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REVIEW 3 major objections 5 minor 48 references

Aspects of supersymmetry breaking driven inflation in orbifold models

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read In a five-dimensional orbifold supergravity setting, the paper argues that scalar power large enough for primordial black hole formation inevitably forces the tensor-to-scalar ratio r above the bounds from current CMB data.

desk verdict Plausible PBH/r trade-off in orbifold SUSY-breaking inflation, but the advertised no-go is asserted beyond the evidence and needs documentation before it can be believed. read the letter →

arxiv 2412.06315 v1 pith:LI7PQTFQ submitted 2024-12-09 hep-th astro-ph.COgr-qchep-ph

G. A. Diamandis , K. Kaskavelis , A. B. Lahanas , G. Pavlopoulos This is my paper · ORCID
classification hep-thastro-ph.COgr-qchep-ph PACS 04.50.Kd98.80.Cq
keywords five-dimensionalsupergravityorbifoldcompactificationsupersymmetrybreakinginflationaryuniverseno-scalemodelsalpha-attractorsprimordialblackholestensor-to-scalarratio
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 investigates gravitationally induced corrections to inflaton potentials that arise when supersymmetry is broken on a hidden brane of a five-dimensional S1/Z2 orbifold and transmitted to the visible brane. Embedding no-scale-inspired and $\alpha$-attractor inflation models in this framework, it finds that parameters generating the enhanced scalar power spectra needed for primordial black hole production push the tensor-to-scalar ratio r above current observational limits. In fact, the paper states that P_zeta ≳ $10^{-2}$ leads to r > O(0.1), while more generally P_zeta > $10^{-3}$ cannot be reconciled with r below 0.08. A sympathetic reader would care because this suggests that these otherwise viable inflation models, when naturally embedded in this higher-dimensional supergravity construction, cannot simultaneously match the cosmic microwave background and produce a population of primordial black holes.

What carries the argument

The central object is the effective brane potential built from the Kähler function F = -3 ln((T + T*)/sqrt2) + $\Delta$^(5) K(phi_i, phi*_i), with $\Delta$^(5) = sqrt2/(T + T*) delta($x^{5}$). Keeping only terms linear in $\Delta$^(5) and fixing the radion field T at a constant value, with its prefactor absorbed into superpotential couplings, yields a flat-space-like F-term potential augmented by gravitationally generated soft terms. Supersymmetry breaking is introduced by a constant hidden-brane superpotential w0, and finite one-loop graphs transmit it to the visible brane as $m_phi^{2}$ K + 3($m_phi^{2}$/m_3/2)(W + c.c.). The resulting potentials contain a logarithmic term that dominates at large inflaton values, and the competition between that term and the brane potential's $\cosh$^-6a factor controls the presence of inflection points, ultra-slow-roll phases, enhanced P_zeta, and the resulting value of r.

What would settle it

Compute the effective brane potential to next order in $\Delta$^(5), or with a stabilized fluctuating radion, and scan for a point with P_zeta ≥ $10^{-3}$, r < 0.06, and n_s inside the 1-$\sigma$ observational window in either model; a single such point would break the paper's claimed general incompatibility, while the absence of such points across a systematic scan would support it.

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Extended reading notes

Core claim

The paper's central claim is that, within this orbifold supergravity framework, there is a systematic conflict between generating enhanced small-scale scalar power and keeping the tensor-to-scalar ratio r within current bounds. For the no-scale-inspired model, parameter choices that develop an inflection point and an ultra-slow-roll phase produce maximum power spectra P_zeta ~ $10^{-4}$ to $10^{-2}$, but at the cost of r ~ 0.10 to 0.15 and a spectral index n_s at or below its lower observational limit; choices fully compatible with data give P_zeta ≲ $10^{-6}$. For the $\alpha$-attractor model, the paper finds r ≳ 0.075 even without seeking primordial black hole production, and achieving P_zeta > $10^{-3}$ pushes r above 0.08. The paper also shows that a modified $\alpha$-attractor version, which removes the $\cosh$^-6a brane term, can satisfy the CMB data with r ~ 0.004 to 0.056, but then it no longer exhibits the ultra-slow-roll phase needed for significant power enhancement.

Load-bearing premise

The load-bearing premise is that the brane-bulk expansion can be cut off at terms linear in $\Delta$^(5) and the radion field can be held fixed at a constant value, with the radion prefactor absorbed into superpotential couplings; if higher-order brane-bulk couplings or radion dynamics substantially alter the effective potential, the computed P_zeta–r trade-off could shift.

Editorial extensions

If this is right

  • Within this orbifold framework, no-scale-inspired inflation cannot simultaneously match the observed r and n_s and produce PBH-relevant scalar power; data-compatible parameter choices give P_zeta ≲ 10^-6.
  • The unmodified alpha-attractor embedding keeps r above about 0.075 even when no PBH production is sought, placing it in tension with the tightest current tensor-mode bounds.
  • Achieving P_zeta > 10^-3 in the alpha-attractor case forces r above about 0.08, while the no-scale case reaches P_zeta ~ 10^-2 only with r ≳ 0.15 and n_s ≲ 0.943.
  • The modified alpha-attractor version, with the cosh^-6a term omitted, can satisfy CMB constraints with r as low as 0.004, but the parameter sets shown do not produce the ultra-slow-roll phase needed for PBH formation.
  • Consequently, PBH production from these models within this framework would require either higher-order brane-bulk corrections or a different Kähler or superpotential choice, neither of which the paper derives from a fundamental principle.

Reading between the lines

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

  • If the paper's trade-off is robust, the same log-term-versus-brane-potential competition should appear in other supergravity inflation models that receive radion-mediated soft terms, making this a possible general signature of the mediation mechanism rather than a feature of the two specific models chosen.
  • A sharper test would be to compute the PBH abundance and merger rate implied by the enhanced spectra the paper exhibits; if PBH dark matter is confirmed by gravitational-wave observations, the parameter sets producing PBHs here would already be excluded by their predicted r values.
  • The paper's decision to freeze the radion and absorb its prefactor into the superpotential couplings means the effective couplings are not fundamental; a stabilized, dynamical radion could introduce additional field-space curvature that alters which parameter combinations satisfy the observational bounds.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper considers gravitational corrections to inflaton potentials induced by supersymmetry breaking in a five-dimensional supergravity compactified on S1/Z2, keeping the brane-bulk coupling to linear order in Delta^(5) and fixing the radion field. The authors embed two classes of supergravity models into this framework: no-scale-inspired models and alpha-attractors, deriving explicit potentials in Eqs. (12), (24), and (25). They compute inflationary observables for several parameter sets, showing that examples consistent with CMB data have small power spectra, while parameter sets that produce enhanced scalar power spectra relevant for primordial black hole production yield tensor-to-scalar ratios r above current bounds. The central claim is the no-go statement that enhanced power spectra (P_zeta > 1e-3 or, in the abstract, P_zeta >= 1e-2) cannot be reconciled with the current upper bound on r. A modified alpha-attractor with the cosh^{-6a} term removed can satisfy the data but only with a moderate power-spectrum maximum of about 4e-4.

Significance. If the no-go claim is correct, it is a useful constraint on primordial black hole production in orbifold-embedded supergravity models, and the explicit potentials in Eqs. (12), (24), and (25) provide a starting point for further studies. The paper does present concrete parameter sets, COBE-normalized scales, and power-spectrum plots, which are strengths. However, the significance is conditional because the universal negative claim rests on numerical scans that are not documented in the manuscript, and the abstract's headline P_zeta >= 1e-2 case is not exhibited. The derivation of the potentials from prior brane-bulk coupling results appears internally consistent, but the lack of reproducibility for the central numerical boundary weakens the paper's contribution as it stands.

major comments (3)
  1. [Section II, text after Eq. (18)] The abstract's headline claim that P_zeta >= 1e-2 implies r > O(0.1) is not supported by any exhibited parameter set in the body. The text says 'One can obtain larger values for the power spectrum, P_zeta ~ 10^-2, for a proper fine tuned values of the parameters involved, at the cost of having even large values of r ≳ 0.15' but gives no parameter values, no V0, and no resulting spectrum plot. Because this is a load-bearing data point for the no-go claim, the parameter set and the associated r, n_s, and Pmax values must be exhibited, or the claim should be removed from the abstract and the body.
  2. [Section III, text near Eqs. (25)-(27)] The claim that 'scanning the parameter space keeping alpha = 1' yields r ≳ 0.075, and the stronger statement that 'High values for the power spectra P_zeta > 10^-3 do not reconcile with values of r below 0.08', is not reproducible as presented. No ranges for b0, b1, b3, m1 or V0 are given, no grid or sampling method is described, and no objective function or acceptance criterion is stated. Only two illustrative points are shown. Since the claim is a universal negative over parameter space, the scan must be documented (parameter ranges, step sizes, stopping criteria) or the conclusion must be weakened to 'we did not find any such cases in our scans.'
  3. [Sections II and III, power-spectrum computations] The numerical method used to compute the scalar power spectrum is never specified. The quoted values of Pmax, r, and n_s depend on whether the spectrum is obtained in the slow-roll approximation or by solving the Mukhanov-Sasaki equation, which matters especially during an ultra-slow-roll phase where the first Hubble-flow function is of order unity. The manuscript should state the method and the equations used, and justify its validity for the parameter sets exhibiting an inflection point.
minor comments (5)
  1. [Abstract and throughout] There are several typos: 'chalenges' should be 'challenges', 'trasformation' should be 'transformation', 'wavelenghts' should be 'wavelengths', and 'specrtum' should be 'spectrum'.
  2. [Figure 1 caption] The caption says 'The second case (left)' but should refer to the right panel; the left panel corresponds to Eq. (16) and the right panel to Eq. (18).
  3. [Equations (24) and (25)] The notation 'a' appears in the cosh factors and in the denominator of the argument, e.g., cosh^{-6a}(φ/√(6a)), while the model parameter is denoted α elsewhere. Please use α consistently throughout these expressions.
  4. [Section III, paragraph after Eq. (27)] 'irrespectively' should be 'irrespective'.
  5. [References] Several references are missing journal volume or article-number details (e.g., Refs. [11], [15], [24], [25], [35], [47], [48]); please standardize the bibliography.

Circularity Check

0 steps flagged · score 2.0 of 10

No material circularity: the orbifold potentials (12), (24), and (25) are constructed from stated Kähler/superpotential inputs with soft terms adopted from prior literature, and the r–P_zeta tension is a numerical output rather than an input.

full rationale

The paper's central derivation starts from the five-dimensional orbifold setup and adopts the soft supersymmetry-breaking terms of Eq. (7) from Refs. [18–20], which include the authors' earlier work [20]. These are inputs to the inflationary potentials, not predictions of the present paper, and the target claim (large P_zeta implies large r) does not appear in the cited papers. Equations (12), (24), and (25) are rearrangements of the stated Kähler potentials and superpotentials (no-scale and alpha-attractor forms) combined with those soft-term inputs; V0 and the dimensionless coefficients are parameter definitions rather than fits to the r–P_zeta conclusion. The numerical results for n_s, r, and P_max are outputs of inflationary dynamics for the chosen parameter sets, and the COBE normalization used to fix V0 is an external amplitude constraint that does not by itself force r or P_max. The no-go statements rest on parameter scans and example points that are underdocumented, especially the P_zeta ~ 1e-2 case and the alpha = 1 scan, but inadequate documentation is a reproducibility concern, not circularity. The acknowledged linear-in-Delta^(5) truncation and fixed radion are stated limitations, not hidden assumptions equivalent to the conclusion. No circular step can be exhibited; at most there are minor self-citations in the foundational formulas, and these are not load-bearing because the same ingredients are attributed to independent prior work as well.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central machinery is built from published soft-term formulas and a truncation assumption, with several parameters tuned to reproduce COBE normalization and to create inflection points. No new particles, forces, or dimensions are introduced. The main axioms are the linear-Delta expansion, the constant-radion assumption, and the ad hoc modified alpha-attractor potential; if any of these fail, the numerical conclusions could shift.

free parameters (4)
  • V0 (inflation scale) = ~1e-10 to ~7.78e-10 depending on model
    Adjusted so that the CMB-scale power spectrum P_{k=0.05} equals roughly 2.1e-9, the COBE normalization; e.g., V0 = 1.3e-10 in the first no-scale example and V0 = 3.3e-9 in an alpha-attractor example.
  • no-scale parameters l2, m1, m3 = e.g., l2 = 1.05, m1 = 7.50638, m3 = -2.97221
    Chosen by hand and fine-tuned to produce an inflection point and a USR phase while keeping the CMB amplitude fixed; the quoted n_s and r values depend on these choices.
  • alpha-attractor parameters b0, b1, b3, m1 = e.g., b0 = 0, b3 = 1.2, b1 = -0.938137, m1 = 0.104430
    Selected to create an inflection point at a specified phi_inf and to match COBE normalization; different choices produce different P_max and r values.
  • M in no-scale Kahler potential = M = 1 in the numerical examples
    Set to 1 for the standard no-scale case; the paper notes that M > 1 would imply transplanckian masses, so M is a model input rather than a derived quantity.
assumptions (5)
  • domain assumption N=2, d=5 supergravity compactified on S1/Z2 yields N=1 supergravity localized on two branes with the given F coupling.
    Standard framework from refs [1-11], not re-derived; the paper starts from Eq. (1) and the brane potential Eq. (4) as given.
  • ad hoc to paper The brane-bulk expansion is truncated at terms linear in Delta^(5), and the radion field is fixed to a constant value.
    Section I states this explicitly and the Conclusion acknowledges that higher-order terms could change the results. This truncation is load-bearing for all subsequent potential formulas.
  • domain assumption The one-loop SUSY-breaking transmission generates the soft terms m_phi^2 K + 3(m_phi^2/m_{3/2})(W + W*) with the mass formulas of Eq. (8).
    Taken from refs [18-20], including the authors' Ref. [20]; the paper does not re-derive these finite one-loop results and assumes they are valid in the linear Delta^(5) approximation.
  • domain assumption Instantaneous reheating and standard slow-roll or linear perturbation theory are used to convert the potential into n_s and r.
    The paper quotes 'Assuming instantaneous reheating' when reporting n_s and r, but gives no equations or code for the cosmological evolution; this is standard practice in the inflation literature.
  • ad hoc to paper In the modified alpha-attractor model, the function f is chosen to cancel the cosh^-6a term, effectively removing that term from the potential.
    Section III introduces this as a way to get closer to the models of Ref. [48]; it is not derived from the orbifold construction, and the paper acknowledges such modifications 'are not easily seen how to emerge from a more fundamental point of view.'

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Pith. "Pith review of Aspects of supersymmetry breaking driven inflation in orbifold models." pith.science (2026). https://pith.science/paper/LI7PQTFQ

@misc{pith2026241206315,
  author       = {Pith},
  title        = {Pith review of: Aspects of supersymmetry breaking driven inflation in orbifold models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LI7PQTFQ}},
  note         = {Machine review of arXiv:2412.06315}
}
abstract

We consider gravitationally induced corrections to inflaton potentials driven by supersymmetry breaking in a five-dimensional supergravity, compactified on a $ S_1/Z_2 $ orbifold. The supersymmetry breaking takes place on the hidden brane and is transmitted to the visible brane through finite one loop graphs giving rise to an inflaton potential which includes gravitationally induced terms. These corrections are significant for inflationary cosmology and have the potential to modify the predictions of widely studied supergravity models if the latter are embedded in this framework. To explore these effects we examine two classes of models those inspired by no-scale supergravity models and $\alpha$-attractors. Both models are compatible with current cosmological observations but face chalenges in reconciling enhanced values for the scalar power spectrum $ P_\zeta$ with cosmological data, particularly regarding the tensor to scalar ratio $r$. In fact $ P_\zeta \gtrsim 10^{-2}$ results to $ r > \mathcal{O} (0.1) $, outside the limits put by current data.

Figures

Figures reproduced from arXiv: 2412.06315 by the authors.

Figure 1
Figure 1. FIG. 1. The power spectrum for the no-scale model for values of the parameters given in Eq.( [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The power spectrum for the [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. The power spectrum for the modified [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

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Works this paper leans on

48 extracted references · 21 canonical work pages

  1. [1]

    de Wit and H

    B. de Wit and H. Nicolai, N=8 Supergravity, Nucl. Phys. B 208, 323 (1982)

    work page 1982

  2. [2]

    Pernici, K

    M. Pernici, K. Pilch, and P. van Nieuwenhuizen, Gauged N=8 D=5 Supergravity, Nucl. Phys. B 259, 460 (1985)

    work page 1985

  3. [3]

    Gunaydin, G

    M. Gunaydin, G. Sierra, and P. K. Townsend, The Geometry of N=2 Maxwell-Einstein Supergravity and Jordan Algebras, Nucl. Phys. B 242, 244 (1984)

    work page 1984

  4. [4]

    Gunaydin, G

    M. Gunaydin, G. Sierra, and P. K. Townsend, Exceptional Supergravity Theories and the MAGIC Square, Phys. Lett. B 133, 72 (1983)

    work page 1983

  5. [5]

    Gunaydin, G

    M. Gunaydin, G. Sierra, and P. K. Townsend, Vanishing Potentials in Gauged N = 2 Supergravity: An Application of Jordan Algebras, Phys. Lett. B 144, 41 (1984)

    work page 1984

  6. [6]

    Special geometry, cubic polynomials and homogeneous quaternionic spaces

    B. de Wit and A. Van Proeyen, Special geometry, cubic polynomials and homogeneous quaternionic spaces, Commun. Math. Phys. 149, 307 (1992), arXiv:hep-th/9112027

    work page Pith review arXiv 1992

  7. [7]

    Gunaydin and M

    M. Gunaydin and M. Zagermann, The Gauging of five-dimensional, N=2 Maxwell-Einstein supergravity theories coupled to tensor multiplets, Nucl. Phys. B 572, 131 (2000), arXiv:hep-th/9912027

    arXiv 2000

  8. [8]

    The Vacua of 5d,N=2 Gauged Yang-Mills/Einstein/Tensor Supergravity: Abelian Case

    M. Gunaydin and M. Zagermann, The Vacua of 5-D, N=2 gauged Yang-Mills/Einstein tensor supergravity: Abelian case, Phys. Rev. D 62, 044028 (2000), arXiv:hep-th/0002228

    work page Pith review arXiv 2000

Show all 48 references
  1. [9]

    J. R. Ellis, Z. Lalak, S. Pokorski, and S. Thomas, Supergravity and supersymmetry breaking in four- dimensions and five-dimensions, Nucl. Phys. B 563, 107 (1999), arXiv:hep-th/9906148

    1999 arXiv

  2. [10]

    Falkowski, Z

    A. Falkowski, Z. Lalak, and S. Pokorski, Five-dimensional gauged supergravities with universal hypermultiplet and warped brane worlds, Phys. Lett. B 509, 337 (2001), arXiv:hep-th/0009167

    2001 arXiv

  3. [11]

    Bergshoeff, R

    E. Bergshoeff, R. Kallosh, and A. Van Proeyen, Supersymmetry in singular spaces, JHEP 10, 033, arXiv:hep- th/0007044

  4. [12]

    G. A. Diamandis, B. C. Georgalas, P. Kouroumalou, and A. B. Lahanas, On the brane coupling of unified orbifolds with gauge interactions in the bulk, Phys. Lett. B 602, 112 (2004), arXiv:hep-th/0402228

    2004 arXiv

  5. [13]

    E. A. Mirabelli and M. E. Peskin, Transmission of supersymmetry breaking from a four-dimensional boundary, Phys. Rev. D 58, 065002 (1998), arXiv:hep-th/9712214

    1998 arXiv

  6. [14]

    J. A. Bagger, F. Feruglio, and F. Zwirner, Generalized symmetry breaking on orbifolds, Phys. Rev. Lett. 88, 101601 (2002), arXiv:hep-th/0107128

    2002 arXiv

  7. [15]

    Bagger, F

    J. Bagger, F. Feruglio, and F. Zwirner, Brane induced supersymmetry breaking, JHEP 02, 010, arXiv:hep- th/0108010

  8. [16]

    Falkowski, Z

    A. Falkowski, Z. Lalak, and S. Pokorski, Supersymmetrizing branes with bulk in five-dimensional supergravity, Phys. Lett. B 491, 172 (2000), arXiv:hep-th/0004093

    2000 arXiv

  9. [17]

    Gherghetta and A

    T. Gherghetta and A. Riotto, Gravity mediated supersymmetry breaking in the brane world, Nucl. Phys. B 623, 97 (2002), arXiv:hep-th/0110022

    2002 arXiv

  10. [18]

    Rattazzi, C

    R. Rattazzi, C. A. Scrucca, and A. Strumia, Brane to brane gravity mediation of supersymmetry breaking, Nucl. Phys. B 674, 171 (2003), arXiv:hep-th/0305184

    2003 arXiv

  11. [19]

    C. A. Scrucca, Mediation of supersymmetry breaking in extra dimensions, Mod. Phys. Lett. A 20, 297 (2005), arXiv:hep-th/0412237

    2005 arXiv

  12. [20]

    G. A. Diamandis, B. C. Georgalas, P. Kouroumalou, and A. B. Lahanas, On the radion mediation of the Su- persymmetry breaking in N=2, D=5 Supergravity Orbifolds, Phys. Lett. B 660, 247 (2008), arXiv:0711.1414 [hep-th]

    2008 arXiv

  13. [21]

    C. M. Peterson and M. Tegmark, Testing multifield inflation: A geometric approach, Phys. Rev. D87, 103507 (2013), arXiv:1111.0927 [astro-ph.CO]

    2013 arXiv

  14. [22]

    R. N. Greenwood, D. I. Kaiser, and E. I. Sfakianakis, Multifield Dynamics of Higgs Inflation, Phys. Rev. D 87, 064021 (2013), arXiv:1210.8190 [hep-ph]

    2013 arXiv

  15. [23]

    D. I. Kaiser and E. I. Sfakianakis, Multifield Inflation after Planck: The Case for Nonminimal Couplings, Phys. Rev. Lett. 112, 011302 (2014), arXiv:1304.0363 [astro-ph.CO]

    2014 arXiv

  16. [24]

    Christodoulidis, D

    P. Christodoulidis, D. Roest, and E. I. Sfakianakis, Scaling attractors in multi-field inflation, JCAP 12, 059, arXiv:1903.06116 [hep-th]

    1903 arXiv

  17. [25]

    Boutivas, I

    K. Boutivas, I. Dalianis, G. P. Kodaxis, and N. Tetradis, The effect of multiple features on the power spectrum in two-field inflation, JCAP 08 (08), 021, arXiv:2203.15605 [astro-ph.CO]

    arXiv

  18. [26]

    B. J. Carr and S. W. Hawking, Black holes in the early Universe, Mon. Not. Roy. Astron. Soc. 168, 399 (1974)

    1974

  19. [27]

    Meszaros, The behaviour of point masses in an expanding cosmological substratum, Astron

    P. Meszaros, The behaviour of point masses in an expanding cosmological substratum, Astron. Astrophys. 37, 225 (1974)

    1974

  20. [28]

    B. J. Carr, The Primordial black hole mass spectrum, Astrophys. J. 201, 1 (1975)

    1975

  21. [29]

    I. D. Novikov, A. G. Polnarev, A. A. Starobinskii, and I. B. Zeldovich, Primordial black holes, Astronomy 10 and Astrophysics 80, 104 (1979)

    1979

  22. [30]

    W. H. Kinney, Horizon crossing and inflation with large eta, Phys. Rev. D 72, 023515 (2005), arXiv:gr- qc/0503017

    2005

  23. [31]

    Ballesteros and M

    G. Ballesteros and M. Taoso, Primordial black hole dark matter from single field inflation, Phys. Rev. D 97, 023501 (2018), arXiv:1709.05565 [hep-ph]

    2018 arXiv

  24. [32]

    Sasaki, T

    M. Sasaki, T. Suyama, T. Tanaka, and S. Yokoyama, Primordial black holes—perspectives in gravitational wave astronomy, Class. Quant. Grav. 35, 063001 (2018), arXiv:1801.05235 [astro-ph.CO]

    2018 arXiv

  25. [33]

    Dalianis, G

    I. Dalianis, G. P. Kodaxis, I. D. Stamou, N. Tetradis, and A. Tsigkas-Kouvelis, Spectrum oscillations from features in the potential of single-field inflation, Phys. Rev. D 104, 103510 (2021), arXiv:2106.02467 [astro- ph.CO]

    2021 arXiv

  26. [34]

    B. J. Carr and A. M. Green, The history of primordial black holes (2024), arXiv:2406.05736 [astro-ph.CO]

    2024 arXiv

  27. [35]

    Choudhury and M

    S. Choudhury and M. Sami, Large fluctuations and primordial black holes (2024), arXiv:2407.17006 [gr-qc]

    2024 arXiv

  28. [36]

    Cremmer, S

    E. Cremmer, S. Ferrara, C. Kounnas, and D. V. Nanopoulos, Naturally Vanishing Cosmological Constant in N=1 Supergravity, Phys. Lett. B 133, 61 (1983)

    1983

  29. [37]

    J. R. Ellis, A. B. Lahanas, D. V. Nanopoulos, and K. Tamvakis, No-Scale Supersymmetric Standard Model, Phys. Lett. B 134, 429 (1984)

    1984

  30. [38]

    Ellis, M

    J. Ellis, M. A. G. Garcia, D. V. Nanopoulos, and K. A. Olive, No-Scale Inflation, Class. Quant. Grav. 33, 094001 (2016), arXiv:1507.02308 [hep-ph]

    2016 arXiv

  31. [39]

    Ellis, M

    J. Ellis, M. A. G. Garc ´ ıa, N. Nagata, D. V. Nanopoulos, K. A. Olive, and S. Verner, Building models of inflation in no-scale supergravity, International Journal of Modern Physics D 29, 2030011 (2020)

    2020

  32. [40]

    Akrami et al

    Y. Akrami et al. (Planck), Planck 2018 results. X. Constraints on inflation, Astron. Astrophys. 641, A10 (2020), arXiv:1807.06211 [astro-ph.CO]

    2020 arXiv

  33. [41]

    Tristram et al., Improved limits on the tensor-to-scalar ratio using BICEP and Planck data, Phys

    M. Tristram et al., Improved limits on the tensor-to-scalar ratio using BICEP and Planck data, Phys. Rev. D 105, 083524 (2022), arXiv:2112.07961 [astro-ph.CO]

    2022 arXiv

  34. [42]

    P. A. R. Ade et al. (BICEP, Keck), Improved Constraints on Primordial Gravitational Waves using Planck, WMAP, and BICEP/Keck Observations through the 2018 Observing Season, Phys. Rev. Lett. 127, 151301 (2021), arXiv:2110.00483 [astro-ph.CO]

    2021

  35. [43]

    Alam et al

    S. Alam et al. (eBOSS), Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Cosmolog- ical implications from two decades of spectroscopic surveys at the Apache Point Observatory, Phys. Rev. D 103, 083533 (2021), arXiv:2007.08991 [astro-ph.CO]

    2021 arXiv

  36. [44]

    Aghanim et al

    N. Aghanim et al. (Planck), Planck 2018 results. VIII. Gravitational lensing, Astron. Astrophys. 641, A8 (2020), arXiv:1807.06210 [astro-ph.CO]

    2020 arXiv

  37. [45]

    Campeti and E

    P. Campeti and E. Komatsu, New Constraint on the Tensor-to-scalar Ratio from the Planck and BICEP/Keck Array Data Using the Profile Likelihood, Astrophys. J. 941, 110 (2022), arXiv:2205.05617 [astro-ph.CO]

    2022 arXiv

  38. [46]

    D. V. Nanopoulos, V. C. Spanos, and I. D. Stamou, Primordial Black Holes from No-Scale Supergravity, Phys. Rev. D 102, 083536 (2020), arXiv:2008.01457 [astro-ph.CO]

    2020 arXiv

  39. [47]

    Kallosh, A

    R. Kallosh, A. Linde, and D. Roest, Superconformal Inflationaryα-Attractors, JHEP 11, 198, arXiv:1311.0472 [hep-th]

    arXiv

  40. [48]

    Dalianis, A

    I. Dalianis, A. Kehagias, and G. Tringas, Primordial black holes from α-attractors, JCAP 01, 037, arXiv:1805.09483 [astro-ph.CO]

    arXiv

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Reviewed August 11, 2026 · model on record in the stance chip above.