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REVIEW 2 major objections 4 minor 97 references

In analytic infinite-derivative gravity, a stable non-singular bounce cannot be built without a negative cosmological constant.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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T0 review · grok-4.5

2026-07-14 03:19 UTC pith:YLZ24QRI

load-bearing objection Clean no-go for healthy positive-Λ bounces in AID gravity once the standard ansatz is granted; the (1+3) form-factor analysis is the real advance. the 2 major comments →

arxiv 2607.11765 v1 pith:YLZ24QRI submitted 2026-07-13 gr-qc hep-th

Is there ghost and tachyon free bounce in UV complete gravity theory?

Hao Hu , Alexey S. Koshelev , Abhishek Naskar This is my paper
classification gr-qc hep-th
keywords analytic infinite derivative gravitybouncing cosmologyghost-free form factorsde Sitter perturbationscosmological constanttensor power spectrumUV complete gravity
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Analytic infinite-derivative gravity is a candidate for a renormalizable, ghost-free completion of Einstein gravity around maximally symmetric backgrounds. It also admits exact non-singular bouncing cosmologies. This paper asks whether those bounces can be free of ghost or tachyon instabilities. By cataloguing the physical degrees of freedom around Minkowski and de Sitter space and matching them to the algebraic conditions that generate the known bouncing solutions, the authors show that a healthy bounce with positive cosmological constant is impossible: either the radiation that supports the bounce is a ghost, or a tachyon appears, or the form factors cease to be entire. The only remaining loopholes are a negative cosmological constant or a super-inflating solution that never approaches de Sitter. Motivated by the singularity problem, the authors nevertheless compute the scalar and tensor spectra; the scalar mode is too massive to affect the CMB, while the tensor amplitude is controlled by the form-factor value at the de-Sitter curvature scale.

Core claim

On a very general basis one cannot construct an instability-free bounce without a negative cosmological constant. Analyticity of the higher-derivative form factors, together with the solution-generating ansatz that all known bouncing solutions obey, forces the radiation that supports the bounce to be a ghost whenever the cosmological constant is non-negative.

What carries the argument

The (1+3) decomposition of linear perturbations around Minkowski and de Sitter, which isolates the scalar and tensor form-factor conditions required for ghost-freedom; these conditions are then joined to the algebraic constraints that the ansatz □R = r₁R + r₂ imposes on the same form factors.

Load-bearing premise

The claim rests on the premise that every cosmologically relevant bouncing solution with only traceless matter must obey the ansatz that freezes the d’Alembertian of the Ricci scalar to a linear function of itself.

What would settle it

An explicit FLRW bouncing solution of the full equations of motion that uses only traceless matter, stays free of ghosts and tachyons, has non-negative cosmological constant, and does not satisfy □R = r₁R + r₂ would falsify the no-go result.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Any ghost-free bounce constructed inside analytic infinite-derivative gravity must either employ a negative cosmological constant or abandon entire form factors.
  • The known positive-Λ bouncing solutions necessarily contain ghost radiation once form-factor analyticity is imposed.
  • Massive scalar modes around the de-Sitter asymptotics decay or are amplitude-suppressed and cannot source the observed CMB temperature fluctuations.
  • The tensor power spectrum acquires an overall multiplicative factor set by the form-factor value at the de-Sitter curvature scale, giving a direct observational constraint on that form factor.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same obstruction is likely to reappear in any higher-derivative completion that insists on entire form factors and an FLRW ansatz of the same type, even outside the analytic-infinite-derivative family.
  • If a graceful-exit mechanism that converts the late de-Sitter phase into radiation domination can be added without reintroducing ghosts, the tensor spectrum computed here would become the leading late-time gravitational-wave signal of the bounce.
  • A systematic search for FLRW solutions that violate the ansatz while remaining ghost-free would either confirm the no-go or open the only remaining window for a healthy positive-Λ bounce.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. The paper studies whether analytic infinite derivative (AID) gravity admits non-singular bouncing cosmologies free of ghosts and tachyons. Using the (1+3) formalism it derives the ghost-free form factors for both scalar and tensor modes around Minkowski and de Sitter backgrounds, then shows that compatibility of these form factors with the solution-generating ansatz □R = r₁R + r₂ forces either ghost radiation or a tachyonic scalar for any non-negative cosmological constant. Known exact bouncing solutions are examined and shown to require ghost radiation once analyticity of the form factors is imposed. Despite the instabilities the authors still compute the late-time scalar and tensor spectra around the de-Sitter asymptotics of the solutions, concluding that the massive scalar decays or is suppressed while the tensor spectrum acquires a form-factor correction e^{-2ω(R/6)}.

Significance. If the no-go result holds under the stated premises it places a sharp, essentially parameter-free obstruction on the use of AID gravity to resolve the cosmological singularity by a bounce while remaining free of instabilities and keeping a positive cosmological constant. The explicit construction of the second-variation actions and the transparent matching of the algebraic conditions (2.7) with the ghost-free form factors (3.19) and (4.13) constitute a solid technical advance for the infinite-derivative framework. The tensor-spectrum calculation supplies a concrete observational constraint on the entire function ω. These strengths remain valuable even if the no-go is later circumvented by non-entire form factors or by solutions outside the ansatz.

major comments (2)
  1. [§5, eq. (5.4)] §2 (after eq. (2.6)) and §5 (eq. (5.4)): the central claim that “on a very general basis one cannot construct an instability-free bounce without a negative cosmological constant” rests on the assumption that the ansatz □R = r₁R + r₂ (r₁ ≠ 0) exhausts cosmologically relevant FLRW solutions with traceless matter. The completeness argument is only cited from [75] and treated as generic; a short quantitative discussion of the measure of possible counter-examples (or an explicit statement that the no-go is conditional on the ansatz) is needed to justify the wording of the abstract and the introduction.
  2. [§6.2] §6.2: the tensor power spectrum is computed after discarding the complex-mass modes that appear around the bounce. While the classical-decay condition Im(m²)² < 9 H_dS² Re(m²) is recalled, no estimate is given for the specific form factors of the solutions under study. Because the observational implication (the factor e^{-2ω(R/6)}) is presented as a constraint, a brief quantitative bound on the residual contribution of those modes is required.
minor comments (4)
  1. [front matter] The arXiv identifier is still written as “26xx.xxxx” in the front matter; replace with the actual number once assigned.
  2. [§2] Eq. (2.14) and the subsequent discussion of F₁ > 0 would be clearer if the sign of λ were fixed once and for all (or if both signs were displayed).
  3. [§4] In §4 the analyticity condition for F_C at □ = 2R/3 is stated, yet the same condition for F_R at □ = −R/3 appears only later; a single unified paragraph would improve readability.
  4. [§7] Several references to “forthcoming papers” on graceful exit and non-entire form factors could be replaced by a short outlook subsection that lists the open questions more systematically.

Circularity Check

1 steps flagged

No significant circularity: the no-go is a genuine sign conflict between ghost-free entire form factors and the radiation energy of known ansatz-based bounces; only a minor self-citation supports ansatz completeness.

specific steps
  1. self citation load bearing [§2 after eq. (2.6); also §1 bullet on the ansatz]
    "it was proven in [75] that under very general assumptions solutions will obey this ansatz, and until now no FLRW type solutions beyond this ansatz for a traceless matter are known (modulo very simple configurations...)"

    The generality of the no-go ('on a very general basis') rests partly on a completeness claim whose only support is a citation to prior work by an overlapping author. This is a mild self-citation; it is not load-bearing for the explicit sign conflict on the known solutions (2.9) and (2.11), which the paper derives independently.

full rationale

The central claim (abstract; §5, eq. (5.4)) is obtained by combining (i) ghost-free entire form-factor shapes re-derived in (1+3) formalism around de Sitter (eqs. (4.2), (4.13), positivity (4.4) and (4.15)) with (ii) the algebraic conditions of the solution-generating ansatz (2.7). This forces r₁ = μ² and F₁ > 0 for a non-tachyonic scalar (eqs. (5.1)–(5.2)), which then makes the radiation energy density at the bounce (2.13)–(2.14) negative for Λ ≥ 0. That is a non-trivial sign obstruction, not a definitional identity or a fitted parameter renamed as a prediction. No parameters are fitted to data; the form-factor analyticity and kinetic-sign requirements are independent inputs. The only mild self-citation is the appeal to [75] for the claim that FLRW solutions with traceless matter generically obey the ansatz; the paper also exhibits the same ghost-radiation conflict for the non-ansatz R = const solution (2.11) via (2.15) vs (4.4), so the completeness citation is not load-bearing for the known-solutions analysis. Prior bouncing solutions ([69,70,74]) are treated as objects of study, not as uniqueness theorems that force the no-go. Score 1 reflects that single non-essential self-citation; the derivation chain itself is self-contained.

Axiom & Free-Parameter Ledger

1 free parameters · 3 axioms · 0 invented entities

The central no-go rests on three domain-level choices already standard in the AID literature (entire form factors, the quadratic-curvature action, the FLRW ansatz) plus the completeness claim that solutions with traceless matter obey □R = r₁R + r₂. No free parameters are fitted to data; the only free functions are the entire functions ω(□) and σ(□) that define the form factors, which remain arbitrary subject to reality and analyticity conditions.

free parameters (1)
  • entire functions ω(□), σ(□) that define F_C and F_R
    Model parameters fixed only by analyticity at special points and reality on the real axis; not fitted to cosmological data but left free for later observational constraints on the tensor spectrum.
axioms (3)
  • domain assumption Form factors F_R(□) and F_C(□) must be entire functions so that the propagator contains no extra poles and the Taylor series has infinite radius of convergence.
    Standard requirement of AID gravity (cited from [9]); invoked throughout §§3–5 to exclude non-analytic form factors that might evade the no-go.
  • domain assumption Cosmologically relevant FLRW solutions with traceless matter obey the ansatz □R = r₁R + r₂ (r₁ ≠ 0).
    Taken from [75] and used to generate the algebraic conditions (2.7); the paper treats exceptions as marginal.
  • standard math The second-order action for a mode with positive kinetic term and real mass-squared is free of ghosts and tachyons.
    Standard stability criterion applied to the reduced actions (3.21) and (4.15).

pith-pipeline@v1.1.0-grok45 · 32495 in / 2306 out tokens · 21973 ms · 2026-07-14T03:19:51.785032+00:00 · methodology

0 comments
read the original abstract

Analytic infinite derivative gravity theories provide a renormalizable and ghost-free description of gravity around covariantly constant backgrounds. These theories can have non-singular bouncing Universe solutions. In this paper we aim to address a question whether it is possible to realize a bouncing solution without the presence of a ghost or a tachyon instability in this framework. We perform a detailed analysis of degrees of freedom in $(1+3)$ formalism around Minkowski and de Sitter space-times. As a result it becomes clear that on a very general basis one cannot construct an instability free bounce without a negative cosmological constant. An analysis of known bouncing solutions in this model shows that an analyticity of higher derivative form factors in combination with solutions parameters result in the presence of a ghost radiation. Being motivated by the idea of resolving the cosmological singularity problem we proceed by analyzing scalar and tensor modes anyway. Scalar modes appear to not influence Cosmic Microwave Background observations at all, while tensor modes spectrum is computed and the corresponding implications are discussed.

discussion (0)

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Reference graph

Works this paper leans on

97 extracted references · 85 linked inside Pith

  1. [1]

    Stelle,Renormalization of Higher Derivative Quantum Gravity,Phys

    K.S. Stelle,Renormalization of Higher Derivative Quantum Gravity,Phys. Rev. D16(1977) 953

    1977

  2. [2]

    Krasnikov,NONLOCAL GAUGE THEORIES,Theor

    N.V. Krasnikov,NONLOCAL GAUGE THEORIES,Theor. Math. Phys.73(1987) 1184

    1987

  3. [3]

    Kuzmin,THE CONVERGENT NONLOCAL GRAVITATION

    Y.V. Kuzmin,THE CONVERGENT NONLOCAL GRAVITATION. (IN RUSSIAN),Sov. J. Nucl. Phys.50(1989) 1011

    1989

  4. [4]

    Tomboulis,Superrenormalizable gauge and gravitational theories,hep-th/9702146

    E.T. Tomboulis,Superrenormalizable gauge and gravitational theories,hep-th/9702146

    Pith/arXiv arXiv

  5. [5]

    Modesto,Super-renormalizable Quantum Gravity,Phys

    L. Modesto,Super-renormalizable Quantum Gravity,Phys. Rev. D86(2012) 044005 [1107.2403]

    Pith/arXiv arXiv 2012

  6. [6]

    Modesto and L

    L. Modesto and L. Rachwal,Super-renormalizable and finite gravitational theories,Nucl. Phys. B 889(2014) 228 [1407.8036]

    Pith/arXiv arXiv 2014

  7. [7]

    Modesto and I.L

    L. Modesto and I.L. Shapiro,Superrenormalizable quantum gravity with complex ghosts,Phys. Lett. B755(2016) 279 [1512.07600]

    Pith/arXiv arXiv 2016

  8. [8]

    Biswas, E

    T. Biswas, E. Gerwick, T. Koivisto and A. Mazumdar,Towards singularity and ghost free theories of gravity,Phys. Rev. Lett.108(2012) 031101 [1110.5249]

    Pith/arXiv arXiv 2012

  9. [9]

    Biswas, A.S

    T. Biswas, A.S. Koshelev and A. Mazumdar,Consistent higher derivative gravitational theories with stable de Sitter and anti–de Sitter backgrounds,Phys. Rev. D95(2017) 043533 [1606.01250]

    Pith/arXiv arXiv 2017

  10. [10]

    Modesto,Finite Quantum Gravity,1305.6741

    L. Modesto,Finite Quantum Gravity,1305.6741

    Pith/arXiv arXiv

  11. [11]

    Koshelev, O

    A.S. Koshelev, O. Melichev and L. Rachwal,Cancellation of UV divergences in ghost-free infinite derivative gravity,2512.18006

    Pith/arXiv arXiv

  12. [12]

    Bas i Beneito, G

    A. Bas i Beneito, G. Calcagni and L. Rachwa l,Classical and Quantum Nonlocal Gravity, (2024), DOI [2211.05606]

    Pith/arXiv arXiv 2024

  13. [13]

    Koshelev,Non-local SFT Tachyon and Cosmology,JHEP04(2007) 029 [hep-th/0701103]

    A.S. Koshelev,Non-local SFT Tachyon and Cosmology,JHEP04(2007) 029 [hep-th/0701103]

    Pith/arXiv arXiv 2007

  14. [14]

    Koshelev and A

    A.S. Koshelev and A. Tokareva,Non-local self-healing of Higgs inflation,Phys. Rev. D102(2020) 123518 [2006.06641]

    Pith/arXiv arXiv 2020

  15. [15]

    Lee and G.C

    T.D. Lee and G.C. Wick,Negative Metric and the Unitarity of the S Matrix,Nucl. Phys. B9(1969) 209

    1969

  16. [16]

    Lee and G.C

    T.D. Lee and G.C. Wick,Finite Theory of Quantum Electrodynamics,Phys. Rev. D2(1970) 1033

    1970

  17. [17]

    Anselmi,Fakeons, unitarity, massive gravitons and the cosmological constant,JHEP12(2019) 027 [1909.04955]

    D. Anselmi,Fakeons, unitarity, massive gravitons and the cosmological constant,JHEP12(2019) 027 [1909.04955]

    Pith/arXiv arXiv 2019

  18. [18]

    Koshelev, K.S

    A.S. Koshelev, K.S. Kumar and A.A. Starobinsky,Analytic infinite derivative gravity,R 2-like inflation, quantum gravity and CMB,Int. J. Mod. Phys. D29(2020) 2043018 [2005.09550]

    Pith/arXiv arXiv 2020

  19. [19]

    Koshelev,Non-local Starobinsky inflation and beyond,accepted in Fundamental Theories of Physics(2025)

    A.S. Koshelev,Non-local Starobinsky inflation and beyond,accepted in Fundamental Theories of Physics(2025)

    2025

  20. [20]

    Barnaby and J.M

    N. Barnaby and J.M. Cline,Large Nongaussianity from Nonlocal Inflation,JCAP07(2007) 017 [0704.3426]. – 24 –

    Pith/arXiv arXiv 2007

  21. [21]

    Koshelev and A

    A.S. Koshelev and A. Naskar,Cosmic inflation in analytic infinite derivative scalar-tensor theories, JCAP07(2025) 081 [2504.06035]

    Pith/arXiv arXiv 2025

  22. [22]

    Dou and R

    D. Dou and R. Percacci,The running gravitational couplings,Class. Quant. Grav.15(1998) 3449 [hep-th/9707239]

    Pith/arXiv arXiv 1998

  23. [23]

    Percacci,Asymptotic Safety,0709.3851

    R. Percacci,Asymptotic Safety,0709.3851

    Pith/arXiv arXiv

  24. [24]

    Reuter,Nonperturbative evolution equation for quantum gravity,Phys

    M. Reuter,Nonperturbative evolution equation for quantum gravity,Phys. Rev. D57(1998) 971 [hep-th/9605030]

    Pith/arXiv arXiv 1998

  25. [25]

    Reuter and F

    M. Reuter and F. Saueressig,Renormalization group flow of quantum gravity in the Einstein-Hilbert truncation,Phys. Rev. D65(2002) 065016 [hep-th/0110054]

    Pith/arXiv arXiv 2002

  26. [26]

    Knorr, C

    B. Knorr, C. Ripken and F. Saueressig,Form Factors in Asymptotic Safety: conceptual ideas and computational toolbox,Class. Quant. Grav.36(2019) 234001 [1907.02903]

    Pith/arXiv arXiv 2019

  27. [27]

    Gasperini and G

    M. Gasperini and G. Veneziano,Pre - big bang in string cosmology,Astropart. Phys.1(1993) 317 [hep-th/9211021]

    Pith/arXiv arXiv 1993

  28. [28]

    Enqvist and M.S

    K. Enqvist and M.S. Sloth,Adiabatic CMB perturbations in pre - big bang string cosmology,Nucl. Phys. B626(2002) 395 [hep-ph/0109214]

    Pith/arXiv arXiv 2002

  29. [29]

    Cardoso and D

    A. Cardoso and D. Wands,Generalised perturbation equations in bouncing cosmologies,Phys. Rev. D 77(2008) 123538 [0801.1667]

    Pith/arXiv arXiv 2008

  30. [30]

    Novello and S.E.P

    M. Novello and S.E.P. Bergliaffa,Bouncing Cosmologies,Phys. Rept.463(2008) 127 [0802.1634]

    Pith/arXiv arXiv 2008

  31. [31]

    Brandenberger,The Matter Bounce Alternative to Inflationary Cosmology,1206.4196

    R.H. Brandenberger,The Matter Bounce Alternative to Inflationary Cosmology,1206.4196

    Pith/arXiv arXiv

  32. [32]

    Battefeld and P

    D. Battefeld and P. Peter,A Critical Review of Classical Bouncing Cosmologies,Phys. Rept.571 (2015) 1 [1406.2790]

    Pith/arXiv arXiv 2015

  33. [33]

    Brandenberger and P

    R. Brandenberger and P. Peter,Bouncing Cosmologies: Progress and Problems,Found. Phys.47 (2017) 797 [1603.05834]

    Pith/arXiv arXiv 2017

  34. [34]

    Raveendran and L

    R.N. Raveendran and L. Sriramkumar,Primordial features from ekpyrotic bounces,Phys. Rev. D99 (2019) 043527 [1809.03229]

    Pith/arXiv arXiv 2019

  35. [35]

    Ijjas and P.J

    A. Ijjas and P.J. Steinhardt,Bouncing cosmology made simple,Class. Quant. Grav.35(2018) 135004 [1803.01961]

    Pith/arXiv arXiv 2018

  36. [36]

    Nariai and K

    H. Nariai and K. Tomita,On the removal of initial singularity in a big-bang universe in terms of a renormalized theory of gravitation. 2. criteria for obtaining a physically reasonable model,Prog. Theor. Phys.46(1971) 776

    1971

  37. [37]

    Abramo, I

    L.R. Abramo, I. Yasuda and P. Peter,Non singular bounce in modified gravity,Phys. Rev. D81 (2010) 023511 [0910.3422]

    Pith/arXiv arXiv 2010

  38. [38]

    Y.-F. Cai, S. Capozziello, M. De Laurentis and E.N. Saridakis,f(T) teleparallel gravity and cosmology,Rept. Prog. Phys.79(2016) 106901 [1511.07586]

    Pith/arXiv arXiv 2016

  39. [39]

    Bamba, A.N

    K. Bamba, A.N. Makarenko, A.N. Myagky, S. Nojiri and S.D. Odintsov,Bounce cosmology from F(R)gravity andF(R)bigravity,JCAP01(2014) 008 [1309.3748]

    Pith/arXiv arXiv 2014

  40. [40]

    Nojiri and S.D

    S. Nojiri and S.D. Odintsov,MimeticF(R)gravity: inflation, dark energy and bounce,1408.3561

    Pith/arXiv arXiv

  41. [41]

    Nojiri, S.D

    S. Nojiri, S.D. Odintsov, V.K. Oikonomou and T. Paul,Nonsingular bounce cosmology from Lagrange multiplierF(R)gravity,Phys. Rev. D100(2019) 084056 [1910.03546]

    Pith/arXiv arXiv 2019

  42. [42]

    Singh, K

    J.K. Singh, K. Bamba, R. Nagpal and S.K.J. Pacif,Bouncing cosmology inf(R, T)gravity,Phys. Rev. D97(2018) 123536 [1807.01157]

    Pith/arXiv arXiv 2018

  43. [43]

    Khoury, B.A

    J. Khoury, B.A. Ovrut, P.J. Steinhardt and N. Turok,The Ekpyrotic universe: Colliding branes and the origin of the hot big bang,Phys. Rev. D64(2001) 123522 [hep-th/0103239]. – 25 –

    Pith/arXiv arXiv 2001

  44. [44]

    Khoury, B.A

    J. Khoury, B.A. Ovrut, P.J. Steinhardt and N. Turok,Density perturbations in the ekpyrotic scenario,Phys. Rev. D66(2002) 046005 [hep-th/0109050]

    Pith/arXiv arXiv 2002

  45. [45]

    Lehners, P

    J.-L. Lehners, P. McFadden, N. Turok and P.J. Steinhardt,Generating ekpyrotic curvature perturbations before the big bang,Phys. Rev. D76(2007) 103501 [hep-th/0702153]

    Pith/arXiv arXiv 2007

  46. [46]

    Buchbinder, J

    E.I. Buchbinder, J. Khoury and B.A. Ovrut,New Ekpyrotic cosmology,Phys. Rev. D76(2007) 123503 [hep-th/0702154]

    Pith/arXiv arXiv 2007

  47. [47]

    A.M. Levy, A. Ijjas and P.J. Steinhardt,Scale-invariant perturbations in ekpyrotic cosmologies without fine-tuning of initial conditions,Phys. Rev. D92(2015) 063524 [1506.01011]

    Pith/arXiv arXiv 2015

  48. [48]

    Brandenberger and Z

    R. Brandenberger and Z. Wang,Ekpyrotic cosmology with a zero-shear S-brane,Phys. Rev. D102 (2020) 023516 [2004.06437]

    Pith/arXiv arXiv 2020

  49. [49]

    Brandenberger,Matter Bounce in Horava-Lifshitz Cosmology,Phys

    R. Brandenberger,Matter Bounce in Horava-Lifshitz Cosmology,Phys. Rev. D80(2009) 043516 [0904.2835]

    Pith/arXiv arXiv 2009

  50. [50]

    Qiu and K.-C

    T. Qiu and K.-C. Yang,Perturbations in Matter Bounce with Non-minimal Coupling,JCAP11 (2010) 012 [1007.2571]

    Pith/arXiv arXiv 2010

  51. [51]

    Cai, S.-H

    Y.-F. Cai, S.-H. Chen, J.B. Dent, S. Dutta and E.N. Saridakis,Matter Bounce Cosmology with the f(T) Gravity,Class. Quant. Grav.28(2011) 215011 [1104.4349]

    Pith/arXiv arXiv 2011

  52. [52]

    Easson, I

    D.A. Easson, I. Sawicki and A. Vikman,G-Bounce,JCAP11(2011) 021 [1109.1047]

    Pith/arXiv arXiv 2011

  53. [53]

    Cai, D.A

    Y.-F. Cai, D.A. Easson and R. Brandenberger,Towards a Nonsingular Bouncing Cosmology,JCAP 08(2012) 020 [1206.2382]

    Pith/arXiv arXiv 2012

  54. [54]

    Qiu and Y.-T

    T. Qiu and Y.-T. Wang,G-Bounce Inflation: Towards Nonsingular Inflation Cosmology with Galileon Field,JHEP04(2015) 130 [1501.03568]

    Pith/arXiv arXiv 2015

  55. [55]

    Koehn, J.-L

    M. Koehn, J.-L. Lehners and B. Ovrut,Nonsingular bouncing cosmology: Consistency of the effective description,Phys. Rev. D93(2016) 103501 [1512.03807]

    Pith/arXiv arXiv 2016

  56. [56]

    Ijjas and P.J

    A. Ijjas and P.J. Steinhardt,Classically stable nonsingular cosmological bounces,Phys. Rev. Lett. 117(2016) 121304 [1606.08880]

    Pith/arXiv arXiv 2016

  57. [57]

    Akama and T

    S. Akama and T. Kobayashi,Generalized multi-Galileons, covariantized new terms, and the no-go theorem for nonsingular cosmologies,Phys. Rev. D95(2017) 064011 [1701.02926]

    Pith/arXiv arXiv 2017

  58. [58]

    Mironov, V

    S. Mironov, V. Rubakov and V. Volkova,Bounce beyond Horndeski with GR asymptotics and γ-crossing,JCAP10(2018) 050 [1807.08361]

    Pith/arXiv arXiv 2018

  59. [59]

    Banerjee, Y.-F

    S. Banerjee, Y.-F. Cai and E.N. Saridakis,Evading the theoretical no-go theorem for nonsingular bounces in Horndeski/Galileon cosmology,Class. Quant. Grav.36(2019) 135009 [1808.01170]

    Pith/arXiv arXiv 2019

  60. [60]

    Ageeva, P

    Y. Ageeva, P. Petrov and V. Rubakov,Generating cosmological perturbations in non-singular Horndeski cosmologies,JHEP01(2023) 026 [2207.04071]

    Pith/arXiv arXiv 2023

  61. [61]

    Kobayashi,Generic instabilities of nonsingular cosmologies in Horndeski theory: A no-go theorem,Phys

    T. Kobayashi,Generic instabilities of nonsingular cosmologies in Horndeski theory: A no-go theorem,Phys. Rev. D94(2016) 043511 [1606.05831]

    Pith/arXiv arXiv 2016

  62. [62]

    Libanov, S

    M. Libanov, S. Mironov and V. Rubakov,Generalized Galileons: instabilities of bouncing and Genesis cosmologies and modified Genesis,JCAP08(2016) 037 [1605.05992]

    Pith/arXiv arXiv 2016

  63. [63]

    Creminelli, D

    P. Creminelli, D. Pirtskhalava, L. Santoni and E. Trincherini,Stability of Geodesically Complete Cosmologies,JCAP11(2016) 047 [1610.04207]

    Pith/arXiv arXiv 2016

  64. [64]

    Kolevatov, S

    R. Kolevatov, S. Mironov, N. Sukhov and V. Volkova,Cosmological bounce and Genesis beyond Horndeski,JCAP08(2017) 038 [1705.06626]

    Pith/arXiv arXiv 2017

  65. [65]

    Ye and Y.-S

    G. Ye and Y.-S. Piao,Bounce in general relativity and higher-order derivative operators,Phys. Rev. D99(2019) 084019 [1901.08283]. – 26 –

    Pith/arXiv arXiv 2019

  66. [66]

    Ilyas, M

    A. Ilyas, M. Zhu, Y. Zheng, Y.-F. Cai and E.N. Saridakis,DHOST Bounce,JCAP09(2020) 002 [2002.08269]

    Pith/arXiv arXiv 2020

  67. [67]

    M. Zhu, A. Ilyas, Y. Zheng, Y.-F. Cai and E.N. Saridakis,Scalar and tensor perturbations in DHOST bounce cosmology,JCAP11(2021) 045 [2108.01339]

    Pith/arXiv arXiv 2021

  68. [68]

    O.S. An, J.U. Kang, Y.J. Kim, U.R. Mun and U.G. Ri,Fully viable DHOST bounce with extra scalar, JHEP05(2025) 005 [2501.09985]

    Pith/arXiv arXiv 2025

  69. [69]

    Biswas, A

    T. Biswas, A. Mazumdar and W. Siegel,Bouncing universes in string-inspired gravity,JCAP03 (2006) 009 [hep-th/0508194]

    Pith/arXiv arXiv 2006

  70. [70]

    Biswas, A.S

    T. Biswas, A.S. Koshelev, A. Mazumdar and S.Y. Vernov,Stable bounce and inflation in non-local higher derivative cosmology,JCAP08(2012) 024 [1206.6374]

    Pith/arXiv arXiv 2012

  71. [71]

    Kol´ aˇ r, F.J.M

    I. Kol´ aˇ r, F.J.M. Torralba and A. Mazumdar,New nonsingular cosmological solution of nonlocal gravity,Phys. Rev. D105(2022) 044045 [2109.02143]

    Pith/arXiv arXiv 2022

  72. [72]

    Kumar, S

    K.S. Kumar, S. Maheshwari, A. Mazumdar and J. Peng,An anisotropic bouncing universe in non-local gravity,JCAP07(2021) 025 [2103.13980]

    Pith/arXiv arXiv 2021

  73. [73]

    Kumar, S

    K.S. Kumar, S. Maheshwari, A. Mazumdar and J. Peng,Stable, nonsingular bouncing universe with only a scalar mode,Phys. Rev. D102(2020) 024080 [2005.01762]

    Pith/arXiv arXiv 2020

  74. [74]

    Koshelev and S.Y

    A.S. Koshelev and S.Y. Vernov,On bouncing solutions in non-local gravity,Phys. Part. Nucl.43 (2012) 666 [1202.1289]

    Pith/arXiv arXiv 2012

  75. [75]

    Koshelev,Mathematical aspects of analytic infinite derivative gravity theories, inHandbook of Quantum Gravity, C

    A.S. Koshelev,Mathematical aspects of analytic infinite derivative gravity theories, inHandbook of Quantum Gravity, C. Bambi, L. Modesto and I. Shapiro, eds., (Singapore), pp. 1–29, Springer Nature Singapore (2023), DOI

    2023

  76. [76]

    Ruhdorfer, J

    M. Ruhdorfer, J. Serra and A. Weiler,Effective Field Theory of Gravity to All Orders,JHEP05 (2020) 083 [1908.08050]

    Pith/arXiv arXiv 2020

  77. [77]

    Hawking and T

    S.W. Hawking and T. Hertog,Living with ghosts,Phys. Rev. D65(2002) 103515 [hep-th/0107088]

    Pith/arXiv arXiv 2002

  78. [78]

    Bateman and N

    S. Bateman and N. Turok,Escape from Ostrogradsky via Hidden Ghost Parity,2607.00096

    Pith/arXiv arXiv

  79. [79]

    Buoninfante,Asymptotic Quantum Dynamics of Ghost Fields,2605.29047

    L. Buoninfante,Asymptotic Quantum Dynamics of Ghost Fields,2605.29047

    Pith/arXiv arXiv

  80. [80]

    Buoninfante,Ghosts versus Unstable Particles in Quantum Field Theory,2606.18349

    L. Buoninfante,Ghosts versus Unstable Particles in Quantum Field Theory,2606.18349

    Pith/arXiv arXiv

Showing first 80 references.