Pith. sign in

REVIEW 3 major objections 5 minor 1 cited by

Generalized Galileon Scenario Inspires Chaotic Inflation

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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

Pith's one-line read A generalized Galileon self-interaction suppresses the tensor-to-scalar ratio by roughly $\sqrt{n}A$, bringing chaotic quadratic and quartic potentials back inside Planck 2018's 95% confidence region for sufficiently large $n$.

desk verdict Clean extension of G-inflation to power-law Galileon couplings, but the headline compatibility with Planck relies on an A>>1 limit that the paper's own stable parameter values violate. read the letter →

arxiv 1908.03155 v1 pith:JIQWCZ4Y submitted 2019-08-08 gr-qc astro-ph.CO

Matías López , Jorge Maggiolo , Nelson Videla , Pablo González , Grigoris Panotopoulos This is my paper · ORCID
classification gr-qcastro-ph.CO PACS 98.80.Cq
keywords Galileoninflationchaotictensor-to-scalarratioslow-rollapproximationPlanck2018constraintsHorndeskitheoryreheatinginstabilitiesscalarpowerspectrum
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

This paper shows that adding a higher-power Galileon self-interaction, $G(\phi,X)\propto X^n$, to the inflaton's dynamics can revive chaotic inflation, a model that current CMB data otherwise rules out. In the regime where the Galileon term dominates the standard kinetic term, the predicted tensor-to-scalar ratio is suppressed by roughly a factor $\sqrt{n}A$ compared with general relativity, while the scalar spectral index shifts only mildly. For the quadratic potential, $n\gtrsim4$ at $N=60$ suffices to enter the 95% confidence region of the 2018 Planck data; for the quartic potential, $n\gtrsim9$ at $N=60$ is needed. The authors also check numerically, for a benchmark quadratic model, that the inflaton can still oscillate after inflation when the mass scale is not too small, avoiding post-inflationary instabilities. The core claim is that a natural power-law generalization of cubic Galileon inflation is phenomenologically viable and observationally distinguishable.

What carries the argument

The load-bearing object is the dimensionless ratio $A = 3\delta_{GX}/\delta_X$, which measures the Galileon self-interaction relative to the standard kinetic term; in slow roll it is approximately $A \propto \dot\phi^{2n-1}H M^{-(4n-1)}$. The suppression mechanism is the large-$A$ limit of the tensor-to-scalar ratio, $r \simeq (4\sqrt{2}/3^{3/2})\, 16\epsilon/(\sqrt{n}A)$, which damps $r$ by a factor $\sim\sqrt{n}A$ relative to the general-relativity result $r=16\epsilon$. The same parameter $A$ enlarges the number of e-folds for a fixed field range and controls the scalar sound speed, $c_s^2 = (1+4A/3)/(1+2nA)$, which approaches $2/(3n)$ when the Galileon dominates. The slow-roll expressions (40)-(41), giving $n_S$ and $r$ as functions of $N$, $n$, and $p$, are what the Planck comparison is built on.

What would settle it

A future CMB experiment measuring $r$ at the values predicted here, for example $r\simeq0.07$ and $n_S\simeq0.968$ for $p=2$, $n=4$, $N=60$, would support the model; measuring $r$ above the prediction for every allowed $n$, or detecting a scalar sound speed different from $c_s^2=2/(3n)$ during inflation, would falsify the suppression mechanism. An immediately checkable calculation is to evaluate $A$ at the benchmark parameters, where $A\sim5$ at $M=1.1\times10^{-3}M_{\rm Pl}$, to see whether the $A\gg1$ approximation holds as claimed.

Watch

Extended reading notes

Core claim

Starting from the Horndeski-restricted action with $K=X-V(\phi)$ and $G(\phi,X)=cX^n/M^{4n-1}$, the paper derives slow-roll expressions for the scalar power spectrum, the scalar spectral index $n_S$, and the tensor-to-scalar ratio $r$ in the Galileon-dominated regime $A\gg1$. The central formulas are $n_S = 1 - [1+(2+3p)n] / [(1+n(2+p))N + np]$ and $r = (64\sqrt{6}/9)\, p\sqrt{n} / [(1+n(2+p))N + np]$, which show that increasing the Galileon power $n$ lowers $r$ while leaving $n_S$ inside the 2018 Planck 95% contours for the chaotic monomial potentials $V\propto\phi^p$. In that sense, the discovery is that a power-law Galileon self-coupling, not just the previously studied $n=1$ case, can rescue chaotic inflation from current observational bounds.

Load-bearing premise

The analysis assumes that slow roll and the Galileon-domination condition $A\gg1$ hold simultaneously; in the benchmark $n=4$ case the quoted mass $M=1.1\times10^{-3}M_{\rm Pl}$ gives only $A\sim5$, so the leading-order formulas may receive $1/A$ corrections and the paper does not demonstrate consistency across the full allowed parameter space.

Editorial extensions

If this is right

  • For the chaotic quadratic potential $V\propto\phi^2$, the model enters the Planck 2018 95% confidence region for $n\gtrsim4$ when $N=60$, with $n_S\simeq0.968$ and $r\simeq0.07$ at $n=4$.
  • For the chaotic quartic potential $V\propto\phi^4$, compatibility requires $n\gtrsim9$ for $N=60$ and $n\gtrsim6$ for $N=70$, while the $N=50$ curve stays outside the 95% region for every $n$ considered.
  • The Galileon-dominated regime imposes lower bounds on the potential amplitude: for $p=2$, $V_0\gg8.49\times10^{-12}M_{\rm Pl}^4$ and $m\gg2.91\times10^{-6}M_{\rm Pl}$; for $p=4$, $\lambda\gg3.67\times10^{-15}$.
  • Post-inflationary stability requires $M\gtrsim1.1\times10^{-3}M_{\rm Pl}$ for the inflaton to oscillate with $c_s^2>0$ and $q_s>0$, while the $A\gg1$ regime used in the analytic predictions requires $M\ll1.42\times10^{-3}M_{\rm Pl}$, leaving a narrow viable window.
  • For large $n$, $r$ tends to zero and $n_S$ tends to $[(2+p)N-2(p+1)]/[(2+p)N+p]$, so the model's predictions asymptote to a curve in the $n_S$-$r$ plane that is distinct from standard chaotic inflation.

Reading between the lines

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

  • The same suppression mechanism should apply to other monomial potentials with $p>2$, since Eqs. (40)-(41) are general in $p$; models like $V\propto\phi^6$ may also be rescued for large enough $n$, though the paper does not compute those cases.
  • The narrow allowed window for $M$ suggests a fine-tuning problem that could be sharpened by requiring reheating to complete within a given number of e-folds, a check the paper leaves to future work.
  • Because the scalar sound speed approaches $2/(3n)$ during inflation, a future measurement of non-Gaussianity or of $c_s$ would be a discriminating test between this generalized Galileon scenario and standard single-field slow-roll inflation.
  • The analytic predictions are derived for $A\gg1$, but the numerical benchmark sits at $A\sim5$; a full numerical scan of $(n,M,V_0)$ would show how much of the claimed viable region survives outside the strictly dominant regime.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper studies chaotic inflation driven by a monomial potential V(φ)=V0(φ/Mpl)^p in a cubic Galileon/Horndeski theory with a power-law self-interaction G(φ,X)=c X^n/M^{4n-1}. Under the slow-roll approximation the authors derive expressions for the background dynamics, the scalar power spectrum, the scalar spectral index, and the tensor-to-scalar ratio. In the regime where the Galileon term dominates over the standard kinetic term (A>>1), they find that r is suppressed by a factor proportional to 1/(sqrt(n) A) relative to standard GR. Applying the formulas to p=2 and p=4, they claim that chaotic quadratic inflation enters the Planck 2018 95% C.L. region for n≳4 (N=60) and quartic inflation for n≳9 (N=60), and they impose a Planck-normalization constraint on V0 and the mass scale M. The final section discusses post-inflationary stability with a numerical integration of the full background equations for a benchmark p=2, n=4 case.

Significance. If the central claim holds, the paper offers a concrete and falsifiable way to revive the otherwise observationally disfavored chaotic quadratic and quartic potentials by extending the Galileon self-coupling from the previously studied linear case to a power-law form, with the index n acting as a new parameter that can bring r down to the level allowed by Planck 2018. The slow-roll derivations are self-contained from the action (4), and the n=1 limit correctly reproduces results of Ref. [52], which strengthens confidence in the algebra. The paper also includes a numerical check of the background dynamics through the oscillatory phase, which goes beyond a purely analytic treatment. However, the central compatibility result relies on the A>>1 limit, and the paper does not demonstrate that this limit is compatible with its own post-inflationary stability bound; for the benchmark parameters the actual value of A is only of order 2.4 rather than much larger than one. Since the quantitative predictions for nS and r are obtained in the A→∞ limit, this gap affects the main phenomenological conclusion and must be addressed before the claim can be accepted.

major comments (3)
  1. [III.C and Eqs. (45), (49)] The benchmark compatibility claim for p=2, n=4, N=60 is made using the A→∞ formulas (40)-(41), but the parameter window allowed by the paper's own stability bound does not realize A>>1. From Eq. (45), A = 3.23e-10 (Mpl/M)^{10/3}. At the stability lower bound M=1.1e-3 Mpl quoted in Eq. (49), A≈2.4; at M=1.0e-3 Mpl one finds A≈3.4, and reaching A=10 requires M≈7e-4 Mpl, which violates Eq. (49). Thus the stable window has 1<A≲2.4, so corrections of order 1/A to Eqs. (40)-(41) are not negligible. The paper does not provide finite-A versions of nS and r, and therefore the stated values nS≈0.968, r≈0.07 at N=60 for n=4 are not quantitatively supported in the regime that satisfies the stability requirement.
  2. [III.C, parameter set (48)] The stability bound M≳1.1e-3 Mpl in Eq. (49) is inferred from a single numerical run with the parameter set (48), not from a scan over M or n. No evidence is given that the stability requirement is actually necessary rather than sufficient, and no stable example with A>>1 is presented. Consequently, the paper leaves open the possibility that the A≫1 regime and the post-inflationary stability requirement are mutually inconsistent for all allowed parameters. For the quartic case (p=4, n≈9), which is the main quartic viability claim, no numerical stability analysis is performed at all, so the consistency of the p=4 result with the reheating-phase constraints is entirely undemonstrated.
  3. [III, Eq. (38)] The Planck-normalization relation for V0 is introduced as resulting from an intermediate solution that is 'not shown'. This relation is load-bearing because it fixes V0 and thereby enters the estimate of A in Eq. (45) and the mass-scale constraints in Eqs. (48)-(49). The derivation should be provided, at least in an appendix, so that the reader can verify the algebra and the consistency of the numerical parameter choices. Without it, the chain from the action to the claimed allowed ranges of n and M is not fully checkable.
minor comments (5)
  1. [End of Sec. II.B] There is a typo: 'With is, Galileon inflation becomes...' should read 'With this, Galileon inflation becomes...'.
  2. [Figure 3 caption and text] The caption says the upper and lower plots depict the evolution of ε1 and the inflaton field, respectively, while the main text states the opposite (upper plot shows the field, lower plot shows ε1). Please correct the mismatch.
  3. [Conclusions, Sec. IV] In the sentence about the specific examples, 'quartic quartic' appears; the second 'quartic' should be removed.
  4. [Eq. (27) and surrounding text] The statement that n≥2/3 avoids Laplacian instabilities is trivial for the positive-integer n used in the paper; it would be clearer to state explicitly that only integer n are considered.
  5. [Fig. 4 discussion] In the comparison between the full c_s^2 and the slow-roll value 1/6, it should be noted that the slow-roll approximation is not valid during the oscillatory phase, so the comparison is only illustrative there.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: nS and r are derived from the stated action and benchmarked externally against Planck, not fitted or self-cited as the result.

full rationale

The central derivation chain does not reduce to its inputs by construction. The paper starts from the explicit action (4) with K = X - V and G = c M^(1-4n) X^n, defines A via Eq. (15), and under the stated slow-roll approximation derives the observables nS and r, specialized to chaotic potentials in Eqs. (40)-(41). These formulas are then compared with the external Planck 2018 contours; the resulting bounds on n are data constraints, not fitted parameters renamed as predictions. The Planck normalization fixes V0 but does not enter Eqs. (40)-(41), so no fitted input is relabelled as an output. The self-citations that appear (Ref. [56] with author Videla for the generalized Galileon ansatz, and Ref. [60] with authors Gonzalez and Videla for post-inflation oscillation behaviour) are motivational or illustrative, and neither is used as a load-bearing uniqueness theorem or as the target result: the tensor-to-scalar suppression is re-derived from the stated action and perturbation equations rather than imported from those references. The possible tension between the A >> 1 limit used for Eqs. (40)-(41) and the post-inflation stability bound M >= 1.1e-3 Mpl is a regime-consistency concern, not a circular-equivalence concern, and does not make the prediction equal to its input by definition.

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

The model introduces four free parameters (n, M, V0, c) that the central constraints depend on. No new particles, fields, or forces are postulated. The derivation assumes the validity of the Horndeski action, slow roll, and the A >> 1 regime, which together form the foundation of the claims.

free parameters (4)
  • n
    Positive integer power in G(phi,X) = c X^n / M^(4n-1). Constrained to be >= 4 (p=2, N=60) or >= 9 (p=4, N=60) from Planck 2018 95% CL contours. It is a free model parameter controlling the suppression of r.
  • M = between 1.1e-3 Mpl and 1.4e-3 Mpl (approximate)
    Mass scale in the Galileon coupling. The A >> 1 regime requires M << 1.42e-3 Mpl, while avoiding post-inflationary instability requires M >= 1.1e-3 Mpl, giving a narrow allowed window. The numerical example uses M = 1.1e-3 Mpl.
  • V0
    Amplitude of the monomial potential. Fixed by the Planck normalization P_s = 2.169e-9 via Eq. (38). This is standard practice but still a parameter set by data.
  • c = -1
    Dimensionless coupling in G(phi,X). Set to c = -1 to avoid ghosts and Laplacian instabilities in the regime where phi_dot < 0. This is a choice rather than a prediction.
assumptions (4)
  • domain assumption The Horndeski/Galileon action (4) with minimal coupling to gravity is the correct description of inflation.
    The paper starts from the restricted Horndeski Lagrangian (2) motivated by GW170817 constraints, and assumes this is the relevant theory for inflation. This is a model assumption, not derived.
  • domain assumption The slow-roll approximation is valid throughout the observable epoch of inflation.
    Equations (14)-(19) and the perturbation formulas (20)-(33) rely on slow roll, with |epsilon_1|, |epsilon_2| << 1. This is standard but not re-derived for the A >> 1 regime.
  • ad hoc to paper The A >> 1 regime (Galileon term dominates) is physically reached with a consistent mass scale M.
    The analytic constraints are derived only in this limit. The paper chooses parameters so that A is large, but for the benchmark n=4 the resulting A ~ 5 is only marginally large, so the leading-order expressions may receive corrections.
  • domain assumption The scalar propagation speed squared c_s^2 remains positive and q_s > 0 during inflation and reheating.
    Stability conditions (no ghosts, no Laplacian instabilities) are imposed, leading to c_s^2 = (1+4A/3)/(1+2nA) and the requirement n >= 2/3. The numerical section checks these for one parameter set.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Generalized Galileon Scenario Inspires Chaotic Inflation." pith.science (2026). https://pith.science/paper/JIQWCZ4Y

@misc{pith2026190803155,
  author       = {Pith},
  title        = {Pith review of: Generalized Galileon Scenario Inspires Chaotic Inflation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JIQWCZ4Y}},
  note         = {Machine review of arXiv:1908.03155}
}
abstract

We study chaotic inflation with a Galileon-like self interaction $G(\phi,X)\Box \phi$, where $G(\phi,X)\propto X^{n}$. General conditions required for successful inflation are deduced and discussed from the background and cosmological perturbations under slow-roll approximation. Interestingly, it is found that in the regime where the Galileon term dominates over the standard kinetic term, the tensor-to-scalar ratio becomes significantly suppressed in comparison to the standard expression in General Relativity (GR). Particularly, we find the allowed range in the space of parameters characterizing the chaotic quadratic and quartic inflation models by considering the current observational data of Planck from the $n_{\mathcal{S}}-r$ plane. Finally, we discuss about the issue if the Galileon term is dominant by the end of inflation, this can affect the field oscillation during reheating.

Figures

Figures reproduced from arXiv: 1908.03155 by the authors.

Figure 1
Figure 1. FIG. 1: Allowed contours at the 68 and 95 % C.L., from the lates [PITH_FULL_IMAGE:figures/full_fig_p012_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Allowed contours at the 68 and 95 % C.L., from the lates [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Upper and lower plot depict the evolution of slow-rol [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4: Upper and lower plot depict the evolution of the scala [PITH_FULL_IMAGE:figures/full_fig_p016_4.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Curvature Perturbations in the Effective Field Theory of Inflation

    gr-qc 2019-08 conditional novelty 7.0 of 10

    In single-field inflation, conservation of the comoving curvature perturbation implies conservation of the unitary and synchronous curvatures, but not the reverse, with observable consequences in ultra-slow-roll and a...

Reference graph

Works this paper leans on

61 extracted references · 24 canonical work pages · cited by 1 Pith paper

  1. [52]

    Tsujikawa, J

    S. Tsujikawa, J. Ohashi, S. Kuroyanagi and A. De Felice, Phys. Rev. D 88 (2013) no.2, 023529 doi:10.1103/PhysRevD.88.023529 [arXiv:1305.3044 [astr o-ph.CO]]

    arXiv 2013

  2. [1]

    A. A. Starobinsky, Phys. Lett. 91B (1980) 99

    work page 1980

  3. [2]

    Guth , Phys

    A. Guth , Phys. Rev. D 23, 347 (1981). 18

    work page 1981

  4. [3]

    Albrecht and P

    A. Albrecht and P. J. Steinhardt, Phys. Rev. Lett. 48, 1220 (1982)

    1982

  5. [4]

    A. D. Linde, Phys. Lett. B 129 (1983) 177

    1983

  6. [5]

    K. N. Abazajian et al. , Astropart. Phys. 63 (2015) 55 [arXiv:1309.5381 [astro-ph.CO]]

    arXiv 2015

  7. [6]

    A. A. Starobinsky, JETP Lett. 30, 682 (1979)

    1979

  8. [7]

    Mukhanov and G.V

    V.F. Mukhanov and G.V. Chibisov , JETP Letters 33, 532(1981)

    work page 1981

Show all 61 references
  1. [8]

    S. W. Hawking,Phys. Lett. B 115, 295 (1982)

    1982

  2. [9]

    Guth and S.-Y

    A. Guth and S.-Y. Pi, Phys. Rev. Lett. 49, 1110 (1982)

    1982

  3. [10]

    A. A. Starobinsky, Phys. Lett. B 117, 175 (1982)

    1982

  4. [11]

    Bardeen, P.J

    J.M. Bardeen, P.J. Steinhardt and M.S. Turner, Phys. Re v.D 28, 679 (1983)

    1983

  5. [12]

    D. H. Lyth and A. R. Liddle, Cambridge, UK: Cambridge Uni v. Pr. (2009) 497 p

    2009

  6. [13]

    L. F. Abbott, E. Farhi and M. B. Wise, Phys. Lett. 117B (1982) 29

    1982

  7. [14]

    Albrecht, P

    A. Albrecht, P. J. Steinhardt, M. S. Turner and F. Wilcze k, Phys. Rev. Lett. 48 (1982) 1437

    1982

  8. [15]

    L. Dai, M. Kamionkowski and J. Wang, Phys. Rev. Lett. 113 (2014) 041302 [arXiv:1404.6704 [astro-ph.CO]]

    2014 arXiv

  9. [16]

    J. B. Munoz and M. Kamionkowski, Phys. Rev. D 91 (2015) no.4, 043521 [arXiv:1412.0656 [astro-ph.CO]]

    2015 arXiv

  10. [17]

    J. L. Cook, E. Dimastrogiovanni, D. A. Easson and L. M. Kr auss, JCAP 1504 (2015) 047 [arXiv:1502.04673 [astro-ph.CO]]

    2015 arXiv

  11. [18]

    A. G. Riess et al. Astron. J. 116, 1009 (1998)

    1998

  12. [19]

    Perlmutter et al., Astrophys

    S. Perlmutter et al., Astrophys. J. 517, 565 (1999)

    1999

  13. [20]

    Hinshaw et al

    G. Hinshaw et al. [WMAP Collaboration], Astrophys. J. Suppl. 208 (2013) 19 [arXiv:1212.5226 [astro-ph.CO]]

    2013 arXiv

  14. [21]

    P. A. R. Ade et al. [Planck Collaboration], Astron. Astrophys. 594 (2016) A13 [arXiv:1502.01589 [astro-ph.CO]]

    2016 arXiv

  15. [22]

    Aghanim et al

    N. Aghanim et al. [Planck Collaboration], arXiv:1807.06209 [astro-ph.CO]

    arXiv

  16. [23]

    D. J. Eisenstein et al. [SDSS Collaboration], Astrophys. J. 633 (2005) 560 [astro-ph/0501171]

    2005 arXiv

  17. [24]

    W. J. Percival et al. [SDSS Collaboration], Mon. Not. Roy. Astron. Soc. 401 (2010) 2148 [arXiv:0907.1660 [astro-ph.CO]]

    2010 arXiv

  18. [25]

    Weinberg, Rev

    S. Weinberg, Rev. Mod. Phys. 61 (1989) 1

    1989

  19. [26]

    T. P. Sotiriou and V. Faraoni, Rev. Mod. Phys. 82 (2010) 451 [arXiv:0805.1726 [gr-qc]]

    2010 arXiv

  20. [27]

    De Felice and S

    A. De Felice and S. Tsujikawa, Living Rev. Rel. 13 (2010) 3 [arXiv:1002.4928 [gr-qc]]. 19

    2010 arXiv

  21. [28]

    Brans and R

    C. Brans and R. H. Dicke, Phys. Rev. 124 (1961) 925

    1961

  22. [29]

    G. R. Dvali, G. Gabadadze and M. Porrati, Phys. Lett. B 485 (2000) 208 [hep-th/0005016]

    2000 arXiv

  23. [30]

    Nicolis, R

    A. Nicolis, R. Rattazzi and E. Trincherini, Phys. Rev. D 79 (2009) 064036 [arXiv:0811.2197 [hep-th]]

    2009 arXiv

  24. [31]

    Clifton, P

    T. Clifton, P. G. Ferreira, A. Padilla and C. Skordis, Ph ys. Rept. 513 (2012) 1 [arXiv:1106.2476 [astro-ph.CO]]

    2012 arXiv

  25. [32]

    G. W. Horndeski, Int. J. Theor. Phys. 10, 363-384 (1974)

    1974

  26. [33]

    De Felice, T

    A. De Felice, T. Kobayashi and S. Tsujikawa, Phys. Lett. B 706 (2011) 123 [arXiv:1108.4242 [gr-qc]]

    2011 arXiv

  27. [34]

    Armendariz-Picon, V

    C. Armendariz-Picon, V. F. Mukhanov and P. J. Steinhard t, Phys. Rev. Lett. 85 (2000) 4438 [astro-ph/0004134]

    2000 arXiv

  28. [35]

    Kobayashi, M

    T. Kobayashi, M. Yamaguchi and J. Yokoyama, Prog. Theor . Phys. 126 (2011) 511 [arXiv:1105.5723 [hep-th]]

    2011 arXiv

  29. [36]

    Kobayashi, M

    T. Kobayashi, M. Yamaguchi and J. Yokoyama, Phys. Rev. L ett. 105 (2010) 231302 [arXiv:1008.0603 [hep-th]]

    2010 arXiv

  30. [37]

    Deffayet, X

    C. Deffayet, X. Gao, D. A. Steer and G. Zahariade, Phys. Rev . D 84 (2011) 064039 [arXiv:1103.3260 [hep-th]]

    2011 arXiv

  31. [38]

    Charmousis, E

    C. Charmousis, E. J. Copeland, A. Padilla and P. M. Saffin, Phys. Rev. Lett. 108 (2012) 051101 [arXiv:1106.2000 [hep-th]]

    2012 arXiv

  32. [39]

    Kobayashi, Rept

    T. Kobayashi, Rept. Prog. Phys. 82, no. 8, 086901 (2019)

    2019

  33. [40]

    B. P. Abbott et al. [LIGO Scientific and Virgo Collaborations], Phys. Rev. Lett . 119 (2017) no.16, 161101 arXiv:1710.05832 [gr-qc]

    2017 arXiv

  34. [41]

    B. P. Abbott et al. [LIGO Scientific and Virgo and Fermi-GBM and INTEGRAL Collab ora- tions], Astrophys. J. 848, no. 2, L13 (2017) arXiv:1710.05834 [astro-ph.HE]

    2017 arXiv

  35. [42]

    Baker, E

    T. Baker, E. Bellini, P. G. Ferreira, M. Lagos, J. Noller and I. Sawicki, Phys. Rev. Lett. 119, no. 25, 251301 (2017)

    2017

  36. [43]

    Langlois, R

    D. Langlois, R. Saito, D. Yamauchi and K. Noui, Phys. Rev . D 97, no. 6, 061501 (2018)

    2018

  37. [44]

    (42) • For N = 60, n /greaterorsimilar4

    when the power n takes the following values: • For N = 50, n /greaterorsimilar8. (42) • For N = 60, n /greaterorsimilar4. (43) • For N = 70, n /greaterorsimilar5. (44) As it can be seen from Fig.1, for n = 1 the tensor to-scalar ratio becomes slowly decreased in comparison to ...

    2018

  38. [45]

    Akrami et al

    Y. Akrami et al. [Planck Collaboration], arXiv:1807.06211 [astro-ph.CO]

    arXiv

  39. [46]

    Pich, arXiv:0705.4264 [hep-ph]

    A. Pich, arXiv:0705.4264 [hep-ph]

    arXiv

  40. [47]

    P. W. Higgs, Phys. Rev. Lett. 13 (1964) 508

    1964

  41. [48]

    Englert and R

    F. Englert and R. Brout, Phys. Rev. Lett. 13 (1964) 321. 20

    1964

  42. [49]

    A. D. Linde, Phys. Lett. 129B (1983) 177

    1983

  43. [50]

    Tenkanen, JCAP 1712 (2017) no.12, 001 [arXiv:1710.02758 [astro-ph.CO]]

    T. Tenkanen, JCAP 1712 (2017) no.12, 001 [arXiv:1710.02758 [astro-ph.CO]]

    2017 arXiv

  44. [51]

    Makino and M

    N. Makino and M. Sasaki, Prog. Theor. Phys. 86 (1991) 103

    1991

  45. [53]

    Ohashi and S

    J. Ohashi and S. Tsujikawa, JCAP 1210 (2012) 035 [arXiv:1207.4879 [gr-qc]]

    2012 arXiv

  46. [54]

    P. A. R. Ade et al. [BICEP2 and Keck Array Collaborations], Phys. Rev. Lett. 121 (2018) 221301 [arXiv:1810.05216 [astro-ph.CO]]

    2018 arXiv

  47. [55]

    Teimoori and K

    Z. Teimoori and K. Karami, Astrophys. J. 864, no. 1, 41 (2018)

    2018

  48. [56]

    De Felice, S

    A. De Felice, S. Tsujikawa, J. Elliston and R. Tavakol, J CAP 1108 (2011) 021 [arXiv:1105.4685 [astro-ph.CO]]

    2011 arXiv

  49. [57]

    Herrera, N

    R. Herrera, N. Videla and M. Olivares, Eur. Phys. J. C 78 (2018) no.11, 934 [arXiv:1806.04232 [gr-qc]]

    2018 arXiv

  50. [58]

    De Felice and S

    A. De Felice and S. Tsujikawa, Phys. Rev. D 84 (2011) 124029 [arXiv:1008.4236 [hep-th]]

    2011 arXiv

  51. [59]

    De Felice and S

    A. De Felice and S. Tsujikawa, Phys. Rev. D 84 (2011) 083504 [arXiv:1107.3917 [gr-qc]]

    2011 arXiv

  52. [60]

    De Felice and S

    A. De Felice and S. Tsujikawa, JCAP 1303 (2013) 030 [arXiv:1301.5721 [hep-th]]

    2013 arXiv

  53. [61]

    Gonzlez, G

    P. Gonzlez, G. A. Palma and N. Videla, JCAP 1812 (2018) no.12, 001 [arXiv:1805.10360 [hep-th]]. 21

    2018 arXiv

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.