pith. sign in

arxiv: 2607.01177 · v1 · pith:5Z4GQKE4new · submitted 2026-07-01 · 🌀 gr-qc · astro-ph.CO· hep-th

Preheating and oscillon formation in Einstein-scalar-Gauss-Bonnet gravity

Areef Waeming , Josu C. Aurrekoetxea , Katy Clough , Pau Figueras , \'Aron D. Kov\'acs This is my paper

Pith reviewed 2026-07-02 08:17 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.COhep-th
keywords oscillonspreheatingGauss-Bonnet gravityeffective field theoryearly universescalar field dynamicsnumerical simulations
0
0 comments X

The pith

In Einstein-scalar-Gauss-Bonnet gravity oscillon properties stay largely unchanged during preheating but large couplings drive the leading-order EFT outside its regime of validity.

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

The paper investigates whether the leading higher-derivative Gauss-Bonnet corrections to scalar-tensor gravity modify the non-perturbative formation of oscillons, which are overdense scalar-field lumps that can arise after inflation. Numerical simulations of the coupled system track the growth, stability, and curvature evolution of these structures. The results show that oscillon characteristics remain similar to the standard case and black holes do not form generically, yet sufficiently strong couplings cause the spacetime curvature in the densest regions to push the evolution beyond the self-consistent domain of the truncated EFT.

Core claim

Whilst the properties of the oscillons are not significantly modified, and black holes do not generically form, for large couplings the period of formation can result in the evolution leaving the regime of validity of the EFT, at which point predictivity is lost. If the oscillons survive their formation, they tend to be stable and the EFT corrections remain bounded. The EFT breakdown is triggered by large curvature terms in the metric in the densest regions of the oscillon.

What carries the argument

Numerical integration of the Einstein-scalar-Gauss-Bonnet equations during preheating, monitoring the local curvature scale against the EFT cutoff.

If this is right

  • Oscillon formation proceeds with only minor changes to amplitude, frequency, and lifetime compared with Einstein gravity.
  • Black-hole collapse is not a typical outcome of the overdense regions that develop.
  • When the Gauss-Bonnet coupling is large the curvature in the oscillon cores grows enough to invalidate the leading EFT truncation.
  • Oscillons that persist after formation keep the higher-curvature corrections bounded.

Where Pith is reading between the lines

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

  • Methods that neglect local metric backreaction during oscillon formation are likely to underestimate the curvature-driven breakdown of the EFT.
  • Continuing the evolution past the reported breakdown requires inclusion of the next term in the EFT expansion.
  • Analogous curvature spikes could appear in other higher-curvature models when scalar fields undergo rapid non-linear clustering.

Load-bearing premise

The numerical solutions remain inside the regime where the leading-order EFT truncation stays self-consistent until the reported breakdown point.

What would settle it

A calculation showing that the next-order curvature invariants or higher-derivative scalar terms remain perturbatively small throughout the formation epoch even at the largest couplings considered.

Figures

Figures reproduced from arXiv: 2607.01177 by Areef Waeming, \'Aron D. Kov\'acs, Josu C. Aurrekoetxea, Katy Clough, Pau Figueras.

Figure 1
Figure 1. Figure 1: FIG. 1. Scalar potential [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. A snapshot of the density contrasts in the [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Evolution of the diagnostic quantities over time: The [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The different characteristic length scales of the weak [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. A 2D-slice from the simulation with positive [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Convergence test with [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
read the original abstract

Non-perturbative processes in the early universe may create overdense structures in scalar fields like the inflaton, called oscillons. In this work, we explore whether the leading order higher derivative contributions to the scalar-tensor theory change the formation and growth of these structures, and investigate the limits in which the effective field theory (EFT) description breaks down. We find that whilst the properties of the oscillons are not significantly modified, and black holes do not generically form, for large couplings the period of formation can result in the evolution leaving the regime of validity of the EFT, at which point predictivity is lost and the next order terms in the EFT should become relevant. If the oscillons survive their formation, they tend to be stable and the EFT corrections remain bounded. The EFT breakdown is triggered by large curvature terms in the metric in the densest regions of the oscillon, meaning that approximations of such modified theories that neglect the local backreaction and non-linear dynamics of the fields may miss important effects.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 2 minor

Summary. The manuscript investigates preheating and oscillon formation in Einstein-scalar-Gauss-Bonnet gravity via numerical simulations of the leading-order EFT. It claims that oscillon properties remain largely unmodified relative to GR, black holes do not form generically, and surviving oscillons are stable with bounded corrections; however, for sufficiently large Gauss-Bonnet couplings the formation epoch drives local curvatures high enough that the evolution exits the regime of validity of the leading-order truncation, after which predictivity is lost and higher-order terms become relevant. The breakdown is attributed to local backreaction in the densest regions rather than to global effects.

Significance. If the central numerical results hold, the work is significant because it supplies a concrete, simulation-based diagnostic for the breakdown of the EFT truncation during non-perturbative scalar dynamics. By showing that large local curvature can push the system outside the controlled regime even when global quantities remain moderate, the paper underscores the necessity of retaining full non-linear backreaction in modified-gravity preheating studies. The explicit identification of a stability window for oscillons inside the EFT is a useful positive result.

major comments (2)
  1. [Numerical Methods / Results] Numerical Methods / Results sections: the central claims rest on simulation outcomes (oscillon properties, absence of generic black-hole formation, and the threshold for EFT breakdown), yet the manuscript supplies no information on spatial or temporal resolution, convergence tests, error estimates, or validation against the GR limit. Without these diagnostics it is impossible to assess whether the reported curvature thresholds are numerically robust.
  2. [EFT validity discussion] § on EFT validity criterion: the statement that the system “leaves the regime of validity” is triggered by “large curvature terms,” but no quantitative threshold (e.g., comparison of the Gauss-Bonnet term to the Einstein-Hilbert term, or an estimate of the size of neglected higher-order operators) is provided. This makes the boundary between “still predictive” and “predictivity lost” difficult to reproduce or falsify.
minor comments (2)
  1. [Abstract] The abstract would be clearer if it briefly indicated the dimensionality and initial conditions of the simulations.
  2. [Introduction / Setup] Notation for the Gauss-Bonnet coupling and the scalar potential should be introduced once and used consistently; occasional redefinitions slow reading.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive report and the positive assessment of the work's significance. We address the two major comments point by point below. Both points identify areas where additional information will improve the manuscript, and we will incorporate the requested details in the revised version.

read point-by-point responses

  1. Referee: [Numerical Methods / Results] Numerical Methods / Results sections: the central claims rest on simulation outcomes (oscillon properties, absence of generic black-hole formation, and the threshold for EFT breakdown), yet the manuscript supplies no information on spatial or temporal resolution, convergence tests, error estimates, or validation against the GR limit. Without these diagnostics it is impossible to assess whether the reported curvature thresholds are numerically robust.

    Authors: We agree that explicit documentation of numerical resolution, convergence, and validation is necessary to establish robustness. In the revised manuscript we will add a new subsection to the Numerical Methods section that reports the spatial and temporal resolutions employed, the results of convergence tests at multiple resolutions, quantitative error estimates, and direct validation runs in the GR limit (vanishing Gauss-Bonnet coupling). These additions will allow readers to assess the reliability of the reported curvature thresholds. revision: yes

  2. Referee: [EFT validity discussion] § on EFT validity criterion: the statement that the system “leaves the regime of validity” is triggered by “large curvature terms,” but no quantitative threshold (e.g., comparison of the Gauss-Bonnet term to the Einstein-Hilbert term, or an estimate of the size of neglected higher-order operators) is provided. This makes the boundary between “still predictive” and “predictivity lost” difficult to reproduce or falsify.

    Authors: We accept that a quantitative criterion is required for reproducibility. In the revised manuscript we will define an explicit threshold, for example by monitoring the local ratio of the Gauss-Bonnet term to the Einstein-Hilbert term (or an estimate of the magnitude of the next-order operators) and will apply this diagnostic to the simulation outputs. This will replace the current qualitative statement with a reproducible, falsifiable boundary between the controlled and uncontrolled regimes. revision: yes

Circularity Check

0 steps flagged

No significant circularity; results are direct numerical outputs

full rationale

The paper performs numerical evolutions of the Einstein-scalar-Gauss-Bonnet system to study oscillon formation and EFT validity. All reported outcomes (oscillon properties unmodified, no generic black hole formation, EFT breakdown at large curvature) are stated as direct simulation results rather than predictions derived from fitted parameters, self-definitions, or load-bearing self-citations. No equations reduce the conclusions to input assumptions by construction, and the analysis explicitly tracks the regime of validity without smuggling ansatze or renaming known results. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities; the work implicitly assumes the validity of the truncated EFT action and the accuracy of the numerical scheme for the reported regime.

pith-pipeline@v0.9.1-grok · 5734 in / 1095 out tokens · 21714 ms · 2026-07-02T08:17:54.639933+00:00 · methodology

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

136 extracted references · 121 canonical work pages · 48 internal anchors

  1. [1]

    (although they will be excited dynamically during the subsequent evolution). Evolution To obtain a well-posed initial value problem for (1) and to solve the equations of motion of this theory numeri- cally, it is necessary to find an appropriate gauge choice and gauge-fixing procedure [113, 114, 123]. Stable nu- merical simulations further require the add...

    2023

  2. [2]

    A. H. Guth, Phys. Rev. D23, 347 (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]

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

    1980

  6. [6]

    A. D. Linde, Phys. Lett. B129, 177 (1983)

    1983

  7. [7]

    Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation

    E. Komatsu, K. M. Smith, J. Dunkley, C. L. Bennett, B. Gold, G. Hinshaw, N. Jarosik, D. Larson, M. R. Nolta, L. Page, D. N. Spergel, M. Halpern, R. S. Hill, A. Kogut, M. Limon, S. S. Meyer, N. Odegard, G. S. Tucker, J. L. Weiland, E. Wollack, and E. L. Wright, ApJS192, 18 (2011), arXiv:1001.4538 [astro-ph.CO]. 2 www.grtlcollaboration.org

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  8. [8]

    Planck 2018 results. VI. Cosmological parameters

    N. Aghanimet al.(Planck), Astron. Astrophys.641, A6 (2020), [Erratum: Astron.Astrophys. 652, C4 (2021)], arXiv:1807.06209 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2020

  9. [9]

    Planck 2018 results. X. Constraints on inflation

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

    work page internal anchor Pith review Pith/arXiv arXiv 2020

  10. [10]

    The Atacama Cosmology Telescope: DR6 Power Spectra, Likelihoods and $\Lambda$CDM Parameters

    T. Louiset al.(Atacama Cosmology Telescope), JCAP 11, 062, arXiv:2503.14452 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv

  11. [11]

    The Atacama Cosmology Telescope: DR6 Constraints on Extended Cosmological Models

    E. Calabreseet al.(Atacama Cosmology Telescope), JCAP11, 063, arXiv:2503.14454 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv

  12. [12]

    SPT-3G D1: CMB temperature and polarization power spectra and cosmology from 2019 and 2020 observations of the SPT-3G Main field

    E. Camphuiset al.(SPT-3G), Phys. Rev. D113, 083504 (2026), arXiv:2506.20707 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  13. [13]

    Superconformal Inflationary $\alpha$-Attractors

    R. Kallosh, A. Linde, and D. Roest, JHEP11, 198, arXiv:1311.0472 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv

  14. [14]

    Non-minimal Inflationary Attractors

    R. Kallosh and A. Linde, JCAP10, 033, arXiv:1307.7938 [hep-th]. 9

    work page internal anchor Pith review Pith/arXiv arXiv

  15. [15]

    Large Field Inflation and Double $\alpha$-Attractors

    R. Kallosh, A. Linde, and D. Roest, JHEP08, 052, arXiv:1405.3646 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv

  16. [16]

    Mohammadi, Q

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

    work page arXiv

  17. [17]

    Y. Zhu, Q. Gao, Y. Gong, and Z. Yi, Eur. Phys. J. C 85, 1227 (2025), arXiv:2508.09707 [astro-ph.CO]

    work page arXiv 2025

  18. [18]

    S. D. Odintsov and V. K. Oikonomou, Phys. Lett. B 868, 139779 (2025), arXiv:2506.08193 [gr-qc]

    work page arXiv 2025

  19. [19]

    Zahoor, S

    M. Zahoor, S. Khan, and I. A. Bhat, JHEAp49, 100458 (2026), arXiv:2507.18684 [astro-ph.CO]

    work page arXiv 2026

  20. [20]

    Addazi, Y

    A. Addazi, Y. Aldabergenov, and S. V. Ketov, Phys. Lett. B869, 139883 (2025), arXiv:2505.10305 [gr-qc]

    work page arXiv 2025

  21. [21]

    S. D. Odintsov and T. Paul, Phys. Lett. B870, 139930 (2025), arXiv:2508.11377 [gr-qc]

    work page arXiv 2025

  22. [22]

    Lovelock, J

    D. Lovelock, J. Math. Phys.12, 498 (1971)

    1971

  23. [23]

    Zwiebach, Phys

    B. Zwiebach, Phys. Lett. B156, 315 (1985)

    1985

  24. [24]

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

    1985

  25. [25]

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

    1974

  26. [26]

    Reheating after Inflation

    L. Kofman, A. D. Linde, and A. A. Starobinsky, Phys. Rev. Lett.73, 3195 (1994), arXiv:hep-th/9405187

    work page internal anchor Pith review Pith/arXiv arXiv 1994

  27. [27]

    Towards the Theory of Reheating After Inflation

    L. Kofman, A. D. Linde, and A. A. Starobinsky, Phys. Rev. D56, 3258 (1997), arXiv:hep-ph/9704452

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  28. [28]

    Albrecht, P

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

    1982

  29. [29]

    J. H. Traschen and R. H. Brandenberger, Phys. Rev. D 42, 2491 (1990)

    1990

  30. [30]

    M. A. Amin, M. P. Hertzberg, D. I. Kaiser, and J. Karouby, Int. J. Mod. Phys. D24, 1530003 (2014), arXiv:1410.3808 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  31. [31]

    I. L. Bogolyubsky and V. G. Makhankov, JETP Lett. 24, 12 (1976)

    1976

  32. [32]

    I. L. Bogolyubsky and V. G. Makhankov, Pisma Zh. Eksp. Teor. Fiz.25, 120 (1977)

    1977

  33. [33]

    Gleiser, Phys

    M. Gleiser, Phys. Rev. D49, 2978 (1994), arXiv:hep- ph/9308279

    work page arXiv 1994

  34. [34]

    E. J. Copeland, M. Gleiser, and H. R. Muller, Phys. Rev. D52, 1920 (1995), arXiv:hep-ph/9503217

    work page internal anchor Pith review Pith/arXiv arXiv 1920

  35. [35]

    I-balls

    S. Kasuya, M. Kawasaki, and F. Takahashi, Phys. Lett. B559, 99 (2003), arXiv:hep-ph/0209358

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  36. [36]

    P. M. Saffin and A. Tranberg, JHEP01, 030, arXiv:hep- th/0610191

    work page arXiv

  37. [37]

    M. P. Hertzberg, Phys. Rev. D82, 045022 (2010), arXiv:1003.3459 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  38. [38]

    Radiation and Relaxation of Oscillons

    P. Salmi and M. Hindmarsh, Phys. Rev. D85, 085033 (2012), arXiv:1201.1934 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  39. [39]

    Gleiser and M

    M. Gleiser and M. Krackow, Phys. Rev. D100, 116005 (2019), arXiv:1906.04070 [hep-th]

    work page arXiv 2019

  40. [40]

    Antusch, F

    S. Antusch, F. Cefal` a, and F. Torrent´ ı, JCAP10, 002, arXiv:1907.00611 [hep-ph]

    work page arXiv 1907

  41. [41]

    M. Ibe, M. Kawasaki, W. Nakano, and E. Sonomoto, JHEP04, 030, arXiv:1901.06130 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 1901

  42. [42]

    Zhang, M

    H.-Y. Zhang, M. A. Amin, E. J. Copeland, P. M. Saffin, and K. D. Lozanov, JCAP07, 055, arXiv:2004.01202 [hep-th]

    work page arXiv 2004

  43. [43]

    van Dissel, O

    F. van Dissel, O. Pujolas, and E. I. Sfakianakis, JHEP07, 194, [Erratum: JHEP 04, 191 (2025)], arXiv:2303.16072 [hep-th]

    work page arXiv 2025

  44. [44]

    Zhou, Rept

    S.-Y. Zhou, Rept. Prog. Phys.88, 046901 (2025), arXiv:2411.16604 [hep-th]

    work page arXiv 2025

  45. [45]

    G. N. Felder and I. Tkachev, Comput. Phys. Commun. 178, 929 (2008), arXiv:hep-ph/0011159

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  46. [46]

    G. N. Felder and L. Kofman, Phys. Rev. D75, 043518 (2007), arXiv:hep-ph/0606256

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  47. [47]

    A. V. Frolov, JCAP11, 009, arXiv:0809.4904 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv

  48. [48]

    M. A. Amin and D. Shirokoff, Phys. Rev. D81, 085045 (2010), arXiv:1002.3380 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  49. [49]

    M. A. Amin, R. Easther, and H. Finkel, JCAP12, 001, arXiv:1009.2505 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv

  50. [50]

    M. A. Amin, R. Easther, H. Finkel, R. Flauger, and M. P. Hertzberg, Phys. Rev. Lett.108, 241302 (2012), arXiv:1106.3335 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  51. [51]

    M. A. Amin, Phys. Rev. D87, 123505 (2013), arXiv:1303.1102 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  52. [52]

    K. D. Lozanov and M. A. Amin, Phys. Rev. D90, 083528 (2014), arXiv:1408.1811 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  53. [53]

    Impact of other scalar fields on oscillons after hilltop inflation

    S. Antusch and S. Orani, JCAP03, 026, arXiv:1511.02336 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv

  54. [54]

    Parametric resonance after hilltop inflation caused by an inhomogeneous inflaton field

    S. Antusch, F. Cefala, D. Nolde, and S. Orani, JCAP 02, 044, arXiv:1510.04856 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv

  55. [55]

    M. P. DeCross, D. I. Kaiser, A. Prabhu, C. Prescod- Weinstein, and E. I. Sfakianakis, Phys. Rev. D97, 023526 (2018), arXiv:1510.08553 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  56. [56]

    M. P. DeCross, D. I. Kaiser, A. Prabhu, C. Prescod- Weinstein, and E. I. Sfakianakis, Phys. Rev. D97, 023527 (2018), arXiv:1610.08868 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  57. [57]

    M. P. DeCross, D. I. Kaiser, A. Prabhu, C. Prescod- Weinstein, and E. I. Sfakianakis, Phys. Rev. D97, 023528 (2018), arXiv:1610.08916 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  58. [58]

    Inflaton condensate fragmentation: Analytical conditions and application to $\alpha$-attractor models

    J. Kim and J. McDonald, Phys. Rev. D95, 123537 (2017), arXiv:1702.08777 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  59. [59]

    K. D. Lozanov and M. A. Amin, Phys. Rev. D97, 023533 (2018), arXiv:1710.06851 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  60. [60]

    Musoke, S

    N. Musoke, S. Hotchkiss, and R. Easther, Phys. Rev. Lett.124, 061301 (2020), arXiv:1909.11678 [astro- ph.CO]

    work page arXiv 2020

  61. [61]

    J. C. Niemeyer and R. Easther, JCAP07, 030, arXiv:1911.01661 [astro-ph.CO]

    work page arXiv 1911

  62. [62]

    Nguyen, J

    R. Nguyen, J. van de Vis, E. I. Sfakianakis, J. T. Giblin, and D. I. Kaiser, Phys. Rev. Lett.123, 171301 (2019), arXiv:1905.12562 [hep-ph]

    work page arXiv 2019

  63. [63]

    Martin, T

    J. Martin, T. Papanikolaou, and V. Vennin, JCAP01, 024, arXiv:1907.04236 [astro-ph.CO]

    work page arXiv 1907

  64. [64]

    D. G. Figueroa, A. Florio, F. Torrenti, and W. Valken- burg, JCAP04, 035, arXiv:2006.15122 [astro-ph.CO]

    work page arXiv 2006

  65. [65]

    D. G. Figueroa, A. Florio, F. Torrenti, and W. Valken- burg, Comput. Phys. Commun.283, 108586 (2023), arXiv:2102.01031 [astro-ph.CO]

    work page arXiv 2023

  66. [66]

    Eggemeier, J

    B. Eggemeier, J. C. Niemeyer, and R. Easther, Phys. Rev. D103, 063525 (2021), arXiv:2011.13333 [astro- ph.CO]

    work page arXiv 2021

  67. [67]

    Iarygina, E

    O. Iarygina, E. I. Sfakianakis, D.-G. Wang, and A. Ach´ ucarro, (2020), arXiv:2005.00528 [astro-ph.CO]

    work page arXiv 2020

  68. [68]

    Sang and Q.-G

    Y. Sang and Q.-G. Huang, Phys. Lett. B823, 136781 (2021), arXiv:2012.14697 [hep-th]

    work page arXiv 2021

  69. [69]

    Martin, T

    J. Martin, T. Papanikolaou, L. Pinol, and V. Vennin, JCAP05, 003, arXiv:2002.01820 [astro-ph.CO]

    work page arXiv 2002

  70. [70]

    van de Vis, R

    J. van de Vis, R. Nguyen, E. I. Sfakianakis, J. T. Gib- lin, and D. I. Kaiser, Phys. Rev. D102, 043528 (2020), arXiv:2005.00433 [astro-ph.CO]

    work page arXiv 2020

  71. [71]

    J. Kost, C. S. Shin, and T. Terada, Phys. Rev. D105, 043508 (2022), arXiv:2105.06939 [hep-ph]

    work page arXiv 2022

  72. [72]

    M. A. G. Garcia, K. Kaneta, Y. Mambrini, K. A. Olive, and S. Verner, JCAP03(03), 016, arXiv:2109.13280 [hep-ph]

    work page arXiv

  73. [73]

    Eggemeier, B

    B. Eggemeier, B. Schwabe, J. C. Niemeyer, and R. East- her, Phys. Rev. D105, 023516 (2022), arXiv:2110.15109 [astro-ph.CO]. 10

    work page arXiv 2022

  74. [74]

    Kim and J

    J. Kim and J. McDonald, Phys. Rev. D105, 063508 (2022), arXiv:2111.12474 [astro-ph.CO]

    work page arXiv 2022

  75. [75]

    D. G. Figueroa, A. Florio, N. Loayza, and M. Pieroni, Phys. Rev. D106, 063522 (2022), arXiv:2202.05805 [astro-ph.CO]

    work page arXiv 2022

  76. [76]

    Mahbub and S

    R. Mahbub and S. S. Mishra, Phys. Rev. D108, 063524 (2023), arXiv:2303.07503 [astro-ph.CO]

    work page arXiv 2023

  77. [77]

    Shafi, E

    M. Shafi, E. J. Copeland, R. Mahbub, S. S. Mishra, and S. Basak, JCAP10, 082, arXiv:2406.00108 [hep-ph]

    work page arXiv

  78. [78]

    X.-B. Sui, J. Liu, and R.-G. Cai, Phys. Rev. D111, 123503 (2025), arXiv:2412.08057 [astro-ph.CO]

    work page arXiv 2025

  79. [79]

    T. Jia, Y. Sang, and X. Zhang, Phys. Rev. D111, 083531 (2025), arXiv:2409.04046 [astro-ph.CO]

    work page arXiv 2025

  80. [80]

    Baeza-Ballesteros, D

    J. Baeza-Ballesteros, D. G. Figueroa, A. Florio, J. Lizarraga, N. Loayza, K. Marschall, T. Opferkuch, B. A. Stefanek, F. Torrent´ ı, and A. Urio, (2025), arXiv:2512.15627 [astro-ph.CO]

    work page arXiv 2025

Showing first 80 references.