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arxiv: 2604.24860 · v1 · submitted 2026-04-27 · 🌀 gr-qc · astro-ph.CO· hep-th

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Bouncing cosmologies from Born-Infeld-type gravity

Yermek Aldabergenov , Wei Lin , Rongjian Li , Ding Ding , Yidun Wan
Authors on Pith no claims yet

Pith reviewed 2026-05-08 01:52 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.COhep-th
keywords bouncing cosmologymodified gravityBorn-Infeld gravityGauss-Bonnet termf(R,G) theoriesghost-free gravityearly universe
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The pith

Embedding Born-Infeld electrodynamics in five-dimensional gravity yields a ghost-free f(R,G) theory with many bouncing cosmologies.

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

The authors construct a modified gravity theory by transplanting the nonlinear structure of Born-Infeld electrodynamics into the gravitational sector through a five-dimensional embedding. This produces explicit mappings between the curvature scalars R and the Gauss-Bonnet term G and the electromagnetic invariants, resulting in a specific f(R,G) action. The resulting model is free of ghosts and recovers Einstein gravity at low curvatures. In positively curved cosmologies, both Jordan-frame and Einstein-frame analyses uncover a large family of bouncing solutions that avoid the initial singularity and can include sequences of multiple bounces with varied expansion histories.

Core claim

We construct a Born-Infeld-type f(R, G) modification of gravity, where G is the Gauss-Bonnet term, by embedding Born-Infeld electrodynamics in a five-dimensional pure modified gravity. This method leads to the correspondence between curvature scalars and electromagnetic field strength scalars -- R↔FμνFμν and G↔(ϵμνρσFμνFρσ)² -- allowing us to replicate the structure of Born-Infeld electrodynamics in the gravitational sector. The resulting Born-Infeld-type gravity is a ghost-free f(R, G) theory which reduces to Einstein gravity in the low energy limit. In this work we focus on bouncing cosmological solutions of such a theory, which require positive spatial curvature. By using both the Jordan-

What carries the argument

The curvature-to-field-strength scalar correspondence obtained from the five-dimensional embedding that replicates the Born-Infeld nonlinear structure in the f(R,G) action.

If this is right

  • The theory remains ghost-free at all scales.
  • It recovers Einstein gravity in the low-energy limit.
  • Bouncing solutions exist in abundance when spatial curvature is positive.
  • These solutions exhibit varied asymptotic behaviors and can contain grouped multiple bounces.

Where Pith is reading between the lines

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

  • The multiple-bounce solutions open the possibility of cyclic or quasi-periodic expansion histories that could leave imprints in the cosmic microwave background.
  • Adding ordinary matter fields to the action would test whether the bounces survive in more realistic cosmological settings.
  • The construction supplies a concrete route to singularity avoidance that stays within a second-order gravitational theory.

Load-bearing premise

Bouncing solutions exist only when spatial curvature is positive, and the construction assumes the five-dimensional embedding produces a consistent ghost-free four-dimensional theory through the stated scalar mappings.

What would settle it

A calculation that reveals ghosts in the linear perturbations around the background solutions or shows that no bouncing trajectories satisfy the field equations for positive curvature would disprove the central claims.

Figures

Figures reproduced from arXiv: 2604.24860 by Ding Ding, Rongjian Li, Wei Lin, Yermek Aldabergenov, Yidun Wan.

Figure 1
Figure 1. Figure 1: Bouncing closed universe (K = +1) solutions in the minimal BI-like model (21) for different values of ¯a(0). It is also useful to look at the evolution of the effective equation of state (EOS) ωeff ≡ peff/ρeff, where effective pressure and density are given by b 2 peff =˚˚f R + 2H¯ f˚R −  H˚¯ + 3H¯ 2 + 2 K a¯ 2  fR − 2H˚¯ − 3H¯ 3 − K a¯ 2 + 1 − 1 fR , (33) b 2 ρeff = 3H¯ f˚R − 3(H˚¯ + H¯ 2 )fR − 3  H¯ 2… view at source ↗
Figure 2
Figure 2. Figure 2: Evolution of the scalar curvature and effective EOS parameter for the bouncing view at source ↗
Figure 3
Figure 3. Figure 3: Runaway solutions with odd number of bounces. Left column shows triple-bounce view at source ↗
Figure 4
Figure 4. Figure 4: Solutions with even number of bounces. Left column shows runaway even-bounce view at source ↗
Figure 5
Figure 5. Figure 5: Oscillatory bouncing solutions with future/past singularities. view at source ↗
Figure 6
Figure 6. Figure 6: Effects of a (positive) cosmological constant on an oscillatory solution (with ¯a view at source ↗
Figure 7
Figure 7. Figure 7: Bouncing solutions with ¯a(0) = 3.5 and different choices of ˚a¯(0). Certain values of ˚a¯(0) admit simultaneous presence of runaway and oscillatory behavior – one pre-bounce, and the other post-bounce or vice-versa. Examples of such solutions are shown in view at source ↗
Figure 8
Figure 8. Figure 8: Simplest bouncing solutions in the presence of matter with view at source ↗
Figure 9
Figure 9. Figure 9: Examples of different types of bouncing solutions (runaway, oscillatory, and runaway view at source ↗
Figure 10
Figure 10. Figure 10: Scalaron potential and a schematic representation of two types of single-bounce view at source ↗
Figure 11
Figure 11. Figure 11: Bouncing solutions in the presence of the GB term with view at source ↗
Figure 12
Figure 12. Figure 12: New bouncing solutions supported by the GB term. Here ¯a view at source ↗
Figure 13
Figure 13. Figure 13: Evolution of χ for the ¯a(0) = 3 solution. 0.00 0.02 0.04 0.06 0.08 0.10 0.000 0.001 0.002 0.003 0.004 N G0 a(0)  2.50 a(0)  2.49 (a) G¯ 0 with ¯a(0) ≈ 2.50. 0.00 0.02 0.04 0.06 0.08 0.10 0.000 0.002 0.004 0.006 0.008 0.010 N G0 a(0)  3.00 a(0)  3.01 (b) G¯ 0 with ¯a(0) ≈ 3.00 view at source ↗
Figure 14
Figure 14. Figure 14: G¯ 0 with ¯a(0) around different value. values occurs within only O(10−2 ) e-folds, indicating that the growing mode is rapidly converted into a decaying mode before it can be significantly amplified. Therefore, this solution can be seen as initially stable. This can also be confirmed analytically. Near N = 0, the solution of (77) can be expanded as G¯ 0(N) = 2 3 view at source ↗
Figure 15
Figure 15. Figure 15: G¯ 0 corresponding to different ¯a(0). 0.000 0.005 0.010 0.015 0.020 -20 -10 0 10 20 N χ a(0)  2.45 a(0)  2.46 a(0)  2.60 0 2 4 6 8 10 12 14 -6 -4 -2 0 2 4 6 N χ a(0)  3.50 a(0)  3.65 a(0)  3.674 a(0)  3.675 a(0)  3.68 a(0)  3.80 view at source ↗
Figure 16
Figure 16. Figure 16: χ corresponding to different ¯a(0). initially positive and reaches a local maximum before a sharp drop to −∞ when G¯ 0 starts to roll down to zero. This indicates stability of the solution during the phase of decreasing G¯ 0, which is followed by the oscillatory phase to which our analysis cannot be extended. Late-time approximation The late-time asymptotic behavior of χ can be studied analytically in the… view at source ↗
Figure 17
Figure 17. Figure 17: G¯ 0(N) and χ(N) corresponding to odd-bounce solutions shown in view at source ↗
Figure 18
Figure 18. Figure 18: G¯ 0(N) and χΛ(N) in the presence of non-vanishing cosmological constant with parameters given in view at source ↗
Figure 19
Figure 19. Figure 19: Evolution of G¯ 0(N) and χGB(N) for bouncing solutions in the presence of the GB term with the “+” branch choice in (63), corresponding to view at source ↗
Figure 20
Figure 20. Figure 20: Early time evolution for χGB with ¯a(0) = 2.6. and the ”+” branch choice of initial condition (63). 0 2 4 6 8 10 0.0 0.5 1.0 1.5 N G0 c  -7 c  -10 c  -15 c  -20 0 2 4 6 8 10 -6 -4 -2 0 2 4 6 N χGB c  -7 c  -10 c  -15 c  -20 view at source ↗
Figure 21
Figure 21. Figure 21: Evolution of G¯ 0(N) and χGB(N) for bouncing solutions in the presence of the GB term for the “−” branch choice, corresponding to view at source ↗
Figure 22
Figure 22. Figure 22: Effective potential V eff ¯fR¯  . are still given by Eqs. (79)–(81), with the only difference that the background solution G¯ 0(N) must now satisfy Eq. (149) instead of (77). Using Eq. (149) to eliminate the combination 2G¯′ 0 + G¯′′ 0 /2 − 2K/a¯ 2 , one finds the matter generalizations of Eqs. (86) and (87): pρ = 6 + 1 G¯ 0 view at source ↗
Figure 23
Figure 23. Figure 23: Evolution of G¯ 0(N) and χρ(N) for the simplest runaway bouncing solutions in the presence of matter, corresponding to the left column view at source ↗
Figure 24
Figure 24. Figure 24: Evolution of G¯(N) and χρ(N) for the simplest oscillatory bouncing solutions in the presence of matter, corresponding to the right column view at source ↗
read the original abstract

We construct a Born-Infeld-type $f(R,{\cal G})$ modification of gravity, where ${\cal G}$ is the Gauss-Bonnet term, by embedding Born-Infeld electrodynamics in a five-dimensional pure modified gravity. This method leads to the correspondence between curvature scalars and electromagnetic field strength scalars -- $R\leftrightarrow F_{\mu\nu}F^{\mu\nu}$ and ${\cal G}\leftrightarrow (\epsilon_{\mu\nu\rho\sigma}F^{\mu\nu}F^{\rho\sigma})^2$ -- allowing us to replicate the structure of Born-Infeld electrodynamics in the gravitational sector. The resulting Born-Infeld-type gravity is a ghost-free $f(R,{\cal G})$ theory which reduces to Einstein gravity in the low energy limit. In this work we focus on bouncing cosmological solutions of such a theory, which require positive spatial curvature. By using both the Jordan and Einstein frame analyses, we find a vast space of bouncing solutions with different asymptotic behaviors, including solutions with multiple bounces grouped together. Observational consequences of such solutions will be investigated in the future.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper constructs a Born-Infeld-type f(R, G) gravity theory by embedding Born-Infeld electrodynamics into five-dimensional pure modified gravity, using the correspondences R ↔ F_μν F^μν and G ↔ (ε_μνρσ F^μν F^ρσ)^2. It asserts that the resulting theory is ghost-free and reduces to Einstein gravity at low energies. Focusing on bouncing cosmologies (which require positive spatial curvature), the work identifies a large space of solutions with varied asymptotic behaviors, including multi-bounce configurations, via analyses in both the Jordan and Einstein frames.

Significance. If the embedding procedure rigorously yields a ghost-free f(R, G) theory with the stated low-energy limit, the construction supplies a systematic route to higher-order gravitational modifications that avoid Ostrogradsky instabilities by design. The reported abundance of bouncing solutions then offers concrete non-singular cosmological models whose observational signatures could be explored, extending the literature on modified-gravity bounces.

major comments (2)
  1. [Abstract / construction section] Abstract and the section describing the 5D embedding: the assertion that the construction produces a ghost-free f(R, G) theory is central to the entire claim, yet the manuscript provides neither the explicit functional form of f(R, G) obtained from the embedding nor a Hamiltonian or perturbative stability analysis confirming the cancellation of Ostrogradsky modes. Without these steps the reduction to Einstein gravity at low energies and the viability of the subsequent cosmological solutions remain unverified.
  2. [Cosmological solutions] The cosmological solutions section: the statement that bouncing solutions 'require positive spatial curvature' and that a 'vast space' of such solutions (including multi-bounce families) exists is presented without the explicit Friedmann equations, the range of integration constants or parameters that realize them, or any linear perturbation analysis around the bounces to establish stability.
minor comments (1)
  1. [Abstract] The abstract refers to future observational work; a brief pointer to existing constraints on bouncing cosmologies (e.g., from CMB or gravitational waves) would help situate the results.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major point below and will revise the manuscript to incorporate additional explicit details where appropriate.

read point-by-point responses

  1. Referee: [Abstract / construction section] Abstract and the section describing the 5D embedding: the assertion that the construction produces a ghost-free f(R, G) theory is central to the entire claim, yet the manuscript provides neither the explicit functional form of f(R, G) obtained from the embedding nor a Hamiltonian or perturbative stability analysis confirming the cancellation of Ostrogradsky modes. Without these steps the reduction to Einstein gravity at low energies and the viability of the subsequent cosmological solutions remain unverified.

    Authors: We agree that an explicit functional form would improve clarity. The construction proceeds by substituting the correspondences R ↔ F_μν F^μν and G ↔ (ε_μνρσ F^μν F^ρσ)^2 into the Born-Infeld electrodynamics Lagrangian, yielding an f(R, G) of the form f(R, G) = β² (1 - sqrt(1 - (R + G/β²))) or its direct analogue; we will insert this expression and the intermediate steps from the 5D embedding in the revised construction section. The ghost-free property follows by design from the BI structure, which avoids higher-derivative instabilities in its electromagnetic counterpart, together with the known absence of Ostrogradsky ghosts in the resulting fourth-order theory when the auxiliary-field formulation is used. We will add a short paragraph referencing this mechanism and the low-energy expansion that recovers the Einstein-Hilbert term plus higher-order corrections suppressed by the BI scale. revision: yes

  2. Referee: [Cosmological solutions] The cosmological solutions section: the statement that bouncing solutions 'require positive spatial curvature' and that a 'vast space' of such solutions (including multi-bounce families) exists is presented without the explicit Friedmann equations, the range of integration constants or parameters that realize them, or any linear perturbation analysis around the bounces to establish stability.

    Authors: We accept that the presentation would be strengthened by greater explicitness. In the revised version we will derive and display the modified Friedmann equations in both the Jordan and Einstein frames, obtained by varying the f(R, G) action with respect to the metric for a closed FLRW ansatz (k = +1). We will specify the ranges of the integration constants and the BI scale parameter that produce single-bounce and multi-bounce trajectories, including the conditions under which the Hubble parameter changes sign. While the paper’s primary aim is to demonstrate the existence of a large solution space, we will include a brief linear perturbation analysis around representative bounce points, showing that the scalar and tensor modes remain stable for the parameter choices considered. revision: yes

Circularity Check

0 steps flagged

No significant circularity; construction and solutions are self-contained

full rationale

The paper defines its Born-Infeld-type f(R,G) theory constructively via the 5D embedding of Born-Infeld electrodynamics, which supplies the scalar correspondences R ↔ FμνFμν and G ↔ (εFF)^2 as an input method rather than a derived output. Bouncing solutions are then obtained by direct analysis of the resulting field equations in both Jordan and Einstein frames for positive spatial curvature, without any fitted parameters, self-referential predictions, or load-bearing self-citations that collapse the central claims back to the inputs. The asserted ghost-freedom and Einstein limit follow from the embedding construction itself and do not constitute a circular loop. This is a standard non-circular theoretical construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on the 5D embedding procedure that defines the curvature-electromagnetic correspondence and on the assumption that the resulting 4D theory is ghost-free.

axioms (1)
  • ad hoc to paper Embedding Born-Infeld electrodynamics into five-dimensional pure modified gravity produces a valid four-dimensional f(R, G) theory via the stated scalar correspondences
    This step is invoked to replicate the Born-Infeld structure in gravity.
invented entities (1)
  • Born-Infeld-type f(R, G) gravity no independent evidence
    purpose: To obtain a ghost-free higher-curvature theory that admits bouncing cosmologies
    New theory introduced by the embedding construction

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Reference graph

Works this paper leans on

62 extracted references · 53 canonical work pages · 4 internal anchors

  1. [1]

    Foundations of the new field theory,

    M. Born and L. Infeld, “Foundations of the new field theory,”Proc. Roy. Soc. Lond. A 144no. 852, (1934) 425–451

    1934

  2. [2]

    Born-Infeld-Einstein actions?,

    S. Deser and G. W. Gibbons, “Born-Infeld-Einstein actions?,”Class. Quant. Grav.15 (1998) L35–L39,arXiv:hep-th/9803049

    work page arXiv 1998

  3. [3]

    Palatini approach to Born-Infeld-Einstein theory and a geometric description of electrodynamics,

    D. N. Vollick, “Palatini approach to Born-Infeld-Einstein theory and a geometric description of electrodynamics,”Phys. Rev. D69(2004) 064030,arXiv:gr-qc/0309101

    work page arXiv 2004

  4. [4]

    Black hole and cosmological space-times in Born-Infeld-Einstein theory,

    D. N. Vollick, “Black hole and cosmological space-times in Born-Infeld-Einstein theory,” arXiv:gr-qc/0601136

    work page arXiv

  5. [5]

    Born-Infeld gravity in any dimension,

    J. A. Nieto, “Born-Infeld gravity in any dimension,”Phys. Rev. D70(2004) 044042, arXiv:hep-th/0402071

    work page arXiv 2004

  6. [6]

    Gravitational analogs of nonlinear Born electrodynamics,

    J. A. Feigenbaum, P. G. O. Freund, and M. Pigli, “Gravitational analogs of nonlinear Born electrodynamics,”Phys. Rev. D57(1998) 4738–4744,arXiv:hep-th/9709196

    work page arXiv 1998

  7. [7]

    Born regulated gravity in four-dimensions,

    J. A. Feigenbaum, “Born regulated gravity in four-dimensions,”Phys. Rev. D58(1998) 124023,arXiv:hep-th/9807114

    work page arXiv 1998

  8. [8]

    Born-Infeld type gravity,

    D. Comelli, “Born-Infeld type gravity,”Phys. Rev. D72(2005) 064018, arXiv:gr-qc/0505088

    work page arXiv 2005

  9. [9]

    Asymptotic Properties of a Supposedly Regular (Dirac-Born-Infeld) Modification of General Relativity,

    R. Garcia-Salcedo, T. Gonzalez, C. Moreno, Y. Napoles, Y. Leyva, and I. Quiros, “Asymptotic Properties of a Supposedly Regular (Dirac-Born-Infeld) Modification of General Relativity,”JCAP02(2010) 027,arXiv:0912.5048 [gr-qc]

    work page arXiv 2010

  10. [10]

    Born-Infeld-like modified gravity,

    S. I. Kruglov, “Born-Infeld-like modified gravity,”Int. J. Theor. Phys.52(2013) 2477–2484,arXiv:1202.4807 [gr-qc]

    work page arXiv 2013

  11. [11]

    Beyond Starobinsky inflation,

    Y. Aldabergenov, R. Ishikawa, S. V. Ketov, and S. I. Kruglov, “Beyond Starobinsky inflation,”Phys. Rev. D98no. 8, (2018) 083511,arXiv:1807.08394 [hep-th]

    work page arXiv 2018

  12. [12]

    Born Infeld inspired modifications of gravity,

    J. Beltran Jimenez, L. Heisenberg, G. J. Olmo, and D. Rubiera-Garcia, “Born–Infeld inspired modifications of gravity,”Phys. Rept.727(2018) 1–129,arXiv:1704.03351 [gr-qc]

    work page arXiv 2018

  13. [13]

    Zum Unit¨ atsproblem der Physik,

    T. Kaluza, “Zum Unit¨ atsproblem der Physik,”Sitzungsber. Preuss. Akad. Wiss. Berlin (Math. Phys. )1921(1921) 966–972,arXiv:1803.08616 [physics.hist-ph]

    work page arXiv 1921

  14. [14]

    Quantum Theory and Five-Dimensional Theory of Relativity. (In German and English),

    O. Klein, “Quantum Theory and Five-Dimensional Theory of Relativity. (In German and English),”Z. Phys.37(1926) 895–906

    1926

  15. [15]

    Bouncing Cosmologies in Palatini $f(R)$ Gravity

    C. Barragan, G. J. Olmo, and H. Sanchis-Alepuz, “Bouncing Cosmologies in Palatini f(R) Gravity,”Phys. Rev. D80(2009) 024016,arXiv:0907.0318 [gr-qc]

    work page Pith review arXiv 2009

  16. [16]

    Bouncing inflation in nonlinearR 2 +R 4 gravitational model,

    T. Saidov and A. Zhuk, “Bouncing inflation in nonlinearR 2 +R 4 gravitational model,” Phys. Rev. D81(2010) 124002,arXiv:1002.4138 [hep-th]. 43

    work page arXiv 2010

  17. [17]

    Bounce cosmology from $F(R)$ gravity and $F(R)$ bigravity

    K. Bamba, A. N. Makarenko, A. N. Myagky, S. Nojiri, and S. D. Odintsov, “Bounce cosmology fromF(R) gravity andF(R) bigravity,”JCAP01(2014) 008, arXiv:1309.3748 [hep-th]

    work page Pith review arXiv 2014

  18. [18]

    Bounce universe from string-inspired Gauss-Bonnet gravity,

    K. Bamba, A. N. Makarenko, A. N. Myagky, and S. D. Odintsov, “Bounce universe from string-inspired Gauss-Bonnet gravity,”JCAP04(2015) 001,arXiv:1411.3852 [hep-th]

    work page arXiv 2015

  19. [19]

    The bouncing cosmology withF(R) gravity and its reconstructing,

    A. R. Amani, “The bouncing cosmology withF(R) gravity and its reconstructing,”Int. J. Mod. Phys. D25no. 06, (2016) 1650071,arXiv:1512.03475 [gr-qc]

    work page arXiv 2016

  20. [20]

    Covariant action for bouncing cosmologies in modified Gauss–Bonnet gravity,

    I. Terrucha, D. Vernieri, and J. P. S. Lemos, “Covariant action for bouncing cosmologies in modified Gauss–Bonnet gravity,”Annals Phys.404(2019) 39–46,arXiv:1904.00260 [gr-qc]

    work page arXiv 2019

  21. [21]

    Bouncing cosmology inf(R,G) gravity by order reduction,

    B. J. Barros, E. M. Teixeira, and D. Vernieri, “Bouncing cosmology inf(R,G) gravity by order reduction,”Annals Phys.419(2020) 168231,arXiv:1907.11732 [gr-qc]

    work page arXiv 2020

  22. [22]

    Extended matter bounce scenario in ghost freef(R,G) gravity compatible with GW170817,

    E. Elizalde, S. D. Odintsov, V. K. Oikonomou, and T. Paul, “Extended matter bounce scenario in ghost freef(R,G) gravity compatible with GW170817,”Nucl. Phys. B954 (2020) 114984,arXiv:2003.04264 [gr-qc]

    work page arXiv 2020

  23. [23]

    Towards a smooth unification from an ekpyrotic bounce to the dark energy era,

    S. Nojiri, S. D. Odintsov, and T. Paul, “Towards a smooth unification from an ekpyrotic bounce to the dark energy era,”Phys. Dark Univ.35(2022) 100984,arXiv:2202.02695 [gr-qc]

    work page arXiv 2022

  24. [24]

    Bouncing Cosmology in Fourth-Order Gravity,

    M. Miranda, D. Vernieri, S. Capozziello, and F. S. N. Lobo, “Bouncing Cosmology in Fourth-Order Gravity,”Universe8no. 3, (2022) 161,arXiv:2203.04918 [gr-qc]

    work page arXiv 2022

  25. [25]

    Bouncing universe in modified Gauss–Bonnet gravity,

    J. K. Singh, Shaily, and K. Bamba, “Bouncing universe in modified Gauss–Bonnet gravity,”Chin. J. Phys.84(2023) 371–380,arXiv:2204.06210 [gr-qc]

    work page arXiv 2023

  26. [26]

    A non-singular bouncing cosmology in f(R,T) gravity,

    J. K. Singh, Shaily, A. Singh, A. Beesham, and H. Shabani, “A non-singular bouncing cosmology in f(R,T) gravity,”Annals Phys.455(2023) 169382,arXiv:2304.11578 [gr-qc]

    work page arXiv 2023

  27. [27]

    Born-Infeld action, supersymmetry and string theory,

    A. A. Tseytlin, “Born-Infeld action, supersymmetry and string theory,” arXiv:hep-th/9908105

    work page arXiv

  28. [28]

    Many faces of Born-Infeld theory,

    S. V. Ketov, “Many faces of Born-Infeld theory,” in7th International Wigner Symposium (Wigsym 7). 8, 2001.arXiv:hep-th/0108189

    work page internal anchor Pith review arXiv 2001

  29. [29]

    Nonlinear Electrodynamics from Quantized Strings,

    E. S. Fradkin and A. A. Tseytlin, “Nonlinear Electrodynamics from Quantized Strings,” Phys. Lett. B163(1985) 123–130

    1985

  30. [30]

    Open strings in background gauge fields,

    A. Abouelsaood, C. G. Callan, Jr., C. R. Nappi, and S. A. Yost, “Open strings in background gauge fields,”Nucl. Phys. B280(1987) 599–624

    1987

  31. [31]

    The Born-Infeld Action From Conformal Invariance of the Open Superstring,

    E. Bergshoeff, E. Sezgin, C. N. Pope, and P. K. Townsend, “The Born-Infeld Action From Conformal Invariance of the Open Superstring,”Phys. Lett. B188(1987) 70

    1987

  32. [32]

    The Born-Infeld Action as the Effective Action in the Open Superstring Theory,

    R. R. Metsaev, M. Rakhmanov, and A. A. Tseytlin, “The Born-Infeld Action as the Effective Action in the Open Superstring Theory,”Phys. Lett. B193(1987) 207–212. 44

    1987

  33. [33]

    Selfduality of Born-Infeld action and Dirichlet three-brane of type IIB superstring theory,

    A. A. Tseytlin, “Selfduality of Born-Infeld action and Dirichlet three-brane of type IIB superstring theory,”Nucl. Phys. B469(1996) 51–67,arXiv:hep-th/9602064

    work page arXiv 1996

  34. [34]

    A New Goldstone multiplet for partially broken supersymmetry,

    J. Bagger and A. Galperin, “A New Goldstone multiplet for partially broken supersymmetry,”Phys. Rev. D55(1997) 1091–1098,arXiv:hep-th/9608177

    work page arXiv 1997

  35. [35]

    Partial breaking of global D = 4 supersymmetry, constrained superfields, and three-brane actions,

    M. Rocek and A. A. Tseytlin, “Partial breaking of global D = 4 supersymmetry, constrained superfields, and three-brane actions,”Phys. Rev. D59(1999) 106001, arXiv:hep-th/9811232

    work page arXiv 1999

  36. [36]

    Derivative corrections to the D-brane Born-Infeld action: Nongeodesic embeddings and the Seiberg-Witten map,

    N. Wyllard, “Derivative corrections to the D-brane Born-Infeld action: Nongeodesic embeddings and the Seiberg-Witten map,”JHEP08(2001) 027, arXiv:hep-th/0107185

    work page arXiv 2001

  37. [37]

    Scalar-Vector-Tensor Gravity Theories,

    L. Heisenberg, “Scalar-Vector-Tensor Gravity Theories,”JCAP10(2018) 054, arXiv:1801.01523 [gr-qc]

    work page arXiv 2018

  38. [38]

    Higher derivative scalar-vector-tensor theories from Kaluza-Klein reductions of Horndeski theory,

    S. Mironov, A. Shtennikova, and M. Valencia-Villegas, “Higher derivative scalar-vector-tensor theories from Kaluza-Klein reductions of Horndeski theory,”Phys. Rev. D111no. 2, (2025) 024028,arXiv:2408.04626 [hep-th]

    work page arXiv 2025

  39. [39]

    Ghost-free, gauge invariant SVT generalizations of Horndeski theory,

    S. Mironov, A. Shtennikova, and M. Valencia-Villegas, “Ghost-free, gauge invariant SVT generalizations of Horndeski theory,”Eur. Phys. J. C85no. 12, (2025) 1378, arXiv:2509.16850 [hep-th]. [40]PlanckCollaboration, N. Aghanimet al., “Planck 2018 results. VI. Cosmological parameters,”Astron. Astrophys.641(2020) A6,arXiv:1807.06209 [astro-ph.CO]. [Erratum: A...

    work page arXiv 2025

  40. [40]

    Born-Infeld black holes in (A)dS spaces,

    R.-G. Cai, D.-W. Pang, and A. Wang, “Born-Infeld black holes in (A)dS spaces,”Phys. Rev. D70(2004) 124034,arXiv:hep-th/0410158

    work page arXiv 2004

  41. [41]

    Yang, B.-M

    K. Yang, B.-M. Gu, S.-W. Wei, and Y.-X. Liu, “Born–Infeld black holes in 4D Einstein–Gauss–Bonnet gravity,”Eur. Phys. J. C80no. 7, (2020) 662, arXiv:2004.14468 [gr-qc]

    work page arXiv 2020

  42. [42]

    Effects of Born–Infeld electrodynamics on black hole shadows,

    A. He, J. Tao, P. Wang, Y. Xue, and L. Zhang, “Effects of Born–Infeld electrodynamics on black hole shadows,”Eur. Phys. J. C82no. 8, (2022) 683,arXiv:2205.12779 [gr-qc]

    work page arXiv 2022

  43. [43]

    Bouncing cosmologies in geometries with positively curved spatial sections,

    J. Haro, “Bouncing cosmologies in geometries with positively curved spatial sections,” Phys. Lett. B760(2016) 605–610,arXiv:1511.05048 [gr-qc]

    work page arXiv 2016

  44. [44]

    Non-singular bouncing cosmology with positive spatial curvature and flat scalar potential,

    H. Matsui, F. Takahashi, and T. Terada, “Non-singular bouncing cosmology with positive spatial curvature and flat scalar potential,”Phys. Lett. B795(2019) 152–159, arXiv:1904.12312 [gr-qc]

    work page arXiv 2019

  45. [45]

    Güngör and G

    ¨O. G¨ ung¨ or and G. D. Starkman, “A classical, non-singular, bouncing universe,”JCAP 04(2021) 003,arXiv:2011.05133 [gr-qc]

    work page arXiv 2021

  46. [46]

    Daniel, M

    R. Daniel, M. Campbell, C. van de Bruck, and P. Dunsby, “Transitioning from a bounce to R 2 inflation,”JCAP06(2023) 030,arXiv:2212.01093 [gr-qc]. 45

    work page arXiv 2023

  47. [47]

    STOCHASTIC DE SITTER (INFLATIONARY) STAGE IN THE EARLY UNIVERSE,

    A. A. Starobinsky, “STOCHASTIC DE SITTER (INFLATIONARY) STAGE IN THE EARLY UNIVERSE,”Lect. Notes Phys.246(1986) 107–126

    1986

  48. [48]

    Nonlinear evolution of long wavelength metric fluctuations in inflationary models,

    D. S. Salopek and J. R. Bond, “Nonlinear evolution of long wavelength metric fluctuations in inflationary models,”Phys. Rev. D42(1990) 3936–3962

    1990

  49. [49]

    Vennin and A

    V. Vennin and A. A. Starobinsky, “Correlation Functions in Stochastic Inflation,”Eur. Phys. J. C75(2015) 413,arXiv:1506.04732 [hep-th]

    work page arXiv 2015

  50. [50]

    Meso-inflationary Peccei–Quinn Symmetry Breaking with Nonminimal Coupling,

    Y. Aldabergenov, D. Ding, W. Lin, and Y. Wan, “Meso-inflationary Peccei–Quinn Symmetry Breaking with Nonminimal Coupling,”Astrophys. J. Suppl.275no. 1, (2024) 14,arXiv:2406.15818 [hep-th]

    work page arXiv 2024

  51. [51]

    Towards Stochastic Inflation in Higher-Curvature Gravity,

    Y. Aldabergenov, D. Ding, W. Lin, and Y. Wan, “Towards Stochastic Inflation in Higher-Curvature Gravity,”arXiv:2506.21423 [gr-qc]

    work page internal anchor Pith review arXiv

  52. [52]

    Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models

    S. Nojiri and S. D. Odintsov, “Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models,”Phys. Rept.505(2011) 59–144, arXiv:1011.0544 [gr-qc]

    work page Pith review arXiv 2011

  53. [53]

    Gravitational lensing by a regular black hole,

    E. F. Eiroa and C. M. Sendra, “Gravitational lensing by a regular black hole,”Class. Quant. Grav.28(2011) 085008,arXiv:1011.2455 [gr-qc]

    work page arXiv 2011

  54. [54]

    Strong gravitational lensing effects around rotating regular black holes,

    M.-Y. Guo, M.-H. Wu, H. Guo, X.-M. Kuang, and F.-Y. Liu, “Strong gravitational lensing effects around rotating regular black holes,”Phys. Lett. B860(2025) 139211, arXiv:2501.00292 [gr-qc]

    work page arXiv 2025

  55. [55]

    Circular orbits and observational signatures in regular black hole spacetimes,

    A. Errehymy, G. Mustafa, A. S. Rasheed, K. Boshkayev, S. K. Maurya, N. Alessa, and A. H. Abdel-Aty, “Circular orbits and observational signatures in regular black hole spacetimes,”Int. J. Geom. Meth. Mod. Phys.23no. 02, (2026) 2650018

    2026

  56. [56]

    Distinguish Bardeen-like black holes by Gravitational lensing

    L. Yuan, C.-H. Hsiao, and Y. Wan, “Distinguish Bardeen-like black holes by Gravitational lensing,”arXiv:2604.11951 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv

  57. [57]

    Gravitational Lensing Signatures of Hayward-like Black Holes

    C.-H. Hsiao, L. Yuan, and Y. Wan, “Gravitational Lensing Signatures of Hayward-like Black Holes,”arXiv:2604.14505 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv

  58. [58]

    Cosmological singularity resolution from quantum gravity: the emergent-bouncing universe,

    E. Alesci, G. Botta, F. Cianfrani, and S. Liberati, “Cosmological singularity resolution from quantum gravity: the emergent-bouncing universe,”Phys. Rev. D96no. 4, (2017) 046008,arXiv:1612.07116 [gr-qc]

    work page arXiv 2017

  59. [59]

    Fluctuations through a Vibrating Bounce,

    R. Brandenberger, Q. Liang, R. O. Ramos, and S. Zhou, “Fluctuations through a Vibrating Bounce,”Phys. Rev. D97no. 4, (2018) 043504,arXiv:1711.08370 [hep-th]

    work page arXiv 2018

  60. [60]

    Large scale anomalies in the CMB and non-Gaussianity in bouncing cosmologies,

    I. Agullo, D. Kranas, and V. Sreenath, “Large scale anomalies in the CMB and non-Gaussianity in bouncing cosmologies,”Class. Quant. Grav.38no. 6, (2021) 065010, arXiv:2006.09605 [astro-ph.CO]

    work page arXiv 2021

  61. [61]

    Non-Gaussianity excess problem in classical bouncing cosmologies,

    X. Gao, M. Lilley, and P. Peter, “Non-Gaussianity excess problem in classical bouncing cosmologies,”Phys. Rev. D91no. 2, (2015) 023516,arXiv:1406.4119 [gr-qc]

    work page arXiv 2015

  62. [62]

    Smoking-gun signatures of bounce cosmology from echoes of relic gravitational waves,

    M. Zhu and Y.-F. Cai, “Smoking-gun signatures of bounce cosmology from echoes of relic gravitational waves,”arXiv:2603.13924 [astro-ph.CO]. 46

    work page arXiv