument that needs a serious check of KK-graviton stability; still worth a careful referee. read the letter →

arxiv 2506.14874 v1 pith:U5AHBKTV submitted 2025-06-17 hep-ph astro-ph.COhep-th

Luis A. Anchordoqui , Alek Bedroya , Dieter Lüst This is my paper · ORCID

classification hep-phastro-ph.COhep-th

keywords primordialblackholesdarkdimensionextradimensionsGregory-LaflammeinstabilitykinationKaluza-Kleingravitonsholeevaporationultra-high-energyneutrino

open problems Dark Matter

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper's target is a sharp exclusion: in a universe with a micron-sized fifth dimension, the usual ways of making primordial black holes—phase transitions and collapsing cosmic strings—cannot make four-dimensional ones. Working from quantum-gravity constraints, the paper argues that before the extra dimension stabilizes at about a gigaelectronvolt, the universe had to be kination-dominated, which lowers the mass of horizon-sized black holes below the threshold at which a four-dimensional black hole becomes unstable to extending along the extra dimension. Cosmic-string black holes are pushed below the same threshold unless they form below the kiloelectronvolt scale, which would require exotic low-mass physics. The observable consequence is that five-dimensional black holes evaporate more slowly, so some can live roughly as long as the universe and could account for a recently observed ultra-high-energy neutrino without a matching gamma ray.

What carries the argument

The load-bearing comparison is between the horizon mass available when a PBH forms and the Gregory-Laflamme threshold $M_{GL}\sim M_{pl}^2/M_{KK}$, the mass below which a four-dimensional black hole is unstable to becoming a five-dimensional object. The new ingredient is the kination-corrected horizon mass $M_H \sim M_{pl}^3 T_*/T^3$, which follows from demanding no overproduction of Kaluza-Klein gravitons before the normalcy temperature $T_*\sim$ GeV; at $T\gtrsim$ TeV it gives $M_H\ll M_{GL}$, forcing five-dimensional black holes. The cosmic-string bound (14) gives the same result unless formation occurs below about a kiloelectronvolt. The final piece is five-dimensional Hawking evaporation, $dM/dt \propto M^{-1}M_{5D,pl}^3$, whose integrated lifetime $\tau\sim M^2/M_{5D,pl}^3$ is much longer than the four-dimensional lifetime for the same mass.

What would settle it

A decisive check would be to measure the dark-matter density in Kaluza-Klein gravitons: if a full calculation allowing decay or dilution shows that a radiation-dominated universe above the normalcy temperature does not overproduce them, the kination premise fails and the universal five-dimensional conclusion loses its foundation. Alternatively, finding a primordial black hole formed above the TeV scale whose mass is above about $10^{14}$ grams and whose Hawking radiation is four-dimensional would break the universality claim.

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Extended reading notes

Core claim

The central claim, stated in the paper's own terms, is that all primordial black holes must become five-dimensional after the normalcy temperature. Phase-transition PBHs form at a kination-corrected horizon mass $M_H \sim M_{pl}^3 T_*/T^3$, which for formation temperatures above about a TeV lies far below the Gregory-Laflamme threshold $M_{GL} \sim M_{pl}^2/M_{KK}$, the largest mass at which a four-dimensional black hole can remain stable against extending into the extra dimension. For cosmic strings, the formation-mass bound is $M_{CS} \lesssim 10^{36}(M_{KK}/M_{pl})^{2/3}(\text{GeV}/T)^2 M_{pl}$, and staying four-dimensional would require formation below roughly a kiloelectronvolt, which is excluded for QCD axions and problematic for other axion models. The authors therefore conclude that, barring exotic low-energy physics, five-dimensional primordial black holes are the generic prediction of the dark-dimension scenario, and their lifetimes $\tau \sim M^2/M_{5D,pl}^3$ can be comparable to the age of the universe.

Load-bearing premise

The argument collapses if the pre-normalcy universe was not kination-dominated; a radiation-dominated epoch above about one GeV would only be safe if the Kaluza-Klein graviton production rate, its order-one coefficients, or subsequent dilution or decay differ from what the paper assumes.

Editorial extensions

If this is right

Any PBH formed by a first-order phase transition above roughly a TeV is below the four-dimensional stability threshold and therefore becomes a five-dimensional black hole after the normalcy temperature.
Cosmic-string PBHs can remain four-dimensional only if they form below about a kiloelectronvolt, a regime that the known axion models cannot accommodate without severe quality problems.
Five-dimensional PBHs evaporate far more slowly than four-dimensional ones, so cosmic-string PBHs can have lifetimes up to about $10^{13}$ years, potentially comparable to the age of the universe.
Late-time five-dimensional PBH evaporation near the Standard-Model brane can emit an ultra-high-energy neutrino without a coincident high-energy photon, matching a recently observed neutrino event.
Phase-transition five-dimensional PBHs generically have lifetimes longer than the age of the universe, making them long-lived relics rather than sources evaporating today.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Editorial extension: if the five-dimensional conclusion is right, standard four-dimensional PBH constraints (microlensing, Hawking photon bounds, dark-matter mass windows) should be re-examined, because the same initial mass evaporates on a much longer timescale and with a different particle spectrum.
Editorial extension: because the kination-corrected horizon mass ties PBH masses to $T_*$ and $M_{KK}$, a future measurement of a PBH mass at any scale would indirectly probe the equation of state of the pre-normalcy universe.
Editorial extension: the same late-time evaporation mechanism would predict a diffuse flux of ultra-high-energy neutrinos from the whole population of near-Hubble-time 5D PBHs, so the single observed event supplies a target rate that future telescopes can test.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague,

This paper makes a sharper claim than its predecessors: not just that 5D black holes are viable dark matter in the Dark Dimension, but that any PBH from inflation, phase transitions, or cosmic strings is inevitably five-dimensional, barring exotic low-energy physics. The route is partly new—they derive a kination-dominated pre-normalcy epoch from the requirement not to overproduce KK gravitons, then use the kination-corrected horizon mass to push phase-transition PBHs below the Gregory-Laflamme threshold.

The paper is explicit about its caveats: the footnote on universal stable phases, the repeated 'barring exotic physics', the assumption of a single extra dimension. The KM3NeT connection is not oversold; they present it as viable rather than certain. That is credit where earned.

The main soft spot is Section II. The kination conclusion depends on KK gravitons being stable enough to reach recombination as dark matter. Their own Ref. [11] is about decaying KK gravitons, and they never explain why decay does not evacuate the overproduction bound. If KK gravitons decay, radiation domination above T* is not excluded, and a phase transition between roughly 0.4 and 10 TeV would yield 4D PBHs. The order-one coefficients in Eq. (2), imported from Ref. [30], are also load-bearing; a factor of a few in the exponent could dissolve the contradiction. This is not a fatal flaw because the paper already bars low-energy phase transitions, but it does make 'inevitably' stronger than the argument supports.

Section IV has a concrete mechanical error: Eq. (16) as printed is satisfied by Dark Dimension values, contradicting the text. An independent recomputation gives the opposite sign and a threshold near 3e-7 μm, not 10^-12 μm. The conclusion—that cosmic-string PBHs sit below M_GL—survives the correction, but the printed derivation is not reliable.

Even with these issues, the core result is not fragile: cosmic-string PBHs formed above ~keV and phase-transition PBHs formed above ~10 TeV are 5D regardless of kination. The kination argument extends the claim to lower scales, where it is more conditional. The paper is worth a serious referee, not a desk reject. Send it to someone who can check the KK production integrals and the modulus evolution bounds. The authors should fix Eq. (16) and address the KK-decay question before publication.

Recommendation: engage with it. It is short, interesting, and mostly honest about its assumptions.

Referee Report

3 major / 4 minor

Summary. The paper argues that within the Dark Dimension Scenario, standard primordial black hole production mechanisms—phase transitions and cosmic strings—inevitably produce five-dimensional PBHs. Section II derives that the pre-normalcy universe (T > T* ~ GeV) must have been kination-dominated, because radiation domination would overproduce Kaluza-Klein gravitons. Section III uses the kination-corrected horizon mass to argue that phase-transition PBHs formed above about a TeV are below the Gregory-Laflamme threshold and hence become 5D. Section IV repeats the mass comparison for cosmic-string PBHs and concludes that they are 5D for all formation temperatures above roughly a keV. Section V estimates the evaporation lifetimes of these 5D PBHs and draws a connection to the KM3NeT high-energy neutrino event.

Significance. If the conclusion holds, the paper is significant: it would turn a generic PBH analysis into a dimension-selection statement in a Swampland-motivated scenario, with testable consequences such as long-lived 5D PBHs, neutrino emission without coincident photons, and a mass scale near the KM3NeT event. The argument is analytic, checkable, and produces falsifiable predictions, which are strengths. The qualitative conclusion survives a sign correction in Section IV, but the central "inevitably 5D" claim rests on the kination assumption, which needs further justification.

major comments (3)

[Section II, Eqs. (4)-(7)] The proof that the pre-normalcy universe was kination-dominated assumes that the KK gravitons produced above T* survive undiluted to recombination as dark matter. This is not established and is in tension with Ref. [11], which the paper itself cites in the preceding paragraph and which analyzes decaying KK gravitons. If decay or dilution is efficient, the lower bound in Eq. (7) is evaded, the contradiction with Eq. (2) disappears, and radiation domination above T* is no longer excluded. Since the kination Hubble rate (10) and the horizon mass (11) are what push phase-transition PBHs below M_GL, the 'inevitably 5D' conclusion depends on this unproven premise. Please either close this gap or state it as an explicit limitation.
[Section IV, Eqs. (16)-(17)] Both inequalities are written with the wrong sign. Inserting Dark Dimension values (M_KK^{-1} ~ micron, T* ~ GeV) into the printed final inequality of Eq. (16) yields 1 micron > 10^{-12} micron, so the stated 4D condition is satisfied; the following sentence claims it is not. For Eq. (17), at T ~ keV the right-hand side is 10^{-12} micron (GeV/keV)^2 ~ 10^6 micron, so the claim that the inequality 'is only satisfied for T <~ keV' is also inverted. The intended 5D conclusion follows from the opposite inequalities, and the derivation needs to be corrected accordingly.
[Section II, Eq. (4)] The printed formula for the KK-graviton energy density at recombination, rho_RC ~ T_RC^3 T*^3 M_KK M_pl, is dimensionally inconsistent (energy density has mass dimension 4, while the expression has dimension 8). The subsequent result in Eq. (5) corresponds to rho_RC ~ T_RC^3 T*^3 / (M_KK M_pl). Please correct the displayed equation and verify the factors in Eqs. (4)-(6).

minor comments (4)

[Section II, Eq. (5)] The numerical evaluation T* ~ GeV is stated without specifying the value of H0 used; please include the assumed Hubble parameter so the reader can reproduce the estimate.
[Section IV, Eq. (16)] The intermediate numerical coefficient changes from 10^36 in Eq. (15) to 10^37 in Eq. (16) without comment; the factors should be reconciled so the derived bound can be checked directly.
[Section V, Eq. (20)] The numerical estimate tau <~ 10^13 yr is presented without showing the substitutions for M_KK and T*; please include the intermediate values so the reader can verify the claimed lifetime range.
[Footnote 1] The 'black hole scale' Lambda_BH is introduced but never defined quantitatively and is not used in the rest of the paper; consider removing the footnote or explaining the scale explicitly.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the 5D-PBH claim follows from mass comparisons fed by an independently cited kination bound, not from an input/output identity.

full rationale

The claimed derivation is not circular. The target statement (that PBHs form 5D objects) is an output of mass comparisons: phase-transition masses are bounded by Eqs. (8) and (11), cosmic-string masses by Eq. (14), and the 5D/4D separation is fixed by the Gregory-Laflamme mass M_GL ~ M_pl^2/M_KK in Eq. (9); none of these bounds is defined in terms of the 5D conclusion. The kination epoch of Sec. II is obtained by a genuine reductio: the moduli-displacement bound (1)-(2), cited to Ref. [30] for its coefficients, and the KK-graviton overproduction lower bound (6)-(7) are opposite inequalities under the assumption of radiation domination, and the contradiction excludes that assumption. The 5D-PBH result does not enter this argument, so importing the kination bound is a normal citation, not a reduction of the conclusion to its input. Ref. [30] has an author overlap (Bedroya), but it supplies a moduli-space bound independent of PBH physics; under the review rules this counts as independent support rather than circularity. The KM3NeT discussion is explicitly framed as a comment on implications, not as a fitted prediction. Two caveats are correctness issues, not circularity: the order-one coefficients of Eq. (1) are deferred to Ref. [30], and the printed chain in Eq. (16) has a sign inconsistency (Dark Dimension values satisfy the displayed inequality, while the intended 4D condition requires the opposite direction); the intended conclusion survives with the corrected sign. Overall, no equation equals its input, no fitted parameter is renamed as a prediction, and no self-citation chain forces the result.

Assumptions & free parameters 3 free parameters · 8 assumptions · 0 invented entities

All numbers the central claim depends on are inherited from the Dark Dimension program (Refs [9-11]) and the same circle's Swampland bounds (Refs [16,30]); the paper itself fits no data and introduces no new entities. The main audit finding is not a fitted parameter but a chain of domain assumptions: the existence of the Dark Dimension, the normalcy temperature value, the kination bound with unspecified coefficients, and the universality of stable black hole phases, each cited to papers overlapping with the present authors. The order-one coefficients of the KK production and kination estimates act as free parameters within the framework.

free parameters (3)

Normalcy temperature T* = ~ 1 GeV
Inherited from Refs [10,11], not fitted here. It enters the kination bound (Eqs. (1)-(2)), the horizon mass (Eq. (11)) and the cosmic string bounds (Eqs. (15)-(17) and (20)); the 4D/5D verdict requires T* not to be far below the GeV scale.
KK mass scale M_KK = 0.01 to 0.1 eV (extra dimension size ~ micron)
Input from Refs [9-11] for the Dark Dimension. It sets M_GL (Eq. (9)) and the cosmic string mass bounds; independent recomputation shows the 4D threshold is M_KK^{-1} <= about 3x10^-7 um, so any Dark Dimension value keeps PBHs 5D.
Order-one coefficients in the KK production and kination estimates = unspecified, O(1)
Eqs. (1)-(5) and (10) are '~' relations with dropped factors; the kination-versus-radiation contradiction and the T* value depend on these coefficients unless they are close to unity.

assumptions (8)

domain assumption The Dark Dimension scenario: Standard Model localized on a brane in one micron-sized fifth dimension, with M_KK in the 0.01 to 0.1 eV range
The whole paper operates inside this scenario (Section I and throughout). Inputs M_KK and T* ~ GeV are inherited from Refs [9-11], produced by the same research circle.
domain assumption Normalcy temperature T* ~ GeV, above which a stabilized extra dimension would overproduce KK gravitons
The kination and 5D arguments use T* ~ GeV repeatedly (Eqs. (5), (10), (15)-(17), (20)). The derivation is only sketched in Eqs. (3)-(5) with dropped order-one factors, and it is inherited from Refs [10,11].
domain assumption Kination bound on moduli displacement: M_KK(T) <= (T/T*)^3 M_KK with order-one coefficients (Eqs. (1)-(2))
Imported from Ref [30], with coefficients deferred ('see [30] for a discussion of coefficients'). This bound is the cornerstone of the claim that the pre-T* universe was kination-dominated.
domain assumption KK graviton overproduction during radiation domination above T* rules out that epoch (excess dark matter)
The contradiction between Eqs. (2) and (7) in Section II forces kination. The disqualifying impact of overproduction is assumed without folding in decay or dilution, despite citing the decaying-KK dark matter framework of Ref [11].
domain assumption The Gregory-Laflamme mass M_GL ~ M_pl^2/M_KK is the boundary between 4D and 5D black holes
Used in Sections III and IV to classify PBHs; requires exactly one extra dimension, as the paper notes in the footnote of Section V.
domain assumption 'Phases that are more stable than black holes are universal in quantum gravity', the black hole scale picture
Footnote 1, cited to Ref [16] (co-authored by a present author). This active proposal underlies the 'inevitably 5D' framing and is not an established theorem.
domain assumption 5D Hawking evaporation scaling dM/dt proportional to M^{-1} M_5D^3 and lifetime tau ~ M^2/M_5D^3 (Eqs. (18)-(19))
Standard five-dimensional black hole thermodynamics, consistent with the authors' own Refs [13-15]; the proportionality constant (species count) is left free and controls the lifetime.
domain assumption The QCD transition is a crossover, not a first-order phase transition, and so is not efficient for PBH production
Used in Section III to exclude QCD-era PBH production and to push phase-transition PBHs to T > 10 TeV; relies on lattice QCD results Refs [31,32].

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Pith. "Pith review of Primordial Black Holes are 5D." pith.science (2026). https://pith.science/paper/U5AHBKTV

@misc{pith2026250614874,
  author       = {Pith},
  title        = {Pith review of: Primordial Black Holes are 5D},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/U5AHBKTV}},
  note         = {Machine review of arXiv:2506.14874}
}

read the original abstract

We revisit well-established mechanisms for primordial black hole (PBH) production, namely inflation, phase transitions, and cosmic strings, in the context of the Dark Dimension Scenario, which is motivated by Swampland principles. Applying quantum gravity constraints, we demonstrate that any viable mechanism, barring exotic new physics at low energies, inevitably leads to the formation of five-dimensional PBHs. We further show that PBHs formed from cosmic strings can have lifetimes comparable to the age of the universe. We comment on the observational implications of this result, including a potential connection to the recent detection of a high-energy neutrino by KM3NeT, whose energy is intriguingly close to the five-dimensional Planck scale in the Dark Dimension Scenario.

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Forward citations

Cited by 2 Pith papers

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Works this paper leans on

41 extracted references · 5 canonical work pages · cited by 2 Pith papers

[11]

Dark dimension and decaying dark matter gravitons,

G. Obied, C. Dvorkin, E. Gonzalo, and C. Vafa, “Dark dimension and decaying dark matter gravitons,” Phys. Rev. D 109 no. 6, (2024) 063540, arXiv:2311.05318 [astro-ph.CO]

arXiv 2024
[30]

A species scale-driven breakdown of effective field theory in time-dependent string backgrounds,

A. Bedroya, H. Lee, and P. Steinhardt, “A species scale-driven breakdown of effective field theory in time-dependent string backgrounds,” arXiv:2504.13260 [hep-th]

arXiv
[1]

The Hypothesis of Cores Retarded during Expansion and the Hot Cosmological Model,

Y. B. Zel’dovich and I. D. Novikov, “The Hypothesis of Cores Retarded during Expansion and the Hot Cosmological Model,” Sov. Astron. 10 (1967) 602

1967
[2]

Gravitationally collapsed objects of very low mass,

S. Hawking, “Gravitationally collapsed objects of very low mass,” Mon. Not. Roy. Astron. Soc. 152 (1971) 75

1971
[3]

Cosmological effects of primordial black holes,

G. F. Chapline, “Cosmological effects of primordial black holes,” Nature 253 no. 5489, (1975) 251–252

work page 1975
[4]

Primordial Black Holes as Dark Matter: Recent Developments,

B. Carr and F. Kuhnel, “Primordial Black Holes as Dark Matter: Recent Developments,” Ann. Rev. Nucl. Part. Sci. 70 (2020) 355–394, arXiv:2006.02838 [astro-ph.CO]

arXiv 2020
[5]

The Hierarchy problem and new dimensions at a millimeter,

N. Arkani-Hamed, S. Dimopoulos, and G. R. Dvali, “The Hierarchy problem and new dimensions at a millimeter,” Phys. Lett. B 429 (1998) 263–272, arXiv:hep-ph/9803315

arXiv 1998
[6]

New dimensions at a millimeter to a Fermi and superstrings at a TeV,

I. Antoniadis, N. Arkani-Hamed, S. Dimopoulos, and G. R. Dvali, “New dimensions at a millimeter to a Fermi and superstrings at a TeV,” Phys. Lett. B 436 (1998) 257–263, arXiv:hep-ph/9804398

arXiv 1998

Show all 41 references

[7]

Lectures on the string landscape and the Swampland,

N. B. Agmon, A. Bedroya, M. J. Kang, and C. Vafa, “Lectures on the string landscape and the Swampland,” arXiv:2212.06187 [hep-th]

arXiv
[8]

AdS and the Swampland,

D. L¨ ust, E. Palti, and C. Vafa, “AdS and the Swampland,” Phys. Lett. B 797 (2019) 134867, arXiv:1906.05225 [hep-th]

2019 arXiv
[9]

The dark dimension and the Swampland,

M. Montero, C. Vafa, and I. Valenzuela, “The dark dimension and the Swampland,” JHEP 02 (2023) 022, arXiv:2205.12293 [hep-th]

2023 arXiv
[10]

Dark dimension gravitons as dark matter,

E. Gonzalo, M. Montero, G. Obied, and C. Vafa, “Dark dimension gravitons as dark matter,” JHEP 11 (2023) 109, arXiv:2209.09249 [hep-ph]

2023 arXiv
[12]

Dynamical Dark Matter: I. Theoretical Overview,

K. R. Dienes and B. Thomas, “Dynamical Dark Matter: I. Theoretical Overview,” Phys. Rev. D 85 (2012) 083523, arXiv:1106.4546 [hep-ph]

2012 arXiv
[13]

Dark dimension, the swampland, and the dark matter fraction composed of primordial black holes,

L. A. Anchordoqui, I. Antoniadis, and D. L¨ ust, “Dark dimension, the swampland, and the dark matter fraction composed of primordial black holes,” Phys. Rev. D 106 no. 8, (2022) 086001, arXiv:2206.07071 [hep-th]

2022 arXiv
[14]

Dark dimension, the swampland, and the dark matter fraction composed of primordial near-extremal black holes,

L. A. Anchordoqui, I. Antoniadis, and D. L¨ ust, “Dark dimension, the swampland, and the dark matter fraction composed of primordial near-extremal black holes,” Phys. Rev. D 109 no. 9, (2024) 095008, arXiv:2401.09087 [hep-th]

2024 arXiv
[15]

More on black holes perceiving the dark dimension,

L. A. Anchordoqui, I. Antoniadis, and D. L¨ ust, “More on black holes perceiving the dark dimension,” Phys. Rev. D 110 no. 1, (2024) 015004, arXiv:2403.19604 [hep-th]

2024 arXiv
[16]

The Tale of Three Scales: the Planck, the Species, and the Black Hole Scales,

A. Bedroya, C. Vafa, and D. H. Wu, “The Tale of Three Scales: the Planck, the Species, and the Black Hole Scales,” arXiv:2403.18005 [hep-th]

arXiv
[17]

Black strings and p-branes are unstable,

R. Gregory and R. Laflamme, “Black strings and p-branes are unstable,” Phys. Rev. Lett. 70 (1993) 2837–2840, arXiv:hep-th/9301052

1993 arXiv
[18]

Selfgravitating fundamental strings,

G. T. Horowitz and J. Polchinski, “Selfgravitating fundamental strings,” Phys. Rev. D 57 (1998) 2557–2563, arXiv:hep-th/9707170

1998 arXiv
[19]

On small black holes in string theory,

B. Balthazar, J. Chu, and D. Kutasov, “On small black holes in string theory,” JHEP 03 (2024) 116, arXiv:2210.12033 [hep-th]

2024 arXiv
[20]

String stars in d ≥ 7,

A. Bedroya and D. Wu, “String stars in d ≥ 7,” arXiv:2412.19888 [hep-th]

arXiv
[21]

Inflation and primordial black holes as dark matter,

P. Ivanov, P. Naselsky, and I. Novikov, “Inflation and primordial black holes as dark matter,” Phys. Rev. D 50 (1994) 7173–7178

1994
[22]

Spontaneous Generation of Density Perturbations in the Early Universe,

M. Crawford and D. N. Schramm, “Spontaneous Generation of Density Perturbations in the Early Universe,” Nature 298 (1982) 538–540

1982
[23]

Black Holes From Cosmic Strings,

S. W. Hawking, “Black Holes From Cosmic Strings,” Phys. Lett. B 231 (1989) 237–239

1989
[24]

Trans-Planckian Censorship and the Swampland,

A. Bedroya and C. Vafa, “Trans-Planckian Censorship and the Swampland,” JHEP 09 (2020) 123, arXiv:1909.11063 [hep-th]

2020 arXiv
[25]

Trans-Planckian Censorship and Inflationary Cosmology,

A. Bedroya, R. Brandenberger, M. Loverde, and C. Vafa, “Trans-Planckian Censorship and Inflationary Cosmology,” Phys. Rev. D 101 no. 10, (2020) 103502, arXiv:1909.11106 [hep-th]

2020 arXiv
[26]

TCC in the interior of moduli space and its implications for the string landscape and cosmology,

A. Bedroya, Q. Lu, and P. Steinhardt, “TCC in the interior of moduli space and its implications for the string landscape and cosmology,” arXiv:2407.08793 [hep-th]

arXiv
[27]

Phenomenology, astrophysics and cosmology of theories with submillimeter dimensions and TeV scale quantum gravity,

N. Arkani-Hamed, S. Dimopoulos, and G. R. Dvali, “Phenomenology, astrophysics and cosmology of theories with submillimeter dimensions and TeV scale quantum gravity,” Phys. Rev. D 59 (1999) 086004, arXiv:hep-ph/9807344

1999 arXiv
[28]

Observation of an ultra-high-energy cosmic neutrino with KM3NeT,

KM3NeT Collaboration, S. Aiello et al., “Observation of an ultra-high-energy cosmic neutrino with KM3NeT,” Nature 638 no. 8050, (2025) 376–382. [Erratum: Nature 640, E3 (2025)]

2025
[29]

Neutrinos from Primordial Black Holes in Theories with Extra Dimensions,

L. A. Anchordoqui, F. Halzen, and D. L¨ ust, “Neutrinos from Primordial Black Holes in Theories with Extra Dimensions,” arXiv:2505.23414 [hep-ph]
[31]

QCD Phase Transition with Chiral Quarks and Physical Quark Masses,

T. Bhattacharya et al., “QCD Phase Transition with Chiral Quarks and Physical Quark Masses,” Phys. Rev. Lett. 113 no. 8, (2014) 082001, arXiv:1402.5175 [hep-lat]

2014 arXiv
[32]

Peaks above the Harrison-Zel’dovich spectrum due to the quark - gluon to hadron transition,

C. Schmid, D. J. Schwarz, and P. Widerin, “Peaks above the Harrison-Zel’dovich spectrum due to the quark - gluon to hadron transition,” Phys. Rev. Lett. 78 (1997) 791–794, arXiv:astro-ph/9606125

1997 arXiv
[33]

Axions in the dark dimension,

N. Gendler and C. Vafa, “Axions in the dark dimension,” JHEP 12 (2024) 127, arXiv:2404.15414 [hep-th]. 6

2024 arXiv
[34]

Planck scale physics and the Peccei-Quinn mechanism,

M. Kamionkowski and J. March-Russell, “Planck scale physics and the Peccei-Quinn mechanism,” Phys. Lett. B 282 (1992) 137–141, arXiv:hep-th/9202003

1992 arXiv
[35]

Planck scale corrections to axion models,

S. M. Barr and D. Seckel, “Planck scale corrections to axion models,” Phys. Rev. D 46 (1992) 539–549

1992
[36]

Solutions to the strong CP problem in a world with gravity,

R. Holman, S. D. H. Hsu, T. W. Kephart, E. W. Kolb, R. Watkins, and L. M. Widrow, “Solutions to the strong CP problem in a world with gravity,” Phys. Lett. B 282 (1992) 132–136, arXiv:hep-ph/9203206

1992 arXiv
[37]

Instability of the invisible axion,

S. Ghigna, M. Lusignoli, and M. Roncadelli, “Instability of the invisible axion,” Phys. Lett. B 283 (1992) 278–281

1992
[38]

Could a Primordial Black Hole Explosion Explain the KM3NeT Event?,

L. F. T. Airoldi, G. F. S. Alves, Y. F. Perez-Gonzalez, G. M. Salla, and R. Z. Funchal, “Could a Primordial Black Hole Explosion Explain the KM3NeT Event?,” arXiv:2505.24666 [hep-ph]
[39]

Neutrino oscillations without neutrino masses or heavy mass scales: A Higher dimensional seesaw mechanism,

K. R. Dienes, E. Dudas, and T. Gherghetta, “Neutrino oscillations without neutrino masses or heavy mass scales: A Higher dimensional seesaw mechanism,” Nucl. Phys. B 557 (1999) 25, arXiv:hep-ph/9811428

1999 arXiv
[40]

Neutrino masses from large extra dimensions,

N. Arkani-Hamed, S. Dimopoulos, G. R. Dvali, and J. March-Russell, “Neutrino masses from large extra dimensions,” Phys. Rev. D 65 (2001) 024032, arXiv:hep-ph/9811448

2001 arXiv
[41]

Probing large extra dimensions with neutrinos,

G. R. Dvali and A. Y. Smirnov, “Probing large extra dimensions with neutrinos,” Nucl. Phys. B 563 (1999) 63–81, arXiv:hep-ph/9904211

1999 arXiv

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

[1] [11]

Dark dimension and decaying dark matter gravitons,

G. Obied, C. Dvorkin, E. Gonzalo, and C. Vafa, “Dark dimension and decaying dark matter gravitons,” Phys. Rev. D 109 no. 6, (2024) 063540, arXiv:2311.05318 [astro-ph.CO]

arXiv 2024

[2] [30]

A species scale-driven breakdown of effective field theory in time-dependent string backgrounds,

A. Bedroya, H. Lee, and P. Steinhardt, “A species scale-driven breakdown of effective field theory in time-dependent string backgrounds,” arXiv:2504.13260 [hep-th]

arXiv

[3] [1]

The Hypothesis of Cores Retarded during Expansion and the Hot Cosmological Model,

Y. B. Zel’dovich and I. D. Novikov, “The Hypothesis of Cores Retarded during Expansion and the Hot Cosmological Model,” Sov. Astron. 10 (1967) 602

1967

[4] [2]

Gravitationally collapsed objects of very low mass,

S. Hawking, “Gravitationally collapsed objects of very low mass,” Mon. Not. Roy. Astron. Soc. 152 (1971) 75

1971

[5] [3]

Cosmological effects of primordial black holes,

G. F. Chapline, “Cosmological effects of primordial black holes,” Nature 253 no. 5489, (1975) 251–252

work page 1975

[6] [4]

Primordial Black Holes as Dark Matter: Recent Developments,

B. Carr and F. Kuhnel, “Primordial Black Holes as Dark Matter: Recent Developments,” Ann. Rev. Nucl. Part. Sci. 70 (2020) 355–394, arXiv:2006.02838 [astro-ph.CO]

arXiv 2020

[7] [5]

The Hierarchy problem and new dimensions at a millimeter,

N. Arkani-Hamed, S. Dimopoulos, and G. R. Dvali, “The Hierarchy problem and new dimensions at a millimeter,” Phys. Lett. B 429 (1998) 263–272, arXiv:hep-ph/9803315

arXiv 1998

[8] [6]

New dimensions at a millimeter to a Fermi and superstrings at a TeV,

I. Antoniadis, N. Arkani-Hamed, S. Dimopoulos, and G. R. Dvali, “New dimensions at a millimeter to a Fermi and superstrings at a TeV,” Phys. Lett. B 436 (1998) 257–263, arXiv:hep-ph/9804398

arXiv 1998