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Primordial non-Gaussianities of scalar and tensor perturbations in general bounce cosmology: Evading the no-go theorem

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Pith's one-line read A no-go theorem for matter bounce cosmology does not hold in the more general Horndeski theory.

desk verdict A careful Horndeski extension of the bounce no-go analysis with a clean tensor-bispectrum discriminant, but the observational claim of evading the no-go theorem is conditional on unproven bounce transfer. read the letter →

arxiv 1908.10663 v2 pith:JVIHNV4K submitted 2019-08-26 gr-qc astro-ph.COhep-th

Shingo Akama , Shin'ichi Hirano , Tsutomu Kobayashi This is my paper · ORCID
classification gr-qcastro-ph.COhep-th PACS 98.80.Cq04.50.Kd
keywords primordialnon-GaussianitymatterbouncecosmologyHorndeskitheorytensor-to-scalarratiotensorcontractinguniverseno-gotheoremcosmologicalperturbations
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper shows that a no-go theorem previously derived for k-essence matter bounce cosmology, which forbids having both a small tensor-to-scalar ratio and small non-Gaussianity of the curvature perturbation, does not hold in the more general Horndeski scalar-tensor framework. Working on a general power-law contracting background $a\propto(-t)^n$ with $0

What carries the argument

The central machinery is the Horndeski action (the most general second-order scalar-tensor theory) combined with the power-law scaling assumption of Eq. (7), that every background term behaves as $(-t)^{2\alpha}$. This scaling makes the coefficients in the quadratic actions for the curvature perturbation $\zeta$ and tensor perturbation $h_{ij}$, namely $G_S,F_S,G_T,F_T$, all proportional to $(-t)^{2(\alpha+1)}$ and hence constant up to a common factor; it selects the scale-invariant contracting branch $\alpha=1-3n$ and guarantees that the dimensionless coefficients $\Lambda_i$ in the cubic scalar Lagrangian are time independent. The scalar bispectrum is computed after a field redefinition that removes the boundary term $F(\zeta)E_S$, whose effect is encoded in the coefficients $A$ and $B$ defined from $\Theta$ and $G_T$; the tensor bispectrum comes from the two interaction terms $\dot{h}^3$ (with coefficient $\mu=-\frac{1}{2}\partial G_T/\partial H$) and $h^2\partial^2h$. The concrete evasion is achieved by a Lagrangian with $G_2(\varphi,X)$ and $G_3(\varphi,X)$ depending on $Y=Xe^{2\varphi/\mu}$ that satisfies five algebraic conditions at $Y=\bar{Y}$, leaving free small parameters $\delta_1,\delta_2,\delta_3$ that control $F_S$, $G_S$, and $\Lambda_1$ independently.

What would settle it

Start from the paper's concrete Lagrangian example, complete it with an explicit non-singular bounce, and evolve the perturbations through the bounce to late times; if the tensor-to-scalar ratio is small but the late-time non-Gaussianity parameter exceeds $O(1)$, or if the tensor bispectrum develops an equilateral peak, the claimed evasion of the no-go theorem fails.

Watch

Extended reading notes

Core claim

The central discovery is that the incompatibility between the observational upper bound on the tensor-to-scalar ratio and the observational upper bound on scalar non-Gaussianity, which excludes matter bounce models built from a k-essence scalar, disappears when the contracting phase is described by the Horndeski theory, the most general second-order scalar-tensor theory. On a power-law contracting background $a=(-t)^n$ with $0<n<1$, the authors impose the scaling behavior $E_i,P_i\sim(-t)^{2\alpha}$ and find scale-invariant power spectra for curvature and tensor perturbations on the branch $\alpha=1-3n$, where superhorizon modes grow as $|\eta|^{-3}$ instead of freezing. Using the in-in formalism, they compute the full scalar bispectrum (with coefficients $\Lambda_i$ made constant by the scaling) and the tensor bispectrum, which receives a new $\dot{h}^3$ contribution from $G_{5X}\neq0$ and a GR-type $h\partial^2h$ contribution. They then construct a concrete example with $G_2=M_{\rm Pl}^2\mu^2e^{-2\varphi/\mu}g_2(Y)$, $G_3=M_{\rm Pl}^2\mu g_3(Y)$, $G_4=M_{\rm Pl}^2/2$, and $G_5=0$, and tune the functions so that $F_S\simeq\frac{3}{5}\delta_1 M_{\rm Pl}^2$ and $G_S\simeq\frac{3}{5}\delta_2 M_{\rm Pl}^2$, giving $r=16\delta_1^{3/2}\delta_2^{-1/2}\ll1$ and $c_s^2=\delta_1/\delta_2=O(1)$ while the dangerous coefficient $\Lambda_1$ is suppressed by a third small number $\delta_3$; the result is $f_{\rm NL}\lesssim1$. For tensor modes, both the new and GR interactions yield bispectra peaked at the squeezed limit with model-dependent amplitudes, whereas generalized G-inflation also allows an equilateral peak and has a model-independent squeezed amplitude.

Load-bearing premise

The load-bearing premise is that the statistical nature of the primordial perturbations does not change during the subsequent bouncing and expanding phases, so that the spectra and bispectra evaluated at the end of the contracting phase are the ones observed.

Editorial extensions

If this is right

  • If the central claim is right, matter bounce models in Horndeski gravity are not excluded by the current bounds $r<0.064$ and $f_{\rm NL}\lesssim O(1)$, so the no-go theorem does not close the door on bounce alternatives to inflation.
  • The tensor bispectrum offers a distinguishing observable: contracting models predict only squeezed-shape tensor non-Gaussianity, so a detected equilateral peak in the tensor bispectrum would rule out this class of bounce models.
  • Because the squeezed tensor non-Gaussianity amplitude from contracting models depends on the Horndeski functions while the inflationary one is fixed, measuring that amplitude can distinguish the two scenarios.
  • Slightly detuning the relation $\alpha=1-3n$ produces a red spectral tilt $n_s\simeq0.96$, consistent with Planck, so the mechanism can accommodate the observed scalar tilt.
  • The computed tensor bispectra agree with those of non-attractor inflation models, because both are conformally equivalent to the matter-dominated contracting scenario; this implies a shared tensor signature between the two scenarios.

Reading between the lines

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

  • A direct test of the weakest assumption would be to complete the model with an explicit beyond-Horndeski bounce and evolve the bispectrum through it; if the bounce amplifies $f_{\rm NL}$ or changes the tensor bispectrum shape, the claimed evasion would not survive in a full non-singular history.
  • The construction requires the Lagrangian functions $g_2(Y)$ and $g_3(Y)$ to satisfy tuned conditions on their first three derivatives at a single point, which raises a potential fine-tuning concern; quantifying the measure of the parameter space satisfying all five conditions would clarify how generic the evasion is.
  • The conformal equivalence to non-attractor inflation implies that the tensor bispectrum alone may not differentiate a bounce from non-attractor inflation; adding scalar non-Gaussianity or other observables would be needed to break the degeneracy.
  • One could search for squeezed tensor non-Gaussianity in CMB B-mode bispectra as a direct test: a null detection of equilateral tensor non-Gaussianity together with a squeezed amplitude inconsistent with inflation's fixed value would favor the contracting scenario.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 3 minor

Summary. This paper studies scalar and tensor primordial perturbations during a power-law contracting phase in Horndeski gravity. Assuming a common scaling law for the background terms (Eq. (7)), the authors derive scale-invariant power spectra for curvature and tensor perturbations, compute the scalar bispectrum and the corresponding nonlinearity parameters at squeezed, equilateral and folded configurations, and compute the tensor bispectrum. They reproduce the previously known k-essence no-go result that small tensor-to-scalar ratio forces large scalar non-Gaussianity, and then construct a G2-G3 example in which r can be made small while f_NL remains O(1), thereby evading the no-go theorem during the contracting phase. They also argue that tensor non-Gaussianity from such contracting models is of squeezed type and model-dependent, in contrast to inflation, and therefore provides a possible observational discriminant.

Significance. If the results hold, the paper gives a concrete existence proof that the matter-bounce no-go theorem is not a generic feature of single-field scalar-tensor theories, and it identifies a potentially useful observational discriminant between contracting and inflationary scenarios. The derivation is systematic, uses established Horndeski perturbation theory, includes the full cubic action in an appendix, and connects the results to existing Planck constraints. The main caveat is that the observational conclusion rests on an explicit assumption about the bounce-to-expansion transition that is not established for the concrete Horndeski example.

major comments (2)
  1. [Sec. I; Eqs. (33), (44), (66)-(68)] The observational claim is load-bearing on the assumption stated in Sec. I that the statistical nature of the perturbations does not change during the subsequent bouncing and expanding phases. The power spectra and f_NL are evaluated at the end of the contracting phase, t=t_b, so any k-dependent rescaling or mode mixing during the bounce would alter the observable r and f_NL. The cited justification, Ref. [23], concerns a Horava-Lifshitz bounce, and no argument is given that it applies to the beyond-Horndeski completion that the authors themselves say is needed to avoid gradient instabilities in the full nonsingular history. The manuscript should either provide a bounce-transfer analysis for the Horndeski example or explicitly limit the conclusions to the contracting phase; as written, the title and abstract claim more than is demonstrated.
  2. [Sec. II, Eq. (7) and Eq. (19)] The central derivation assumes that all background terms E_i and P_i scale as (-t)^{2 alpha} with a common exponent, and then asserts that Sigma, Theta, G_T, F_T, G_S and F_S scale as in Eq. (19). This is a nontrivial ansatz rather than a consequence of the Horndeski field equations. The subsequent spectral-index conditions in Eqs. (25)-(32) and the f_NL formulas in Eqs. (66)-(68) all depend on this scaling. The explicit example in Sec. IV B satisfies the ansatz, but the paper does not characterize which Horndeski theories admit such backgrounds for general n. The authors should either state this as a restriction on the class of models considered or prove that Eq. (19) follows from Eq. (7) and the structure of the field equations.
minor comments (3)
  1. [Appendix B] The text says "The case of alpha = -2 (nu_s = nu_t = 2/3)" and "alpha = 1 - 3n (nu_s = nu_t = -2/3)"; the correct values from Eq. (25) are 3/2 and -3/2, respectively.
  2. [Appendix B] The expression "O(GT) /greaterorsimilarO(mu H)" is a LaTeX artifact and should read "O(G_T) \gtrsim O(mu H)".
  3. [Sec. IV B] The assertion that functions g2(Y) and g3(Y) satisfying the local conditions (75)-(81) exist is standard, but the paper would be more self-contained if it exhibited an explicit class of smooth functions, for instance polynomials, satisfying these conditions.

Circularity Check

0 steps flagged · score 2.0 of 10

No substantive circularity: the Horndeski evasion is an existence construction from derived formulas; self-citations are technical and not load-bearing.

full rationale

The paper's central derivation is self-contained. The quadratic actions (11)-(16) and cubic actions (54) and (84) are taken from published Horndeski perturbation theory, with the Lambda_i and Theta, Sigma expressions reproduced in Appendix C; the paper does not assume the no-go theorem or the observational bounds as inputs. Scale-invariance conditions nu_s = +/-3/2 follow from solving the mode equations (24)/(38), and the growing branch alpha = 1 - 3n is selected by the physics of contracting solutions, not by fitting to P_zeta or r. The example in Sec. IV B is an existence argument: conditions (75)-(81) are constraints on free functions g2(Y), g3(Y), and r, c_s, and f_NL are then evaluated from the previously derived formulas. This is not a fitted input called prediction, because no data are used to fix parameters; the parameters are chosen to exhibit compatibility. The no-go theorem of Ref. [21] is an external result and is reproduced in Eqs. (69)-(72) before being evaded. Several self-citations appear (e.g., [25], [28-30], [36]), but they are technical references to standard second-order scalar-tensor perturbation theory; the central claim does not reduce to a self-citation chain. The explicit assumption in Sec. I that the statistical nature of perturbations does not change during the bounce is load-bearing for observational applicability, but it is a physical assumption, not a circular reduction; it is a correctness risk rather than evidence of circularity. Accordingly, no circular step is identified.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central derivation rests on the Horndeski framework and a scaling ansatz for the background, plus the explicit assumption that perturbation statistics survive the bounce. The example Lagrangian is tuned through the small parameters delta_1, delta_2, delta_3 to meet the observational constraints, which is appropriate for an existence argument but means the 'predictions' of small r and small fNL are imposed rather than derived. No new physical entities are introduced.

free parameters (3)
  • delta_1 = unspecified, small positive, delta_1 ~ delta_2 << 1
    Introduced in Sec. IV.B to control FS and the tensor-to-scalar ratio; chosen by hand to make r small.
  • delta_2 = unspecified, small positive
    Controls GS and the scalar sound speed; chosen so c_s^2 = delta_1/delta_2 = O(1).
  • delta_3 = unspecified, delta_3 <= delta_1
    Introduced in Eq. (81) to cancel the leading contribution to Lambda_1 and keep fNL O(1).
assumptions (6)
  • ad hoc to paper Background terms in the Horndeski equations scale as E_i, P_i ~ (-t)^{2alpha}, with GT, FT, GS, FS ~ (-t)^{2(alpha+1)}.
    Stated in Sec. II around Eq. (7) and used to solve the mode equations; not derived from a concrete action but defines the class of backgrounds considered.
  • domain assumption Perturbation statistics are unchanged during the bounce and expanding phases.
    Explicit assumption in Sec. I; needed to connect contracting-phase spectra to observations.
  • domain assumption Beyond-Horndeski operators intervene to avoid gradient instabilities, and the bounce occurs before anisotropies grow.
    Stated in Sec. II and Appendix B; the paper does not construct the full nonsingular history.
  • standard math Bunch-Davies vacuum initial condition for mode functions at eta -> -infinity.
    Standard choice in Eqs. (27) and (40), used for quantization and spectrum normalization.
  • standard math Field redefinition and boundary term equivalence for the cubic action, following Refs. [31-33].
    Used in Sec. IV.A to remove the F(zeta) E_S term; prior published results are invoked.
  • ad hoc to paper Smooth functions g2(Y), g3(Y) exist satisfying the local conditions (75)-(81).
    Assumed in Sec. IV.B; the paper asserts existence without exhibiting explicit functions.

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Cite this review

Pith. "Pith review of Primordial non-Gaussianities of scalar and tensor perturbations in general bounce cosmology: Evading the no-go theorem." pith.science (2026). https://pith.science/paper/JVIHNV4K

@misc{pith2026190810663,
  author       = {Pith},
  title        = {Pith review of: Primordial non-Gaussianities of scalar and tensor perturbations in general bounce cosmology: Evading the no-go theorem},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JVIHNV4K}},
  note         = {Machine review of arXiv:1908.10663}
}
read the original abstract

It has been pointed out that matter bounce cosmology driven by a k-essence field cannot satisfy simultaneously the observational bounds on the tensor-to-scalar ratio and non-Gaussianity of the curvature perturbation. In this paper, we show that this is not the case in more general scalar-tensor theories. To do so, we evaluate the power spectra and the bispectra of scalar and tensor perturbations on a general contracting background in the Horndeski theory. We then discuss how one can discriminate contracting models from inflation based on non-Gaussian signatures of tensor perturbations.

Figures

Figures reproduced from arXiv: 1908.10663 by the authors.

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Works this paper leans on

52 extracted references · 20 canonical work pages

  1. [23]

    Fluctuations in a Ho\v{r}ava-Lifshitz Bouncing Cosmology

    X. Gao, Y. Wang, W. Xue and R. Brandenberger, “Fluctuations in a Horava-Lifshitz Bouncing Cosmol- ogy,” JCAP 1002, 020 (2010) [arXiv:0911.3196 [hep-th]]

    work page Pith review arXiv 2010

  2. [1]

    new” (respectively, “GR

    064, but then the nonlinearity parameters are too large to be consistent with observations: f local NL , f equil NL , f folded NL ∼ 1 c2 s = ( 24 r ) 2 > O(105), (72) indicating that any matter bounce models in the k- essence theory are excluded. (Observational constraints are given by f local NL = 0. 8 ± 5. 0 and f equil NL = −4 ± 43 [ 35].) Although sma...

    work page

  3. [2]

    A New Type of Isotropic Cosmolog- ical Models Without Singularity,

    A. A. Starobinsky, “A New Type of Isotropic Cosmolog- ical Models Without Singularity,” Phys. Lett. B 91, 99 (1980)

    work page 1980

  4. [3]

    This result implies the contracting background we are considering requires some mechanism to evade the unwanted growth of anisotropies

    The case of α = −2 (νs = νt = 2/ 3) corresponds to the former, while α = 1 − 3n (νs =νt = −2/ 3) to the lat- ter. This result implies the contracting background we are considering requires some mechanism to evade the unwanted growth of anisotropies. In the present paper, we simply assume that the contracting universe enjoys a bounce before the anisotropie...

    work page

  5. [4]

    The Inflationary Universe: A Possible Solu- tion to the Horizon and Flatness Problems,

    A. H. Guth, “The Inflationary Universe: A Possible Solu- tion to the Horizon and Flatness Problems,” Phys. Rev. D 23, 347 (1981)

    work page 1981

  6. [5]

    A Critical Review of Clas- sical Bouncing Cosmologies,

    D. Battefeld and P. Peter, “A Critical Review of Clas- sical Bouncing Cosmologies,” Phys. Rept. 571, 1 (2015) [arXiv:1406.2790 [astro-ph.CO]]

    arXiv 2015

  7. [6]

    First Order Phase Transition of a Vacuum and Expansion of the Universe,

    K. Sato, “First Order Phase Transition of a Vacuum and Expansion of the Universe,” Mon. Not. Roy. Astron. Soc. 195, 467 (1981)

    work page 1981

  8. [7]

    Singularities in inflationary cosmology: A Review,

    A. Borde and A. Vilenkin, “Singularities in inflationary cosmology: A Review,” Int. J. Mod. Phys. D 5, 813 (1996) [gr-qc/9612036]

    arXiv 1996

Show all 52 references
  1. [8]

    The Effective Field Theory of nonsingular cosmology,

    Y. Cai, Y. Wan, H. G. Li, T. Qiu and Y. S. Piao, “The Effective Field Theory of nonsingular cosmology,” JHEP 1701, 090 (2017) [arXiv:1610.03400 [gr-qc]]

    2017 arXiv

  2. [9]

    Generalized Galileons: instabilities of bouncing and Genesis cosmolo- gies and modified Genesis,

    M. Libanov, S. Mironov and V. Rubakov, “Generalized Galileons: instabilities of bouncing and Genesis cosmolo- gies and modified Genesis,” JCAP 1608, no. 08, 037 (2016) [arXiv:1605.05992 [hep-th]]

    2016 arXiv

  3. [10]

    Generic instabilities of nonsingular co s- mologies in Horndeski theory: A no-go theorem,

    T. Kobayashi, “Generic instabilities of nonsingular co s- mologies in Horndeski theory: A no-go theorem,” Phys. Rev. D 94, no. 4, 043511 (2016) [arXiv:1606.05831 [hep- th]]

    2016 arXiv

  4. [11]

    The Effective Field Theory of nonsingular cosmology: II,

    Y. Cai, H. G. Li, T. Qiu and Y. S. Piao, “The Effective Field Theory of nonsingular cosmology: II,” Eur. Phys. J. C 77, no. 6, 369 (2017) [arXiv:1701.04330 [gr-qc]]

    2017 arXiv

  5. [12]

    Stability of Geodesically Complete Cosmologies,

    P. Creminelli, D. Pirtskhalava, L. Santoni and E. Trincherini, “Stability of Geodesically Complete Cosmologies,” JCAP 1611, no. 11, 047 (2016) [arXiv:1610.04207 [hep-th]]

    2016 arXiv

  6. [13]

    Generalized multi- Galileons, covariantized new terms, and the no-go the- orem for nonsingular cosmologies,

    S. Akama and T. Kobayashi, “Generalized multi- Galileons, covariantized new terms, and the no-go the- orem for nonsingular cosmologies,” Phys. Rev. D 95, no. 6, 064011 (2017) [arXiv:1701.02926 [hep-th]]

    2017 arXiv

  7. [14]

    Implication of GW170817 for cosmological bounces,

    G. Ye and Y. S. Piao, “Implication of GW170817 for cosmological bounces,” Commun. Theor. Phys. 71, no. 4, 427 (2019) [arXiv:1901.02202 [gr-qc]]

    2019 arXiv

  8. [15]

    A covariant Lagrangian for stable nonsingular bounce,

    Y. Cai and Y. S. Piao, “A covariant Lagrangian for stable nonsingular bounce,” JHEP 1709, 027 (2017) [arXiv:1705.03401 [gr-qc]]

    2017 arXiv

  9. [16]

    Cosmological bounce and Genesis beyond Horndeski,

    R. Kolevatov, S. Mironov, N. Sukhov and V. Volkova, “Cosmological bounce and Genesis beyond Horndeski,” 12 JCAP 1708, no. 08, 038 (2017) [arXiv:1705.06626 [hep- th]]

    2017 arXiv

  10. [17]

    On the generation of a scale invariant spectrum of adiabatic fluctuations in cos- mological models with a contracting phase,

    F. Finelli and R. Brandenberger, “On the generation of a scale invariant spectrum of adiabatic fluctuations in cos- mological models with a contracting phase,” Phys. Rev. D 65, 103522 (2002) [hep-th/0112249]

    2002 arXiv

  11. [18]

    Bounce in general relativity and higher-order derivative operators,

    G. Ye and Y. S. Piao, “Bounce in general relativity and higher-order derivative operators,” Phys. Rev. D 99, no. 8, 084019 (2019) [arXiv:1901.08283 [gr-qc]]

    2019 arXiv

  12. [19]

    Duality invariance of cosmological pertur- bation spectra,

    D. Wands, “Duality invariance of cosmological pertur- bation spectra,” Phys. Rev. D 60, 023507 (1999) [gr- qc/9809062]

    1999

  13. [20]

    Viable scalar spectral tilt and tensor-to-scalar ratio in near-matter bounces,

    R. N. Raveendran and L. Sriramkumar, “Viable scalar spectral tilt and tensor-to-scalar ratio in near-matter bounces,” arXiv:1812.06803 [astro-ph.CO]

    arXiv

  14. [21]

    Quintin, Z

    J. Quintin, Z. Sherkatghanad, Y. F. Cai and R. H. Bran- denberger, “Evolution of cosmological perturbations and the production of non-Gaussianities through a nonsin- gular bounce: Indications for a no-go theorem in single field matter bounce cosmologies,” Phys. Rev. D 92, no. 6...

    2015 arXiv

  15. [22]

    Viable tensor-to-scalar ratio in a symmetric mat- ter bounce,

    R. N. Raveendran, D. Chowdhury and L. Sriramku- mar, “Viable tensor-to-scalar ratio in a symmetric mat- ter bounce,” JCAP 1801, 030 (2018) [arXiv:1703.10061 [gr-qc]]

    2018 arXiv

  16. [24]

    Mat- ter bounce cosmology with a generalized single field: non-Gaussianity and an extended no-go theorem,

    Y. B. Li, J. Quintin, D. G. Wang and Y. F. Cai, “Mat- ter bounce cosmology with a generalized single field: non-Gaussianity and an extended no-go theorem,” JCAP 1703, no. 03, 031 (2017) [arXiv:1612.02036 [hep-th]]

    2017 arXiv

  17. [25]

    Second-order scalar-tensor field equ a- tions in a four-dimensional space,

    G. W. Horndeski, “Second-order scalar-tensor field equ a- tions in a four-dimensional space,” Int. J. Theor. Phys. 10, 363 (1974)

    1974

  18. [26]

    Planck 2018 results. X. Constraints on inflation,

    Y. Akrami et al. [Planck Collaboration], “Planck 2018 results. X. Constraints on inflation,” arXiv:1807.06211 [astro-ph.CO]

    2018 arXiv

  19. [27]

    The Matter Bounce Alternative to Inflationary Cosmology,

    R. H. Brandenberger, “The Matter Bounce Alternative to Inflationary Cosmology,” arXiv:1206.4196 [astro-ph.CO]

    arXiv

  20. [28]

    Gen- eralized G-inflation: Inflation with the most general second-order field equations,

    T. Kobayashi, M. Yamaguchi and J. Yokoyama, “Gen- eralized G-inflation: Inflation with the most general second-order field equations,” Prog. Theor. Phys. 126, 511 (2011) [arXiv:1105.5723 [hep-th]]

    2011 arXiv

  21. [29]

    Inflationary non- Gaussianities in the most general second-order scalar- tensor theories,

    A. De Felice and S. Tsujikawa, “Inflationary non- Gaussianities in the most general second-order scalar- tensor theories,” Phys. Rev. D 84, 083504 (2011) [arXiv:1107.3917 [gr-qc]]

    2011 arXiv

  22. [30]

    Can non-minimal cou- pling restore the consistency condition in bouncing uni- verses?,

    D. Nandi and L. Sriramkumar, “Can non-minimal cou- pling restore the consistency condition in bouncing uni- verses?,” arXiv:1904.13254 [gr-qc]

    1904 arXiv

  23. [31]

    Inflation and primordial non- Gaussianities of ’generalized Galileons’,

    X. Gao and D. A. Steer, “Inflation and primordial non- Gaussianities of ’generalized Galileons’,” JCAP 1112, 019 (2011) [arXiv:1107.2642 [astro-ph.CO]]

    2011 arXiv

  24. [32]

    Gauge invariance and non-Gaussianity in Inflation,

    G. Rigopoulos, “Gauge invariance and non-Gaussianity in Inflation,” Phys. Rev. D 84, 021301 (2011) [arXiv:1104.0292 [astro-ph.CO]]

    2011 arXiv

  25. [33]

    Full bispectra from pri- mordial scalar and tensor perturbations in the most gen- eral single-field inflation model,

    X. Gao, T. Kobayashi, M. Shiraishi, M. Yamaguchi, J. Yokoyama and S. Yokoyama, “Full bispectra from pri- mordial scalar and tensor perturbations in the most gen- eral single-field inflation model,” PTEP 2013, 053E03 (2013) [arXiv:1207.0588 [astro-ph.CO]]

    2013 arXiv

  26. [34]

    A note on the role of the boundary terms for the non-Gaussianity in general k- inflation,

    F. Arroja and T. Tanaka, “A note on the role of the boundary terms for the non-Gaussianity in general k- inflation,” JCAP 1105, 005 (2011) [arXiv:1103.1102 [astro-ph.CO]]

    2011 arXiv

  27. [35]

    Planck 2018 results. IX. Constraints on primordial non-Gaussianity,

    Y. Akrami et al. [Planck Collaboration], “Planck 2018 results. IX. Constraints on primordial non-Gaussianity,” arXiv:1905.05697 [astro-ph.CO]

    2018 arXiv

  28. [36]

    Large slow-roll corrections to the bispectrum of noncanonical inflation,

    C. Burrage, R. H. Ribeiro and D. Seery, “Large slow-roll corrections to the bispectrum of noncanonical inflation,” JCAP 1107, 032 (2011) [arXiv:1103.4126 [astro-ph.CO]]

    2011 arXiv

  29. [37]

    Non-Gaussianity in a Matter Bounce,

    Y. F. Cai, W. Xue, R. Brandenberger and X. Zhang, “Non-Gaussianity in a Matter Bounce,” JCAP 0905, 011 (2009) [arXiv:0903.0631 [astro-ph.CO]]

    2009 arXiv

  30. [38]

    B-Mode auto-bispectrum due to matter bounce,

    R. Kothari and D. Nandi, “B-Mode auto-bispectrum due to matter bounce,” arXiv:1901.06538 [astro-ph.CO]

    1901 arXiv

  31. [39]

    Primordial non-Gaussianities of gravitational waves in the most general single-field inflation model,

    X. Gao, T. Kobayashi, M. Yamaguchi and J. Yokoyama, “Primordial non-Gaussianities of gravitational waves in the most general single-field inflation model,” Phys. Rev. Lett. 107, 211301 (2011) [arXiv:1108.3513 [astro- ph.CO]]

    2011 arXiv

  32. [40]

    The tensor bi-spectrum in a matter bounce,

    D. Chowdhury, V. Sreenath and L. Sriramkumar, “The tensor bi-spectrum in a matter bounce,” JCAP 1511, 002 (2015) [arXiv:1506.06475 [astro-ph.CO]]

    2015 arXiv

  33. [41]

    Oscillatory approach to a singular point in the relativis- tic cosmology,

    V. A. Belinsky, I. M. Khalatnikov and E. M. Lifshitz, “Oscillatory approach to a singular point in the relativis- tic cosmology,” Adv. Phys. 19, 525 (1970)

    1970

  34. [42]

    Squeezed tensor non- Gaussianity in non-attractor inflation,

    O. Ozsoy, M. Mylova, S. Parameswaran, C. Pow- ell, G. Tasinato and I. Zavala, “Squeezed tensor non- Gaussianity in non-attractor inflation,” arXiv:1902.0497 6 [hep-th]

    1902

  35. [43]

    CMB B-mode auto- bispectrum produced by primordial gravitational waves,

    H. W. H. Tahara and J. Yokoyama, “CMB B-mode auto- bispectrum produced by primordial gravitational waves,” PTEP 2018, no. 1, 013E03 (2018) [arXiv:1704.08904 [astro-ph.CO]]

    2018 arXiv

  36. [44]

    Anisotropy in a Nonsingular Bounce,

    Y. F. Cai, R. Brandenberger and P. Peter, “Anisotropy in a Nonsingular Bounce,” Class. Quant. Grav. 30, 075019 (2013) [arXiv:1301.4703 [gr-qc]]

    2013 arXiv

  37. [45]

    The Ekpyrotic universe: Colliding branes and the origin of the hot big bang,

    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. D 64, 123522 (2001) [hep-th/0103239]

    2001 arXiv

  38. [46]

    Ekpyrotic and Cyclic Cosmology,

    J. L. Lehners, “Ekpyrotic and Cyclic Cosmology,” Phys. Rept. 465, 223 (2008) [arXiv:0806.1245 [astro-ph]]

    2008 arXiv

  39. [47]

    Generalized Galilean Gen- esis,

    S. Nishi and T. Kobayashi, “Generalized Galilean Gen- esis,” JCAP 1503, no. 03, 057 (2015) [arXiv:1501.02553 [hep-th]]

    2015 arXiv

  40. [48]

    Towards anisotropy-free and nonsingular bounce cosmology with scale-invariant perturbations,

    T. Qiu, X. Gao and E. N. Saridakis, “Towards anisotropy-free and nonsingular bounce cosmology with scale-invariant perturbations,” Phys. Rev. D 88, no. 4, 043525 (2013) [arXiv:1303.2372 [astro-ph.CO]]

    2013 arXiv

  41. [49]

    Massive gravity and the suppression of anisotropies and gravi- tational waves in a matter-dominated contracting uni- verse,

    C. Lin, J. Quintin and R. H. Brandenberger, “Massive gravity and the suppression of anisotropies and gravi- tational waves in a matter-dominated contracting uni- verse,” JCAP 1801, 011 (2018) [arXiv:1711.10472 [hep- th]]

    2018 arXiv

  42. [51]

    General theory of cosmo- logical perturbations in open and closed universes from the Horndeski action,

    S. Akama and T. Kobayashi, “General theory of cosmo- logical perturbations in open and closed universes from the Horndeski action,” Phys. Rev. D 99, no. 4, 043522 (2019) [arXiv:1810.01863 [gr-qc]]

    2019 arXiv

  43. [52]

    Self-anisotropizing inflationary universe in Horndeski theory and beyond,

    H. W. H. Tahara, S. Nishi, T. Kobayashi and J. Yokoyama, “Self-anisotropizing inflationary universe in Horndeski theory and beyond,” JCAP 1807, no. 07, 058 (2018) [arXiv:1805.00186 [gr-qc]]

    2018 arXiv

  44. [88]

    and ( 89), whichever is dominant. Finally, notice that the non-Gaussian amplitudes ( 88) and ( 89) agree with those obtained in a kind of non- attractor inflation models, where tensor perturbations grow on superhorizon scales during inflation due to non- attractor dynamics of th...

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