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REVIEW 2 major objections 3 cited by

Exponential and sech Gauss–Bonnet couplings can move quintessential inflation into the ACT 1σ region for ns and r, while a tanh coupling cannot.

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

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T0 review · grok-4.5

2026-07-12 20:07 UTC pith:632VNK3Q

load-bearing objection Solid existence proof that exponential/sech EGB couplings can rescue quintessential inflation for ACT ns; the tanh sign argument is the real clarifying bit. the 2 major comments →

arxiv 2604.14659 v2 pith:632VNK3Q submitted 2026-04-16 astro-ph.CO gr-qc

Constraining Quintessential Inflation with ACT: A Gauss-Bonnet Gateway

Yogesh , Imtiyaz Ahmad Bhat , Mayukh R. Gangopadhyay , M. Sami This is my paper
classification astro-ph.CO gr-qc
keywords quintessential inflationEinstein–Gauss–Bonnet gravityscalar spectral indexACT constraintsnon-minimal Gauss–Bonnet couplingreheatingtensor-to-scalar ratio
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.

ACT’s higher, tighter measurement of the scalar spectral index leaves standard quintessential inflation near or outside the allowed 2σ region. This paper embeds the same runaway potential in Einstein–Gauss–Bonnet gravity, where a scalar field couples non-minimally to the Gauss–Bonnet invariant. With exponential or sech-type couplings the predicted (r, ns) trajectories can be shifted into the ACT 1σ contour; a tanh coupling systematically fails. The same setups still permit viable reheating histories, even though the potential has no minimum, with temperatures above Big Bang nucleosynthesis bounds. The work therefore claims that a geometric correction of this form is enough to keep a single-field inflation-plus-dark-energy model observationally alive.

Core claim

When the quintessential potential V = V0 exp(−λ ϕ^n) is non-minimally coupled to the Gauss–Bonnet term through an exponential or sech function, the resulting slow-roll trajectories for r and ns enter the 1σ region preferred by ACT; a tanh coupling leaves the model outside that region because the positive sign of its derivative reverses the Gauss–Bonnet correction to ns.

What carries the argument

The effective potential Veff = −U²/V + ξ/3, together with the slow-roll hierarchy expressed through it. The sign of ξ′ fixes the sign of the first Gauss–Bonnet slow-roll parameter δ1 and thereby decides whether the correction to ns raises or lowers the spectral index.

Load-bearing premise

That the slow-roll hierarchy stays uniformly small over the last sixty e-folds once the chosen Gauss–Bonnet coupling is turned on, so the effective-potential formulas still map correctly onto CMB scales.

What would settle it

A full numerical integration of the background equations without the slow-roll approximation that shows the exponential and sech models never reach ns ≈ 0.974 for any parameters that keep r below current upper limits, or a future CMB data release whose 1σ contour excludes every trajectory plotted for those two couplings.

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

If this is right

  • Quintessential inflation need not be abandoned after ACT if the gravitational sector includes a suitable Gauss–Bonnet coupling.
  • The functional form of the coupling can be observationally discriminated: exponential and sech work; tanh does not.
  • Reheating remains consistent with BBN even without a potential minimum, via a constant effective equation-of-state parameter.
  • The allowed ranges of λ, n and the coupling strength ξ1 are narrowed to the slices that place (r, ns) inside the ACT 1σ contour.

Where Pith is reading between the lines

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

  • Any other coupling whose derivative stays negative during inflation should produce a similar rescue of the spectral index; the paper’s sign argument generalizes beyond the three examples studied.
  • If future r upper bounds tighten below the lowest values reached by the viable couplings, the entire EGB rescue of this potential would be ruled out.
  • The same sign criterion could be used as a quick filter when scanning larger libraries of modified-gravity inflation models against ACT or next-generation CMB data.

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 / 0 minor

Summary. The paper revisits quintessential inflation with the runaway potential V = V0 exp(-λ ϕ^n) in Einstein–Gauss–Bonnet gravity, motivated by the ACT DR6 preference for a higher scalar spectral index ns = 0.9743 ± 0.0034 that places the standard GR realization near or beyond the 2σ contour. A non-minimal coupling ξ(ϕ) to the Gauss–Bonnet invariant is introduced, and three representative forms (exponential, sech, tanh) are scanned over n, λ and ξ1. Using the effective-potential formalism, the authors show that exponential and sech couplings can move the (r, ns) predictions into the ACT 1σ region, while the tanh coupling cannot. Section VII supplies an analytic diagnosis: the sign of ξ' controls the sign of δ1 and thereby the direction of the GB correction to ns. A model-independent reheating analysis with constant wre further shows that both viable couplings admit thermal histories consistent with BBN bounds.

Significance. If the slow-roll mapping remains valid, the work supplies a concrete geometric rescue of a well-motivated unified inflation–dark-energy potential that is otherwise in tension with ACT. The analytic sign argument of Sec. VII is a clean, falsifiable diagnostic that elevates the result above a pure parameter scan: couplings with ξ' < 0 during inflation can raise ns, while those with ξ' > 0 push it the wrong way. The reheating maps demonstrate internal consistency even without a potential minimum. The paper therefore contributes both a viable model-building pathway and a structural selection rule for GB couplings in the post-ACT landscape.

major comments (2)
  1. Secs. II–III and V–VI: the central claim rests on the assumption that |ϵ1|, |δi| ≪ 1 remain uniformly valid over the last ~60 e-folds once ξ(ϕ) is active, so that Eqs. (18)–(23) and the numerical integration of (17) correctly map onto CMB scales. The manuscript does not report the maximum values of the higher slow-roll parameters (or of |δ1|, |δ2|) along the successful trajectories of Figs. 1–2. A short validation plot or table for a few benchmark points inside the ACT 1σ region would confirm that the effective-potential expressions remain accurate where the observables are evaluated.
  2. Eq. (24) and Secs. V–VI: the scalar amplitude As is written but never used to fix V0 (or U). Without this normalization it is unclear whether the end-of-inflation energy density that enters the reheating formulae (27)–(28) and Fig. 4 is consistent with the observed As ≈ 2.1 × 10^-9. A brief statement that V0 is fixed by As for each successful (λ, n, ξ1) point, or an explicit check that the resulting Vend yields Tre above the BBN floor, would close this gap.

Circularity Check

1 steps flagged

No significant circularity: existence scan over free couplings is standard model-building, and the tanh failure is an independent sign argument from the paper's own equations.

specific steps
  1. self citation load bearing [Sec. III, Eq. (15); citation [155]]
    "A particularly elegant way to analyze inflationary dynamics in EGB gravity is through the effective potential [155]: Veff(ϕ)=−U2/V(ϕ)+1/3 ξ(ϕ)."

    The organizing object Veff is imported from prior work coauthored by Sami (Pozdeeva–Sami–Toporensky–Vernov). This is a minor self-citation of formalism, not a uniqueness theorem that forces the ACT-compatible parameter regions or the tanh no-go; the sign argument and numerical scans are independent of that citation. Flagged only for completeness; not load-bearing for the central claim.

full rationale

The paper's central claim is an existence result (exponential and sech ξ(ϕ) can place V=V0 exp(−λϕ^n) inside the ACT 1σ r–ns contour for some scanned n, λ, ξ1) plus a structural no-go for tanh. Scanning free parameters until (r,ns) lands inside an external contour is ordinary model-building, not a fitted-input-called-prediction: the paper does not claim a unique first-principles prediction of ns, nor does it fit one observable and then re-label a correlated quantity as an independent forecast. The load-bearing analytic content is Sec. VII, which derives from the paper's own slow-roll expressions (18)–(23) and the signs of ξ′_exp, ξ′_sech < 0 versus ξ′_tanh > 0, propagating through V′_eff, δ1, and the GB correction term in ns; that chain does not reduce to the ACT fit. The effective-potential formalism is taken from prior literature that includes a coauthor, but it is used as a calculational tool rather than as a uniqueness theorem that forces the result. Reheating uses a standard model-independent (Nre, Tre, wre) parametrization and only checks BBN consistency. No self-definitional loop, no uniqueness imported from the authors, and no renaming of a known empirical pattern. Score 1 only for the minor, non-load-bearing self-citation of the EGB effective-potential setup; the derivation against external ACT/BBN benchmarks is otherwise self-contained.

Axiom & Free-Parameter Ledger

5 free parameters · 4 axioms · 0 invented entities

The central claim rests on the standard EGB action, the slow-roll hierarchy, three hand-chosen coupling functions, and a multi-parameter scan whose free parameters are adjusted until the observables sit inside the ACT contour. No new particles or forces are invented; the geometric coupling is already motivated by string effective actions. The ledger therefore lists the free parameters that control the fit and the domain assumptions that convert the action into the plotted (r, ns) points.

free parameters (5)
  • ξ1 (coupling strength) = O(0.001–0.2) depending on coupling
    Scanned in [0, 0.03] (exp/tanh) or [0, 0.2] (sech) until trajectories enter the ACT 1σ region; not fixed by theory.
  • λ (potential slope) = 10^{-8}–10^{-3}
    Scanned over 10^{-8}–10^{-3}; controls the steepness of V and therefore the baseline GR values of ns and r.
  • n (potential power) = 4–12
    Integer scanned 4–12; changes the shape of the runaway and the resulting r–ns locus.
  • w_re (reheating equation of state) = discrete set
    Assumed constant and varied over discrete values (−1/3, 0, 2/3, 1) to map Nre–Tre; not derived from microphysics.
  • U (non-minimal Einstein-frame coefficient) = set to 1 (Mp units)
    Positive constant kept in the action; effectively absorbed into the overall normalization of V and As.
axioms (4)
  • domain assumption Spatially flat FLRW metric and the EGB action (1) with constant U > 0.
    Standard starting point for the entire derivation (Sec. II).
  • domain assumption Slow-roll hierarchy |ϵi| ≪ 1, |δi| ≪ 1 throughout the observable window, allowing the effective-potential reduction (15)–(23).
    Invoked to obtain the analytic expressions for r and ns used in all figures.
  • ad hoc to paper The three coupling functions (26) are representative and the overall 1/V0 factor is harmless.
    Chosen by hand; no derivation from a UV completion is supplied.
  • domain assumption Reheating can be parametrized by a single constant wre even though the potential has no minimum.
    Standard model-independent reheating formalism (Cook et al.) adopted in Sec. IV B.

pith-pipeline@v1.1.0-grok45 · 20636 in / 3058 out tokens · 28161 ms · 2026-07-12T20:07:00.251794+00:00 · methodology

0 comments
read the original abstract

Recent results from the Atacama Cosmology Telescope (ACT), indicating a higher and more tightly constrained scalar spectral index, $n_s = 0.9743 \pm 0.0034$, place several inflationary models under tension, with quintessential inflation pushed close to or beyond the $2\sigma$ boundary in the $r$--$n_s$ plane. In this work, we revisit quintessential inflation within the framework of Einstein--Gauss--Bonnet (EGB) gravity, where a scalar field non-minimally coupled to the Gauss--Bonnet invariant modifies the inflationary dynamics. We consider three representative coupling functions -- exponential, hyperbolic secant, and hyperbolic tangent -- and show that the exponential and sech-type couplings can shift the predicted values of $r$ and $n_s$ into the $1\sigma$ region allowed by ACT, thereby restoring consistency with observations. In contrast, the tanh-type coupling remains disfavored, underscoring the sensitivity of inflationary observables to the coupling structure. We further investigate the reheating phase using a model-independent parametrization and demonstrate that viable thermal histories can be realized even in the absence of a potential minimum, with reheating temperatures consistent with Big Bang nucleosynthesis bounds. Overall, our analysis shows that EGB corrections provide a viable and robust extension that reconciles quintessential inflation with current precision cosmological data, and we identify the corresponding allowed parameter space.

Figures

Figures reproduced from arXiv: 2604.14659 by Imtiyaz Ahmad Bhat, Mayukh R. Gangopadhyay, M. Sami, Yogesh.

Figure 1
Figure 1. Figure 1: FIG. 1. The [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Reheating parameters [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

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Forward citations

Cited by 3 Pith papers

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

  1. Running into tension: primordial black holes from ultra-slow-roll inflation, spectral running, and the Hubble tension

    astro-ph.CO 2026-06 unverdicted novelty 5.0

    EDE models increase inferred α_s from CMB data, strengthening tension with USR PBH models that predict negative running.

  2. ACT-DR6 consistent inflation in generalised entropic cosmology and $f(Q)$ gravity

    gr-qc 2026-07 conditional novelty 4.0

    Reconstruction produces explicit f(Q) and generalised-entropic inflation models (and scalar-coupled versions) whose slow-roll parameters match ACT-DR6 + Planck-BAO constraints on n_s and r.

  3. String-inspired Gauss-Bonnet Gravity Inflation and ACT

    gr-qc 2026-04 unverdicted novelty 4.0

    MCMC analysis of sixteen ghost-free f(R,G) inflation models shows all reproduce ns ≈ 0.97 at 60 e-folds with stable μ ≈ 0.1, preference set by Hubble parametrization.

Reference graph

Works this paper leans on

155 extracted references · 118 linked inside Pith · cited by 3 Pith papers

  1. [1]

    A. H. Guth, Phys. Rev. D23, 347 (1981)

    1981

  2. [2]

    Sato, Mon

    K. Sato, Mon. Not. Roy. Astron. Soc.195, 467 (1981)

    1981

  3. [3]

    A. D. Linde, Phys. Lett. B108, 389 (1982)

    1982

  4. [4]

    Albrecht and P

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

    1982

  5. [5]

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

    1981

  6. [6]

    A. A. Starobinsky, Phys. Lett. B117, 175 (1982)

    1982

  7. [7]

    A. A. Starobinsky, Sov. Astron. Lett.9, 302 (1983)

    1983

  8. [8]

    A. A. Starobinsky, Phys. Lett. B91, 99 (1980). 7

    1980

  9. [9]

    Hinshawet al.(WMAP), Astrophys

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

    Pith/arXiv arXiv 2013

  10. [10]

    P. A. R. Adeet al.(Planck), Astron. Astrophys.594, A20 (2016), arXiv:1502.02114 [astro-ph.CO]

    Pith/arXiv arXiv 2016

  11. [11]

    Akramiet al.(Planck), Astron

    Y. Akramiet al.(Planck), Astron. Astrophys.641, A10 (2020), arXiv:1807.06211 [astro-ph.CO]

    Pith/arXiv arXiv 2020

  12. [12]

    Barenboim and W

    G. Barenboim and W. H. Kinney, JCAP0703, 014 (2007), arXiv:astro-ph/0701343 [astro-ph]

    Pith/arXiv arXiv 2007

  13. [13]

    S. D. Odintsov and V. K. Oikonomou, Phys. Lett. B870, 139907 (2025), arXiv:2509.06251 [gr-qc]

    arXiv 2025

  14. [14]

    Franche, R

    P. Franche, R. Gwyn, B. Underwood, and A. Wissanji, Phys. Rev.D82, 063528 (2010), arXiv:1002.2639 [hep-th]

    Pith/arXiv arXiv 2010

  15. [15]

    Unnikrishnan, V

    S. Unnikrishnan, V. Sahni, and A. Toporensky, JCAP 1208, 018 (2012), arXiv:1205.0786 [astro-ph.CO]

    Pith/arXiv arXiv 2012

  16. [16]

    Saaidi, A

    K. Saaidi, A. Mohammadi, and T. Golanbari, Adv. High Energy Phys.2015, 926807 (2015), arXiv:1708.03675 [gr- qc]

    Pith/arXiv arXiv 2015

  17. [17]

    Mohammadi, Z

    A. Mohammadi, Z. Ossoulian, T. Golanbari, and K. Saaidi, Astrophys. Space Sci.359, 7 (2015)

    2015

  18. [18]

    Fairbairn and M

    M. Fairbairn and M. H. G. Tytgat, Phys. Lett.B546, 1 (2002), arXiv:hep-th/0204070 [hep-th]

    Pith/arXiv arXiv 2002

  19. [19]

    Aghamohammadi, A

    A. Aghamohammadi, A. Mohammadi, T. Golanbari, and K. Saaidi, Phys. Rev.D90, 084028 (2014), arXiv:1502.07578 [gr-qc]

    Pith/arXiv arXiv 2014

  20. [20]

    Bessada, W

    D. Bessada, W. H. Kinney, and K. Tzirakis, JCAP0909, 031 (2009), arXiv:0907.1311 [gr-qc]

    Pith/arXiv arXiv 2009

  21. [21]

    J. M. Weller, C. van de Bruck, and D. F. Mota, JCAP 1206, 002 (2012), arXiv:1111.0237 [astro-ph.CO]

    Pith/arXiv arXiv 2012

  22. [22]

    Nazavari, A

    N. Nazavari, A. Mohammadi, Z. Ossoulian, and K. Saaidi, Phys. Rev.D93, 123504 (2016), arXiv:1708.03676 [gr-qc]

    Pith/arXiv arXiv 2016

  23. [23]

    Amani, K

    R. Amani, K. Rezazadeh, A. Abdolmaleki, and K. Karami, Astrophys. J.853, 188 (2018), arXiv:1802.06075 [astro-ph.CO]

    Pith/arXiv arXiv 2018

  24. [24]

    Golanbari, A

    T. Golanbari, A. Mohammadi, and K. Saaidi, Phys. Dark Univ.27, 100456 (2020), arXiv:1808.07246 [gr-qc]

    Pith/arXiv arXiv 2020

  25. [25]

    Berera, Physical Review Letters75, 3218 (1995)

    A. Berera, Physical Review Letters75, 3218 (1995)

    1995

  26. [26]

    Berera, Nuclear Physics B585, 666 (2000)

    A. Berera, Nuclear Physics B585, 666 (2000)

    2000

  27. [27]

    Bastero-Gil and A

    M. Bastero-Gil and A. Berera, Phys. Rev.D71, 063515 (2005), arXiv:hep-ph/0411144 [hep-ph]

    Pith/arXiv arXiv 2005

  28. [28]

    Sayar, A

    K. Sayar, A. Mohammadi, L. Akhtari, and K. Saaidi, Phys. Rev.D95, 023501 (2017), arXiv:1708.01714 [gr-qc]

    Pith/arXiv arXiv 2017

  29. [29]

    Akhtari, A

    L. Akhtari, A. Mohammadi, K. Sayar, and K. Saaidi, Astropart. Phys.90, 28 (2017), arXiv:1710.05793 [astro- ph.CO]

    Pith/arXiv arXiv 2017

  30. [30]

    Sheikhahmadi, A

    H. Sheikhahmadi, A. Mohammadi, A. Aghamohammadi, T. Harko, R. Herrera, C. Corda, A. Abebe, and K. Saaidi, Eur. Phys. J.C79, 1038 (2019), arXiv:1907.10966 [gr-qc]

    Pith/arXiv arXiv 2019

  31. [31]

    Motohashi, A

    H. Motohashi, A. A. Starobinsky, and J. Yokoyama, JCAP1509, 018 (2015), arXiv:1411.5021 [astro-ph.CO]

    Pith/arXiv arXiv 2015

  32. [32]

    S. D. Odintsov, V. K. Oikonomou, and L. Sebastiani, Nucl. Phys.B923, 608 (2017), arXiv:1708.08346 [gr-qc]

    Pith/arXiv arXiv 2017

  33. [33]

    V. K. Oikonomou, Mod. Phys. Lett.A32, 1750172 (2017), arXiv:1706.00507 [gr-qc]

    Pith/arXiv arXiv 2017

  34. [34]

    Mohammadi, T

    A. Mohammadi, T. Golanbari, and K. Saaidi, Phys. Dark Univ.28, 100505 (2020), arXiv:1912.07006 [gr-qc]

    Pith/arXiv arXiv 2020

  35. [35]

    Mohammadi, T

    A. Mohammadi, T. Golanbari, S. Nasri, and K. Saaidi, Phys. Rev. D101, 123537 (2020), arXiv:2004.12137 [gr- qc]

    Pith/arXiv arXiv 2020

  36. [36]

    Mohammadi, Phys

    A. Mohammadi, Phys. Dark Univ.36, 101055 (2022), arXiv:2203.06643 [gr-qc]

    Pith/arXiv arXiv 2022

  37. [37]

    Adhikari, M

    R. Adhikari, M. R. Gangopadhyay, and Yogesh, Eur. Phys. J. C80, 899 (2020), arXiv:2002.07061 [astro- ph.CO]

    Pith/arXiv arXiv 2020

  38. [38]

    Zahoor, K

    Yogesh, M. Zahoor, K. A. Wani, and I. A. Bhat, Phys. Dark Univ.47, 101732 (2025), arXiv:2505.11429 [astro- ph.CO]

    Pith/arXiv arXiv 2025

  39. [39]

    Y. Yang, X. Ren, B. Wang, Y.-F. Cai, and E. N. Sari- dakis, Mon. Not. Roy. Astron. Soc.533, 2232 (2024), arXiv:2404.12140 [astro-ph.CO]

    Pith/arXiv arXiv 2024

  40. [40]

    Mohammadi and F

    A. Mohammadi and F. Kheirandish, Phys. Dark Univ.42, 101362 (2023)

    2023

  41. [41]

    Sahni, M

    V. Sahni, M. Sami, and T. Souradeep, Phys. Rev. D65, 023518 (2002), arXiv:gr-qc/0105121

    Pith/arXiv arXiv 2002

  42. [42]

    A. O. Barvinsky and A. Y. Kamenshchik, Phys. Lett. B 332, 270 (1994), arXiv:gr-qc/9404062

    Pith/arXiv arXiv 1994

  43. [43]

    J. L. Cervantes-Cota and H. Dehnen, Nucl. Phys. B442, 391 (1995), arXiv:astro-ph/9505069

    Pith/arXiv arXiv 1995

  44. [44]

    A. O. Barvinsky, A. Y. Kamenshchik, and A. A. Starobin- sky, JCAP11, 021 (2008), arXiv:0809.2104 [hep-ph]

    Pith/arXiv arXiv 2008

  45. [45]

    De Simone, M

    A. De Simone, M. P. Hertzberg, and F. Wilczek, Phys. Lett. B678, 1 (2009), arXiv:0812.4946 [hep-ph]

    Pith/arXiv arXiv 2009

  46. [46]

    I. D. Gialamas, A. Karam, A. Lykkas, and T. D. Pappas, Phys. Rev. D102, 063522 (2020), arXiv:2008.06371 [gr- qc]

    Pith/arXiv arXiv 2020

  47. [47]

    F. L. Bezrukov, A. Magnin, and M. Shaposhnikov, Phys. Lett. B675, 88 (2009), arXiv:0812.4950 [hep-ph]

    Pith/arXiv arXiv 2009

  48. [48]

    Kallosh and A

    R. Kallosh and A. Linde, JCAP06, 027 (2013), arXiv:1306.3211 [hep-th]

    Pith/arXiv arXiv 2013

  49. [49]

    A. O. Barvinsky, A. Y. Kamenshchik, C. Kiefer, A. A. Starobinsky, and C. F. Steinwachs, Eur. Phys. J. C72, 2219 (2012), arXiv:0910.1041 [hep-ph]

    Pith/arXiv arXiv 2012

  50. [50]

    Rubio, Front

    J. Rubio, Front. Astron. Space Sci.5, 50 (2019), arXiv:1807.02376 [hep-ph]

    Pith/arXiv arXiv 2019

  51. [51]

    I. D. Gialamas, A. Karam, T. D. Pappas, and E. Tomberg, Int. J. Geom. Meth. Mod. Phys.20, 2330007 (2023), arXiv:2303.14148 [gr-qc]

    Pith/arXiv arXiv 2023

  52. [52]

    I. D. Gialamas and K. Tamvakis, JCAP03, 042 (2023), arXiv:2212.09896 [gr-qc]

    Pith/arXiv arXiv 2023

  53. [53]

    I. D. Gialamas, A. Karam, T. D. Pappas, and V. C. Spanos, Phys. Rev. D104, 023521 (2021), arXiv:2104.04550 [astro-ph.CO]

    Pith/arXiv arXiv 2021

  54. [54]

    I. D. Gialamas, A. Karam, and A. Racioppi, JCAP11, 014 (2020), arXiv:2006.09124 [gr-qc]

    Pith/arXiv arXiv 2020

  55. [55]

    J. Kim, Z. Yang, and Y.-l. Zhang, (2025), arXiv:2503.16907 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  56. [56]

    J. Kim, X. Wang, Y.-l. Zhang, and Z. Ren, (2025), arXiv:2504.12035 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  57. [57]

    A. S. Koshelev, K. S. Kumar, and A. A. Starobinsky, Int. J. Mod. Phys. D29, 2043018 (2020), arXiv:2005.09550 [hep-th]

    Pith/arXiv arXiv 2020

  58. [58]

    Louiset al.(ACT), arXiv preprint (2025), arXiv:2503.14452 [astro-ph.CO]

    T. Louiset al.(ACT), arXiv preprint (2025), arXiv:2503.14452 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  59. [59]

    Calabreseet al.(ACT), arXiv preprint (2025), arXiv:2503.14454 [astro-ph.CO]

    E. Calabreseet al.(ACT), arXiv preprint (2025), arXiv:2503.14454 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  60. [60]

    Abdul Karimet al.(DESI), Phys

    M. Abdul Karimet al.(DESI), Phys. Rev. D112, 083514 (2025), arXiv:2503.14739 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  61. [61]

    P. J. E. Peebles and A. Vilenkin, Physical Review D59 (1999), 10.1103/physrevd.59.063505

    doi:10.1103/physrevd.59.063505 1999

  62. [63]

    Kallosh, A

    R. Kallosh, A. Linde, and D. Roest, (2025), arXiv:2503.21030 [hep-th]

    Pith/arXiv arXiv 2025

  63. [64]

    S. Aoki, H. Otsuka, and R. Yanagita, (2025), arXiv:2504.01622 [hep-ph]

    Pith/arXiv arXiv 2025

  64. [65]

    Dioguardi, A

    C. Dioguardi, A. J. Iovino, and A. Racioppi, Phys. Lett. B868, 139664 (2025), arXiv:2504.02809 [gr-qc]

    Pith/arXiv arXiv 2025

  65. [66]

    Salvio, (2025), arXiv:2504.10488 [hep-ph]

    A. Salvio, (2025), arXiv:2504.10488 [hep-ph]

    Pith/arXiv arXiv 2025

  66. [67]

    Brahma and J

    S. Brahma and J. Calder´ on-Figueroa, (2025), arXiv:2504.02746 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  67. [68]

    Q. Gao, Y. Gong, Z. Yi, and F. Zhang, (2025), arXiv:2504.15218 [astro-ph.CO]

    arXiv 2025

  68. [69]

    Drees and Y

    M. Drees and Y. Xu, (2025), arXiv:2504.20757 [astro- ph.CO]

    arXiv 2025

  69. [71]

    Yin, (2025), arXiv:2505.03004 [hep-ph]

    W. Yin, (2025), arXiv:2505.03004 [hep-ph]

    Pith/arXiv arXiv 2025

  70. [72]

    L. Liu, Z. Yi, and Y. Gong, (2025), arXiv:2505.02407 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  71. [73]

    I. D. Gialamas, T. Katsoulas, and K. Tamvakis, (2025), arXiv:2505.03608 [gr-qc]

    arXiv 2025

  72. [74]

    M. R. Haque, S. Pal, and D. Paul, (2025), arXiv:2505.01517 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  73. [75]

    M. R. Haque, S. Pal, and D. Paul, (2025), arXiv:2505.04615 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  74. [76]

    Dioguardi and A

    C. Dioguardi and A. Karam, (2025), arXiv:2504.12937 [gr-qc]

    Pith/arXiv arXiv 2025

  75. [77]

    I. D. Gialamas, A. Karam, A. Racioppi, and M. Raidal, (2025), arXiv:2504.06002 [astro-ph.CO]

    arXiv 2025

  76. [78]

    Mohammadi, Q

    Yogesh, A. Mohammadi, Q. Wu, and T. Zhu, JCAP10, 010 (2025), arXiv:2505.05363 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  77. [80]

    N. S. Risdianto, R. H. S. Budhi, N. Shobcha, and A. S. Adam, (2025), arXiv:2507.12868 [gr-qc]

    Pith/arXiv arXiv 2025

  78. [81]

    E. G. Ferreira, E. McDonough, L. Balkenhol, R. Kallosh, and L. Knox, (2025), arXiv:2507.12459 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  79. [82]

    Mohammadi, Yogesh, and A

    A. Mohammadi, Yogesh, and A. Wang, (2025), arXiv:2507.06544 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  80. [83]

    Pallis, (2025), arXiv:2507.02219 [hep-ph]

    C. Pallis, (2025), arXiv:2507.02219 [hep-ph]

    arXiv 2025

Showing first 80 references.