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Gravitino production by primordial black hole evaporation and constraints on the inhomogeneity of the early Universe

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M. Yu Khlopov, A. Barrau, J. Grain

Astrophysics · Submitted 28 Jun 2004 · 46 references

Pith's verdict: A real extension of PBH limits into the sub-10^9 g window, but the beta curves are unverifiable as printed and the abstract overstates what the body shows.

T0 · AI review

How this review was made: An AI referee (selfhosted/deepseek-v4.1-flash) read the paper on November 11, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

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arXiv IDastro-ph/0406621 (version 2)
Pith IDD67NN6I3, Pith's permanent record of this paper and its review
CitationA. Barrau, J. Grain, M. Yu Khlopov. "Gravitino production by primordial black hole evaporation and constraints on the inhomogeneity of the early Universe." arXiv:astro-ph/0406621 (2004). https://pith.science/paper/D67NN6I3
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The paper

The paper claims

Gravitino emission from evaporating primordial black holes below 10^9 g yields new upper limits on their abundance, which translate into a bound on small-scale density power (spectral index n < 1.20).

The reading

Primordial black holes are hypothetical black holes formed in the first fraction of a second after the Big Bang, when the universe was dense enough for small patches to collapse. Hawking radiation makes them evaporate, and the smallest ones, below about a billion grams, are gone by now. Because the evaporation products are produced gravitationally, even very weakly interacting particles should come out, including the gravitino, the superpartner of the graviton in supergravity models. This paper asks what happens next. In minimal supergravity the gravitino is unstable and decays after Big Bang nucleosynthesis, producing gluons and gluinos whose fragmentation makes antiprotons. Those antiprotons knock light nuclei out of helium-4, changing the abundances of lithium-6, lithium-7 and beryllium-7. The authors take a previously published Monte Carlo bound on how many gravitinos can be tolerated and convert it into a bound on how many small black holes could have existed. In gauge-mediated models the gravitino is stable, so the bound instead comes from requiring that the leftover gravitinos do not overclose the universe. The resulting limits on the black hole mass fraction are stronger than earlier ones for initial masses below 10^9 g. Feeding them into the standard relation between black hole abundance and the amplitude of density fluctuations gives a bound on the spectral index of the primordial power spectrum, n < 1.20, and on the running of the index, alpha_s < 2 x 10^-3. The authors argue this rules out blue spectra and substantial small-scale inhomogeneity.
Extended reading notes

Core claim

Evaporating primordial black holes with initial masses below 10^9 g produce enough gravitinos that, in minimal supergravity, their decay products violate light-element abundance bounds, and in gauge-mediated models they would overclose the universe. The resulting upper limits on the black hole mass fraction beta are stronger than earlier ones in this mass range and translate, via the standard Hubble-mass scaling relations, into a bound on the small-scale spectral index of n < 1.20 (n < 1.19 for a dust-like pre-evaporation stage) and on the running alpha_s < 2 x 10^-3.

Load-bearing premise

The gravitino concentration bound n_3/2 < 1.1 x 10^-13 m_3/2^{-1/4}, taken from the authors' earlier Monte Carlo work [29], is assumed to apply unchanged to gravitinos emitted by black holes. That bound was derived for a thermal gravitino population produced at reheating. Black hole emission produces a different energy spectrum, and the lithium-6, lithium-7 and beryllium-7 yields from antiproton cascades depend on that spectrum. The paper does not check whether the constraint is spectrum-independent before using it as the load-bearing input to every beta limit in Figures 1 and 2.

Original abstract

In supergravity models, the evaporation of light Primordial Black Holes (PBHs) should be a source of gravitinos. By considering this process, new stringent limits are derived on the abundance of small black holes with initial masses less than 10^9 g. In minimal supergravity, the subsequent decay of evaporated gravitinos into cascades of non-equilibrium particles leads to the formation of elements whose abundance is constrained by observations. In gauge mediated supersymmetry breaking models, their density is required not to overclose the Universe. As a result, cosmological models with substantial inhomogeneities on small scales are excluded.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,241 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.16 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.83 · compares with prior results 0.11 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

In supergravity models, the evaporation of light Primordial Black Holes (PBHs) should be a source of gravitinos. By considering this process, new stringent limits are derived on the abundance of small black holes with initial masses less than 10^9 g. In minimal supergravity, the subsequent decay of evaporated gravitinos into cascades of non-equilibrium particles leads to the formation of elements whose abundance is constrained by observations. In gauge mediated supersymmetry breaking models, their density is required not to overclose the Universe. As a result, cosmological models with substantial inhomogeneities on small scales are excluded.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 In supergravity models, the evaporation of light Primordial Black Holes (PBHs) should be a source of gravitinos. background 1.00 0.06 0.05 asserted 0.50
s1 By considering this process, new stringent limits are derived on the abundance of small black holes with initial masses less than 10^9 g. result 0.94 0.91 0.42 asserted 1.00
s2 In minimal supergravity, the subsequent decay of evaporated gravitinos into cascades of non-equilibrium particles leads to the formation of elements whose abundance is constrained by observations. interpretation 0.36 0.24 0.10 asserted 0.99
s3 In gauge mediated supersymmetry breaking models, their density is required not to overclose the Universe. result 0.62 0.32 0.08 asserted 0.95
s4 As a result, cosmological models with substantial inhomogeneities on small scales are excluded. interpretation 0.72 0.73 0.76 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.88.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. Constraints on the fraction of the Universe going into PBH
Figure 2. Constraints on the fraction of the Universe going into PBH
Figure 3. Upper limit on the spectral index of the power spectrum as

Figures reproduced from arXiv:astro-ph/0406621 by the authors.

References
How later papers used it

72 later papers cite it

Evidence: thin. 64 of the citing papers share no author with it, and 1 of those carries a confident label from Pith's citation classifier.

Pith read 10 of the 101 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

Uses its data or values 1 paper · 1 by the same authors

By the same authors

  • Presented a figure taken from this paper showing its limits, which become extremely stringent when p is small enough, for both the radiation-dominated and the dust-like cases.

    Primordial Black Holes (2008) (same authors) · 0.87 · paraphrased: the licence does not allow quoting

How the literature uses it

62 arXiv papers cite this in 85 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 49 sentences without a confident label

Uses its method or tool 1 paper
  • Instead of using the usual photon-photino decay channel, the study of [ref] relied on the more sensitive gluon-gluino channel.

    Primordial Black Holes · Limits on the PBH density · 0.89

Uses its data or values 1 paper
  • Figure [ref], taken from [ref] , shows those limits, which become extremely stringent when $p$ is small enough, for both the radiation-dominated and the dust-like cases.

    Primordial Black Holes · Cosmological consequences · 0.87

Compares with it 1 paper
Cites it as support 1 paper
Cites it as background 31 papers
  • DM production during EMD eras has been intensively studied in the literature, usually triggered by a long-lived massive particle [ref] , or by primordial black holes [ref] .

    From WIMPs to FIMPs: Impact of Early Matter Domination · Introduction · 0.92

  • DM production with a low reheating temperature has been intensively studied in the literature, usually triggered by the decay of a long-lived massive particle [ref] , or by Hawking evaporation of primordial black holes [ref] .[For studies on baryogenesis with a low reheating temperature or during an early matter-dominated phase, see Refs. [ref] and [ref] , respectively.

    From WIMPs to FIMPs with Low Reheating Temperatures · Introduction · 0.90

  • In both cases, several works have recently studied the imprints of such PBHs Hawking evaporation on particle and astrophysical data by studying its effect on the dark matter (DM) relic density and phase space distribution [ref] , the effective number of relativistic degrees of freedom, $N_eff$, at the time of CMB emission [ref] , the dynamics of Baryo/Leptogenesis [ref] , the hydrogen 21-cm line [ref] , the production of gravitational waves [ref] , and the electroweak vacuum stability [ref] .

    Evaporation of Primordial Black Holes in the Early Universe: Mass and Spin Distributions · Introduction · 0.85

Discussion

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