Pith. sign in

REVIEW 2 major objections 5 minor 120 references

A single phase variable turns Einstein–Gauss–Bonnet inflation into closed analytic formulas for CMB observables that stay valid past slow-roll.

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 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · grok-4.5

2026-07-13 06:36 UTC pith:IBEZSQSW

load-bearing objection Clean technical extension of GR phase-θ to EGB that stays regular past slow-roll and matches full mode integration for a tuned Starobinsky+linear-GB example. the 2 major comments →

arxiv 2607.08807 v1 pith:IBEZSQSW submitted 2026-07-09 gr-qc hep-th

Einstein--Gauss--Bonnet Inflationary Cosmology in Phase-θ Formalism

Gevorg D. Manucharyan , Igor V. Fomin , Shivam Kumar Mishra , B.Mishra This is my paper
classification gr-qc hep-th
keywords Einstein–Gauss–Bonnet gravityphase-θ parametrizationStarobinsky inflationslow-roll beyond leading ordertensor-to-scalar ratiorelic gravitational wavesACT DR6 constraints
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.

The paper’s goal is to give inflationary predictions that remain trustworthy after the usual slow-roll approximations break down, specifically inside Einstein–Gauss–Bonnet gravity. The authors introduce a phase-θ parametrization: the inflaton’s kinetic energy and potential are written as two trigonometric components whose single angle θ advances monotonically from the inflationary plateau to the end of inflation. With that angle and the Hubble rate alone, every background quantity, every coefficient in the quadratic action for scalar and tensor modes, the Hankel indices, and the observables ns, r, αs and nT become closed algebraic expressions. The map stays regular even when ε1 reaches 1, so the conventional consistency relations are no longer needed. Applied to a Starobinsky potential plus a linear Gauss–Bonnet coupling, the formulas produce ns ≈ 0.973 and r ≈ 5.8 × 10^{-3} at 55 e-folds—values inside the ACT DR6 1σ band and well below the BICEP/Keck limit—while the associated relic gravitational-wave spectrum is shown to sit above the sensitivity floor of planned decihertz interferometers.

Core claim

The phase-θ polar representation of the first Friedmann equation in Einstein–Gauss–Bonnet gravity reduces the entire background evolution and the coefficients QS, QT, cS, cT of the quadratic action for perturbations to explicit closed-form functions of a single monotonic phase θ and the Hubble parameter H. The resulting analytic expressions for the tensor-to-scalar ratio, spectral indices and runnings remain regular through the end of inflation, and for Starobinsky inflation with linear Gauss–Bonnet coupling they reproduce full Mukhanov–Sasaki numerics to better than ACT DR6 precision.

What carries the argument

The phase-θ parametrization: the identities φ̇/√6 = −H √(1−4H ξ̇) sin θ and √(V/3) = H √(1−4H ξ̇) cos θ that convert the Friedmann constraint into a polar radius and a single angle θ, from which every slow-roll parameter, sound speed and observable is obtained by algebra and chain rule.

Load-bearing premise

The linear Gauss–Bonnet coupling strength is chosen by hand so that the resulting shift in the scalar spectral index lands inside the ACT DR6 window; a different functional form or sign would reverse or erase that agreement.

What would settle it

Recompute ns and r for the same Starobinsky potential with a different coupling function (for example quadratic or exponential) or with the opposite sign of ξ0; if the new predictions fall outside the ACT DR6 1σ band while the pure-Starobinsky values remain outside, the claimed consistency is coupling-dependent rather than generic.

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

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 / 5 minor

Summary. The manuscript develops a phase-θ parametrization for single-field Einstein–Gauss–Bonnet inflation that rewrites the first Friedmann equation in polar form (Eq. 3.1), expressing the background trajectory, geometric slow-roll parameters, quadratic-action coefficients QS, QT, sound speeds, Hankel indices and the observables ns, r, αs, nT as closed algebraic functions of a single monotonic phase θ and H. The construction is claimed to remain regular through the end of inflation (ε1 = 1). As an application the authors take the Starobinsky potential with linear coupling ξ(φ) = ξ0 φ, integrate the background and Mukhanov–Sasaki equations, and report ns = 0.9730, r = 5.78 × 10^{-3} at N* = 55, inside the ACT DR6 1σ and BICEP/Keck windows. Three pipelines (EGB leading-order, second-order phase-θ, full MS) are compared quantity-by-quantity (Table 4, Figs. 8–9). The associated relic GW spectrum is evaluated for a range of reheating temperatures and confronted with detector PLS curves.

Significance. If the closed algebraic mapping is correct and remains regular at ε1 = 1, the paper supplies a practical analytic interface between arbitrary V(φ), ξ(φ) and second-order inflationary observables that is more transparent than conventional slow-roll expansions and that can be used for rapid model scans against updated CMB data. The explicit three-pipeline cross-check (Table 4) and the demonstration that residuals on ns and r lie well below ACT DR6 uncertainties are concrete strengths. The Starobinsky + linear-GB example is only illustrative, but it shows that a controlled positive shift in ns can be obtained without spoiling the small-r prediction or the matter-like reheating phase. The relic-GW section is standard but useful for placing the model relative to DECIGO/BBO and ultra-high-frequency targets.

major comments (2)
  1. The central technical claim is that the phase-θ map remains regular and accurate through the end of inflation. The only quantitative validation of accuracy is performed at the pivot N* = 55 (Table 4, Figs. 8–9), deep in the slow-roll regime where |δi| ≲ 10^{-2}. No analogous comparison of the closed-form expressions (3.33), (3.34)–(3.37) against full Mukhanov–Sasaki spectra is shown near ε1 o 1 (or for modes that exit near the end of inflation). Without that check the claim that the formalism is superior precisely where conventional consistency relations break down remains untested.
  2. Section 4 and Table 1: the linear coupling and the specific numerical value ξ0 = 4.3768 imes 10^7 M_Pl^{-2} are chosen so that Δns = -2δ1 moves the pure-Starobinsky prediction into the ACT DR6 1σ window. While this is ordinary model-building, the abstract and conclusion present the resulting consistency as a demonstration of the formalism. The paper should either (i) scan a modest range of ξ0 (or of other simple ξ(φ)) and show the locus of predictions, or (ii) clearly separate the general mapping from the single tuned example so that the reader does not over-read the data agreement as a generic success of EGB Starobinsky.
minor comments (5)
  1. Eq. (2.11) for c_S^2 still contains an explicit sin θ / cos 2θ dependence that is not rewritten in terms of the slow-roll parameters used elsewhere; a short remark on how it reduces to (3.26) would improve readability.
  2. Figure 1 caption: “Sratobinsky” is a typo; also the left panel uses φ while the text uses φ consistently only after Sec. 4.
  3. Table 4: the 7 % residual on |δ2| and s_S is attributed to Friedmann-constraint drift, yet the Hamiltonian residual is quoted as ≤ 10^{-10}. A one-sentence clarification of how a 10^{-10} constraint violation amplifies to 7 % on δ2 would help.
  4. The PLS sensitivity bands in Fig. 10 and Table 5 are taken from the literature; a brief note on the assumed observation time and SNR threshold (already mentioned in the text) would make the figure self-contained.
  5. Several references appear with incomplete or slightly non-standard formatting (e.g., arXiv-only entries without journal data when available); a quick pass would improve polish.

Circularity Check

1 steps flagged

Phase-θ is a non-circular algebraic reparametrization of the EGB Friedmann equations; the only mild circularity is ordinary one-parameter tuning of ξ0 to place ns inside ACT DR6, after which consistency is reported.

specific steps
  1. fitted input called prediction [Sec. 4 (paragraph after Eq. (4.2)) + Table 1 + abstract claim]
    "the sign choice ξ0>0 gives δ1=4Hξ0φ̇<0 along the inflationary trajectory (φ̇<0), producing a positive shift Δns=-2δ1>0 relative to the GR Starobinsky prediction nGRs=1-2/N∗. This is precisely the sign required to move the Starobinsky model into the central part of the ACT DR6 1σ window for ns … Using the proposed formalism, we demonstrate that the resulting predictions of the Starobinsky model are consistent with the most recent constraints from ACT DR6 and BICEP/Keck"

    ξ0 is fixed (Table 1: 4.3768 imes10^7 M_Pl^{-2}) expressly so that the GB-induced Δns places the model inside the ACT DR6 window; the subsequent numerical evaluation of ns=0.9730 is then reported as a successful prediction. The value of the observable is therefore statistically forced by the prior choice of the free parameter rather than being an independent output of the phase-θ map.

full rationale

The core construction (Secs. 3.1–3.4, App. A) defines θ via the polar identities (3.1) that identically solve the first Friedmann equation, then rewrites ε1, QA, cA, sA, ν A, r, ns, nT as closed functions of (θ,H,ξ̇,ξ̈). This is a change of variables, not a tautology that forces the numerical values of the observables. The Starobinsky+ξ=ξ0φ application solves the autonomous system (4.11)–(4.16) and confronts the output with external ACT DR6 + BICEP/Keck data that were never used to derive the mapping. The single free parameter ξ0 (and V0 for As normalization) is chosen by hand so that the GB shift Δns=-2δ1 moves the model into the ACT 1σ window; that is standard model-building, not a self-definitional loop or a load-bearing self-citation. No uniqueness theorem is imported, no ansatz is smuggled via overlapping-author citation, and the full Mukhanov–Sasaki cross-check (Tables 3–4, Figs. 8–9) is independent. Score 2 reflects only the mild fitted-input element; the central technical claim remains self-contained.

Axiom & Free-Parameter Ledger

3 free parameters · 4 axioms · 0 invented entities

The central claim rests on the standard EGB action, the FRW ansatz, the polar reparametrization of the first Friedmann equation, and two free parameters (V0, ξ0) fixed to the observed scalar amplitude and the ACT ns window. No new particles or forces are postulated; phase θ is a coordinate choice.

free parameters (3)
  • V0 = 1.83924 × 10^{-10} M_Pl^4
    Overall scale of the Starobinsky potential; iteratively rescaled so that Δ²_s(k*) = 2.1 × 10^{-9} (Sec. 4.2).
  • ξ0 = 4.3768 × 10^7 M_Pl^{-2}
    Strength of the linear Gauss–Bonnet coupling; chosen positive and of magnitude ~4 × 10^7 M_Pl^{-2} so that the GB shift places ns inside the ACT DR6 1σ band (Sec. 4, Table 1).
  • N* = 55
    Pivot e-fold number; nominal value 55 selected inside the reheating window [42.9, 56.35] that follows from Trh and w̄rh (Sec. 4.4).
axioms (4)
  • domain assumption Spatially flat FRW metric and the Einstein–Gauss–Bonnet action (2.1) with arbitrary ξ(φ).
    Standard starting point of the EGB-inflation literature; invoked from Sec. 2 onward.
  • ad hoc to paper Polar representation (3.1) that solves the first Friedmann equation identically by writing kinetic and potential terms as trigonometric components of a rescaled radius √(1−4Hξ̇).
    Direct generalization of the GR phase-θ of Ref. [69]; introduced in Sec. 3.1 as the defining step of the formalism.
  • domain assumption Second-order slow-roll expansion of the Hankel indices νA (Eq. 3.28 / Appendix A) is sufficient for observational accuracy at the present precision.
    Standard approximation in the inflation literature; validated a posteriori by comparison with full Mukhanov–Sasaki integration (Table 4).
  • domain assumption Reheating is described by a coherent-oscillation average w̄rh ≈ 0 that follows from the quadratic minimum of the Starobinsky potential.
    Used to convert Trh into the allowed N* window (Sec. 4.4, Eq. 4.26).

pith-pipeline@v1.1.0-grok45 · 41707 in / 3299 out tokens · 28084 ms · 2026-07-13T06:36:24.706748+00:00 · methodology

0 comments
read the original abstract

A central challenge in testing inflationary scenarios with cosmic microwave background (CMB) data is to derive predictions for cosmological observables that remain accurate beyond the slow-roll regime, where the standard consistency relations are no longer applicable. We address this issue in the context of Einstein--Gauss--Bonnet (EGB) gravity by introducing a phase-$\theta$ parametrization of the inflationary dynamics. Within this framework, the background evolution and the coefficients governing scalar and tensor perturbations are expressed entirely in terms of a single monotonic phase variable and the Hubble parameter. This construction provides a closed, analytical mapping between the background parameters of a given model and the associated inflationary observables. A notable advantage of the proposed parametrization is that it remains regular throughout the inflationary epoch, including the end-of-inflation regime, in which the conventional slow-roll consistency relations no longer hold. As an illustrative application, we consider a Starobinsky-type potential supplemented by a linear coupling between the inflaton and the Gauss--Bonnet invariant. Using the proposed formalism, we demonstrate that the resulting predictions of the Starobinsky model are consistent with the most recent constraints from ACT DR6 and BICEP/Keck, explicitly incorporating the impact of the non-minimal Gauss--Bonnet coupling on the expected values of the cosmological perturbation parameters. Finally, we compute the corresponding relic stochastic gravitational-wave background and evaluate its detectability with current and forthcoming gravitational-wave observatories.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

120 extracted references · 106 linked inside Pith

  1. [1]

    LIGO Scientific, Virgo collaboration, Observation of Gravitational Waves from a Binary Black Hole Merger , Phys. Rev. Lett. 116 (2016) 061102 [1602.03837]

    Pith/arXiv arXiv 2016

  2. [2]

    LIGO Scientific, Virgo collaboration, GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral , Phys. Rev. Lett. 119 (2017) 161101 [1710.05832]

    Pith/arXiv arXiv 2017

  3. [3]

    Abbott et al., Multi-messenger Observations of a Binary Neutron Star Merger , Astrophys

    B.P. Abbott et al., Multi-messenger Observations of a Binary Neutron Star Merger , Astrophys. J. Lett. 848 (2017) L12 [1710.05833]

    Pith/arXiv arXiv 2017

  4. [4]

    Baumann and L

    D. Baumann and L. McAllister, Inflation and String Theory , Cambridge Monographs on Mathematical Physics, Cambridge University Press (5, 2015 ), 10.1017/CBO9781316105733, [1404.2601]

    Pith/arXiv arXiv doi:10.1017/cbo9781316105733 2015

  5. [5]

    Zwiebach, Curvature Squared Terms and String Theories , Phys

    B. Zwiebach, Curvature Squared Terms and String Theories , Phys. Lett. 156B (1985) 315

    1985

  6. [6]

    Zumino, Gravity Theories in More Than Four-Dimensions , Phys

    B. Zumino, Gravity Theories in More Than Four-Dimensions , Phys. Rept. 137 (1986) 109

    1986

  7. [7]

    Boulware and S

    D.G. Boulware and S. Deser, String Generated Gravity Models , Phys. Rev. Lett. 55 (1985) 2656

    1985

  8. [8]

    Boulware and S

    D.G. Boulware and S. Deser, Effective Gravity Theories With Dilatons , Phys. Lett. B175 (1986) 409

    1986

  9. [9]

    Gasperini, M

    M. Gasperini, M. Maggiore and G. Veneziano, Towards a nonsingular pre - big bang cosmology, Nucl. Phys. B494 (1997) 315 [hep-th/9611039]

    Pith/arXiv arXiv 1997

  10. [10]

    Hwang and H

    J.-c. Hwang and H. Noh, Classical evolution and quantum generation in generalized gravity theories including string corrections and tachyon: Unified ana lyses, Phys. Rev. D 71 (2005) 063536 [gr-qc/0412126]

    Pith/arXiv arXiv 2005

  11. [11]

    Guo and D.J

    Z.-K. Guo and D.J. Schwarz, Power spectra from an inflaton coupled to the Gauss-Bonnet term, Phys. Rev. D 80 (2009) 063523 [0907.0427]

    Pith/arXiv arXiv 2009

  12. [12]

    Guo and D.J

    Z.-K. Guo and D.J. Schwarz, Slow-roll inflation with a Gauss-Bonnet correction , Phys. Rev. D 81 (2010) 123520 [1001.1897]

    Pith/arXiv arXiv 2010

  13. [13]

    Satoh, Slow-roll Inflation with the Gauss-Bonnet and Chern-Simons Co rrections, JCAP 11 (2010) 024 [1008.2724]

    M. Satoh, Slow-roll Inflation with the Gauss-Bonnet and Chern-Simons Co rrections, JCAP 11 (2010) 024 [1008.2724]

    Pith/arXiv arXiv 2010

  14. [14]

    Jiang, J.-W

    P.-X. Jiang, J.-W. Hu and Z.-K. Guo, Inflation coupled to a Gauss-Bonnet term , Phys. Rev. D 88 (2013) 123508 [1310.5579]

    Pith/arXiv arXiv 2013

  15. [15]

    Koh, B.-H

    S. Koh, B.-H. Lee, W. Lee and G. Tumurtushaa, Observational constraints on slow-roll inflation coupled to a Gauss-Bonnet term , Phys. Rev. D 90 (2014) 063527 [1404.6096]

    Pith/arXiv arXiv 2014

  16. [16]

    Kanti, R

    P. Kanti, R. Gannouji and N. Dadhich, Gauss-Bonnet Inflation , Phys. Rev. D 92 (2015) 041302 [1503.01579]

    Pith/arXiv arXiv 2015

  17. [17]

    Kanti, R

    P. Kanti, R. Gannouji and N. Dadhich, Early-time cosmological solutions in Einstein-scalar-Gauss-Bonnet theory, Phys. Rev. D 92 (2015) 083524 [1506.04667]

    Pith/arXiv arXiv 2015

  18. [18]

    Gauss-Bonnet inflation

    G. Hikmawan, J. Soda, A. Suroso and F.P. Zen, Comment on “Gauss-Bonnet inflation” , Phys. Rev. D 93 (2016) 068301 [1512.00222]

    Pith/arXiv arXiv 2016

  19. [19]

    Koh, B.-H

    S. Koh, B.-H. Lee and G. Tumurtushaa, Reconstruction of the Scalar Field Potential in Inflationary Models with a Gauss-Bonnet term , Phys. Rev. D 95 (2017) 123509 [1610.04360]

    Pith/arXiv arXiv 2017

  20. [20]

    Koh, B.-H

    S. Koh, B.-H. Lee and G. Tumurtushaa, Constraints on the reheating parameters after Gauss-Bonnet inflation from primordial gravitational waves , Phys. Rev. D 98 (2018) 103511 [1807.04424]

    Pith/arXiv arXiv 2018

  21. [21]

    Fomin and S.V

    I.V. Fomin and S.V. Chervon, Exact inflation in Einstein-Gauss-Bonnet gravity , Grav. Cosmol. 23 (2017) 367 [1704.03634]. – 32 –

    Pith/arXiv arXiv 2017

  22. [22]

    Fomin and S.V

    I.V. Fomin and S.V. Chervon, A new approach to exact solutions construction in scalar cosmology with a Gauss-Bonnet term , Mod. Phys. Lett. A32 (2017) 1750129 [1704.07786]

    Pith/arXiv arXiv 2017

  23. [23]

    Fomin, Cosmological Inflation with Einstein-Gauss-Bonnet Gravity , Phys

    I.V. Fomin, Cosmological Inflation with Einstein-Gauss-Bonnet Gravity , Phys. Part. Nucl. 49 (2018) 525

    2018

  24. [24]

    Fomin and S.V

    I.V. Fomin and S.V. Chervon, Reconstruction of general relativistic cosmological solut ions in modified gravity theories , Phys. Rev. D100 (2019) 023511 [1903.03974]

    Pith/arXiv arXiv 2019

  25. [25]

    Z. Yi, Y. Gong and M. Sabir, Inflation with Gauss-Bonnet coupling , Phys. Rev. D 98 (2018) 083521 [1804.09116]

    Pith/arXiv arXiv 2018

  26. [26]

    Odintsov and V.K

    S.D. Odintsov and V.K. Oikonomou, Viable Inflation in Scalar-Gauss-Bonnet Gravity and Reconstruction from Observational Indices , Phys. Rev. D 98 (2018) 044039 [1808.05045]

    Pith/arXiv arXiv 2018

  27. [27]

    Nojiri, S.D

    S. Nojiri, S.D. Odintsov, V.K. Oikonomou, N. Chatzarak is and T. Paul, Viable inflationary models in a ghost-free Gauss–Bonnet theory of gravity , Eur. Phys. J. C 79 (2019) 565 [1907.00403]

    Pith/arXiv arXiv 2019

  28. [28]

    Odintsov and V.K

    S.D. Odintsov and V.K. Oikonomou, Inflationary Phenomenology of Einstein Gauss-Bonnet Gravity Compatible with GW170817 , Phys. Lett. B 797 (2019) 134874 [1908.07555]

    Pith/arXiv arXiv 2019

  29. [29]

    Pozdeeva, M

    E.O. Pozdeeva, M. Sami, A.V. Toporensky and S.Y. Vernov , Stability analysis of de Sitter solutions in models with the Gauss-Bonnet term , Phys. Rev. D 100 (2019) 083527 [1905.05085]

    Pith/arXiv arXiv 2019

  30. [30]

    Fomin, Gauss–Bonnet term corrections in scalar field cosmology , Eur

    I. Fomin, Gauss–Bonnet term corrections in scalar field cosmology , Eur. Phys. J. C 80 (2020) 1145 [2004.08065]

    Pith/arXiv arXiv 2020

  31. [31]

    Odintsov, V.K

    S.D. Odintsov, V.K. Oikonomou and F.P. Fronimos, Rectifying Einstein-Gauss-Bonnet Inflation in View of GW170817 , Nucl. Phys. B 958 (2020) 115135 [2003.13724]

    Pith/arXiv arXiv 2020

  32. [32]

    Odintsov and V.K

    S.D. Odintsov and V.K. Oikonomou, Swampland implications of GW170817-compatible Einstein-Gauss-Bonnet gravity , Phys. Lett. B 805 (2020) 135437 [2004.00479]

    Pith/arXiv arXiv 2020

  33. [33]

    Odintsov, V.K

    S.D. Odintsov, V.K. Oikonomou and F.P. Fronimos, Non-minimally coupled Einstein–Gauss–Bonnet inflation phenomenology in view of G W170817, Annals Phys. 420 (2020) 168250 [2007.02309]

    Pith/arXiv arXiv 2020

  34. [34]

    Oikonomou and F.P

    V.K. Oikonomou and F.P. Fronimos, A Nearly Massless Graviton in Einstein-Gauss-Bonnet Inflation with Linear Coupling Implies Constant-roll for the S calar Field, EPL 131 (2020) 30001 [2007.11915]

    Pith/arXiv arXiv 2020

  35. [35]

    Odintsov, V.K

    S.D. Odintsov, V.K. Oikonomou, F.P. Fronimos and S.A. V enikoudis, GW170817-compatible constant-roll Einstein–Gauss–Bonnet inflation and non-Ga ussianities, Phys. Dark Univ. 30 (2020) 100718 [2009.06113]

    Pith/arXiv arXiv 2020

  36. [36]

    Pozdeeva, Generalization of cosmological attractor approach to Eins tein–Gauss–Bonnet gravity, Eur

    E.O. Pozdeeva, Generalization of cosmological attractor approach to Eins tein–Gauss–Bonnet gravity, Eur. Phys. J. C 80 (2020) 612 [2005.10133]

    Pith/arXiv arXiv 2020

  37. [37]

    Pozdeeva, M.R

    E.O. Pozdeeva, M.R. Gangopadhyay, M. Sami, A.V. Topore nsky and S.Y. Vernov, Inflation with a quartic potential in the framework of Einstein-Gauss-B onnet gravity , Phys. Rev. D 102 (2020) 043525 [2006.08027]

    Pith/arXiv arXiv 2020

  38. [38]

    Oikonomou and F.P

    V.K. Oikonomou and F.P. Fronimos, Non-minimally coupled Einstein–Gauss–Bonnet gravity with massless gravitons: the constant-roll case , Eur. Phys. J. Plus 135 (2020) 917 [2011.03828]

    Pith/arXiv arXiv 2020

  39. [39]

    Vernov and E

    S. Vernov and E. Pozdeeva, De Sitter Solutions in Einstein–Gauss–Bonnet Gravity , Universe 7 (2021) 149 [2104.11111]

    Pith/arXiv arXiv 2021

  40. [40]

    Nojiri, S.D

    S. Nojiri, S.D. Odintsov and V.K. Oikonomou, Propagation of gravitational waves in Einstein-Gauss-Bonnet gravity for cosmological and spheri cally symmetric spacetimes , Phys. Rev. D 109 (2024) 044046 [2311.06932]. – 33 –

    Pith/arXiv arXiv 2024

  41. [41]

    Odintsov and T

    S.D. Odintsov and T. Paul, From inflation to reheating and their dynamical stability an alysis in Gauss–Bonnet gravity , Phys. Dark Univ. 42 (2023) 101263 [2305.19110]

    Pith/arXiv arXiv 2023

  42. [42]

    Oikonomou, P

    V.K. Oikonomou, P. Tsyba and O. Razina, Einstein–Gauss–Bonnet cosmological theories at reheating and at the end of the inflationary era , Annals Phys. 462 (2024) 169597 [2401.11273]

    Pith/arXiv arXiv 2024

  43. [43]

    Oikonomou, Revisiting Einstein-Gauss-Bonnet theories after GW170817 , Phys

    V.K. Oikonomou, Revisiting Einstein-Gauss-Bonnet theories after GW170817 , Phys. Lett. B 856 (2024) 138890 [2407.12155]

    Pith/arXiv arXiv 2024

  44. [44]

    Manucharyan, I.V

    G.D. Manucharyan, I.V. Fomin, V.O. Gladyshev and V.L. K auts, Relic Gravitational Waves in Cosmological Models Based on Einstein–Gauss–Bonnet Gra vity, Phys. Atom. Nucl. 88 (2025) 500

    2025

  45. [45]

    Pozdeeva, M.A

    E.O. Pozdeeva, M.A. Skugoreva, A.V. Toporensky and S.Y . Vernov, New slow-roll approximations for inflation in Einstein-Gauss-Bonnet gra vity, JCAP 09 (2024) 050 [2403.06147]

    Pith/arXiv arXiv 2024

  46. [46]

    Mohammadi, Q

    Yogesh, A. Mohammadi, Q. Wu and T. Zhu, Starobinsky like inflation and EGB Gravity in the light of ACT , JCAP 10 (2025) 010 [2505.05363]

    Pith/arXiv arXiv 2025

  47. [47]

    Chen and T.-J

    P.-B. Chen and T.-J. Gao, Gravitational waves and primordial black holes from inflatio n with Gauss–Bonnet correction , Mod. Phys. Lett. A 41 (2026) 2550218 [2501.12242]

    Pith/arXiv arXiv 2026

  48. [48]

    Odintsov and T

    S.D. Odintsov and T. Paul, ACT inflation and its influence on reheating era in Einstein-Gauss-Bonnet gravity , Phys. Lett. B 870 (2025) 139930 [2508.11377]

    arXiv 2025

  49. [49]

    Ahghari and M

    Z. Ahghari and M. Farhoudi, Inflation with Gauss–Bonnet correction and Higgs potential , Eur. Phys. J. C 86 (2026) 601 [2512.12286]

    Pith/arXiv arXiv 2026

  50. [50]

    Mudrunka and K

    K. Mudrunka and K. Nakayama, Inflation with Gauss-Bonnet correction: beyond slow-roll , JCAP 02 (2026) 070 [2504.01365]

    Pith/arXiv arXiv 2026

  51. [51]

    Herrera and C

    R. Herrera and C. Ríos-Morales, Reconstructing inflation in Einstein-Gauss-Bonnet gravity in light of ACT data , JCAP 06 (2026) 083 [2601.18958]

    arXiv 2026

  52. [52]

    Nojiri, S.D

    S. Nojiri, S.D. Odintsov and M. Sasaki, Gauss-Bonnet dark energy , Phys. Rev. D 71 (2005) 123509 [hep-th/0504052]

    Pith/arXiv arXiv 2005

  53. [53]

    Nojiri and S.D

    S. Nojiri and S.D. Odintsov, Modified Gauss-Bonnet theory as gravitational alternative fo r dark energy , Phys. Lett. B 631 (2005) 1 [hep-th/0508049]

    Pith/arXiv arXiv 2005

  54. [54]

    Cognola, E

    G. Cognola, E. Elizalde, S. Nojiri, S.D. Odintsov and S. Zerbini, Dark energy in modified Gauss-Bonnet gravity: Late-time acceleration and the hier archy problem, Phys. Rev. D 73 (2006) 084007 [hep-th/0601008]

    Pith/arXiv arXiv 2006

  55. [55]

    Cognola, E

    G. Cognola, E. Elizalde, S. Nojiri, S. Odintsov and S. Ze rbini, String-inspired Gauss-Bonnet gravity reconstructed from the universe expansion history and yielding the transition from matter dominance to dark energy , Phys. Rev. D 75 (2007) 086002 [hep-th/0611198]

    Pith/arXiv arXiv 2007

  56. [56]

    Koivisto and D.F

    T. Koivisto and D.F. Mota, Gauss-Bonnet Quintessence: Background Evolution, Large S cale Structure and Cosmological Constraints , Phys. Rev. D 75 (2007) 023518 [hep-th/0609155]

    Pith/arXiv arXiv 2007

  57. [57]

    Nojiri and S.D

    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 [1011.0544]

    Pith/arXiv arXiv 2011

  58. [58]

    Nojiri, S.D

    S. Nojiri, S.D. Odintsov and V.K. Oikonomou, Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution , Phys. Rept. 692 (2017) 1 [1705.11098]

    Pith/arXiv arXiv 2017

  59. [59]

    Lohakare, F

    S.V. Lohakare, F. Tello-Ortiz, B. Mishra and S.K. Tripa thy, The Fate of the Universe Evolution in the Quadratic Form of Ricci–Gauss–Bonnet Cosmo logy, Grav. Cosmol. 29 (2023) 443 [2203.11676]. – 34 –

    Pith/arXiv arXiv 2023

  60. [60]

    Lohakare, K

    S.V. Lohakare, K. Rathore and B. Mishra, Observational constrained gravity cosmological model and the dynamical system analysis , Class. Quant. Grav. 40 (2023) 215009 [2303.14575]

    Pith/arXiv arXiv 2023

  61. [61]

    Lohakare, S

    S.V. Lohakare, S. Niyogi and B. Mishra, Cosmology in modified f ( G ) gravity: a late-time cosmic phenomena, Mon. Not. Roy. Astron. Soc. 535 (2024) 1136 [2408.03683]

    Pith/arXiv arXiv 2024

  62. [62]

    Odintsov, V.K

    S.D. Odintsov, V.K. Oikonomou and G.S. Sharov, Einstein-Gauss-Bonnet cosmology confronted with observations , JHEAp 47 (2025) 100398 [2503.17946]

    Pith/arXiv arXiv 2025

  63. [63]

    Atacama Cosmology Telescope collaboration, The Atacama Cosmology Telescope: DR6 constraints on extended cosmological models , JCAP 11 (2025) 063 [2503.14454]

    Pith/arXiv arXiv 2025

  64. [64]

    Atacama Cosmology Telescope collaboration, The Atacama Cosmology Telescope: DR6 power spectra, likelihoods and Λ CDM parameters, JCAP 11 (2025) 062 [2503.14452]

    Pith/arXiv arXiv 2025

  65. [65]

    DESI collaboration, DESI 2024 VI: cosmological constraints from the measurement s of baryon acoustic oscillations , JCAP 02 (2025) 021 [2404.03002]

    Pith/arXiv arXiv 2024

  66. [66]

    Planck collaboration, Planck 2018 results. VI. Cosmological parameters , Astron. Astrophys. 641 (2020) A6 [1807.06209]

    Pith/arXiv arXiv 2018

  67. [67]

    BICEP, Keck collaboration, Improved Constraints on Primordial Gravitational Waves usin g Planck, WMAP, and BICEP/Keck Observations through the 2018 Ob serving Season , Phys. Rev. Lett. 127 (2021) 151301 [2110.00483]

    arXiv 2018

  68. [68]

    NANOGra vcollaboration, The NANOGrav 15 yr Data Set: Evidence for a Gravitational-wave Background, Astrophys. J. Lett. 951 (2023) L8 [2306.16213]

    Pith/arXiv arXiv 2023

  69. [69]

    M. Kaur, D. Nandi and S.R. B, Unifying inflationary and reheating solution , JCAP 05 (2024) 045 [2309.10570]

    Pith/arXiv arXiv 2024

  70. [70]

    Q. Wu, T. Zhu and A. Wang, Primordial Spectra of slow-roll inflation at second-order wi th the Gauss-Bonnet correction, Phys. Rev. D 97 (2018) 103502 [1707.08020]

    Pith/arXiv arXiv 2018

  71. [71]

    Kuroyanagi, T

    S. Kuroyanagi, T. Chiba and N. Sugiyama, Prospects for Direct Detection of Inflationary Gravitational Waves by Next Generation Interferometric Detec tors, Phys. Rev. D 83 (2011) 043514 [1010.5246]

    Pith/arXiv arXiv 2011

  72. [72]

    Turner, Coherent Scalar Field Oscillations in an Expanding Universe , Phys

    M.S. Turner, Coherent Scalar Field Oscillations in an Expanding Universe , Phys. Rev. D 28 (1983) 1243

    1983

  73. [73]

    Starobinsky, A New Type of Isotropic Cosmological Models Without Singulari ty, Phys

    A.A. Starobinsky, A New Type of Isotropic Cosmological Models Without Singulari ty, Phys. Lett. B 91 (1980) 99

    1980

  74. [74]

    De Felice and S

    A. De Felice and S. Tsujikawa, f(R) theories, Living Rev. Rel. 13 (2010) 3 [ 1002.4928]

    Pith/arXiv arXiv 2010

  75. [75]

    Martin, C

    J. Martin, C. Ringeval and V. Vennin, Encyclopædia Inflationaris: Opiparous Edition , Phys. Dark Univ. 5-6 (2014) 75 [1303.3787]

    Pith/arXiv arXiv 2014

  76. [76]

    Kallosh, A

    R. Kallosh, A. Linde and D. Roest, Superconformal Inflationary α -Attractors, JHEP 11 (2013) 198 [1311.0472]

    Pith/arXiv arXiv 2013

  77. [77]

    Kallosh and A

    R. Kallosh and A. Linde, Universality Class in Conformal Inflation , JCAP 07 (2013) 002 [1306.5220]

    Pith/arXiv arXiv 2013

  78. [78]

    Kallosh, A

    R. Kallosh, A. Linde and D. Roest, Large field inflation and double α -attractors, JHEP 08 (2014) 052 [1405.3646]

    Pith/arXiv arXiv 2014

  79. [79]

    Galante, R

    M. Galante, R. Kallosh, A. Linde and D. Roest, Unity of Cosmological Inflation Attractors , Phys. Rev. Lett. 114 (2015) 141302 [1412.3797]

    Pith/arXiv arXiv 2015

  80. [80]

    Kanti, N.E

    P. Kanti, N.E. Mavromatos, J. Rizos, K. Tamvakis and E. W instanley, Dilatonic black holes in higher curvature string gravity , Phys. Rev. D 54 (1996) 5049 [hep-th/9511071]. – 35 –

    Pith/arXiv arXiv 1996

Showing first 80 references.