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REVIEW 4 major objections 5 minor 1 cited by

Numerical simulations on First-order phase transition through thermal fluctuation

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Thermal fluctuations alone can drive a first-order phase transition in the early universe, with oscillons seeding bubbles that collide and emit gravitational waves.

desk verdict A genuinely new 3+1D simulation of spontaneous bubble nucleation and GWs from thermal initial conditions, but the no-heat-bath setup means the 'thermal fluctuation' interpretation is provisional until a control run is done. read the letter →

arxiv 2505.15360 v1 pith:K3MXX6AP submitted 2025-05-21 hep-ph astro-ph.COhep-th

Ligong Bian , Yuefeng Di , Yongtao Jia , Yang Li , Kehao Zeng This is my paper
classification hep-phastro-ph.COhep-th
keywords first-orderphasetransitionthermalfluctuationsoscillonsbubblenucleationgravitationalwaveslatticesimulationfalsevacuumdecayearlyuniverse
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 claims that a first-order phase transition in the early universe can be completed by thermal fluctuations alone, without placing bubble seeds in the initial conditions. In a (3+1)-dimensional lattice simulation of a real scalar field initialized with a Bose-Einstein spectrum at temperature slightly above the field mass, the authors observe that long-lived localized field lumps called oscillons form first, then bubble-like configurations nucleate, expand, and collide to finish the transition. They find the false vacuum fraction follows the double-exponential law $h(t) = \exp(-\exp(\beta(t - t_f)))$ and that the produced gravitational waves scale as $(H R_* \Omega_{\rm vac})^2$, matching the quantum-tunneling route. If the mechanism holds, thermal noise by itself can convert the symmetric vacuum into the broken one and source a gravitational wave background.

What carries the argument

The central machinery is the (3+1)-dimensional lattice simulation of a single real scalar field with potential $V(\phi) = \frac{1}{2} M^2 \phi^2 + \frac{1}{3} \delta \phi^3 + \frac{1}{4} \lambda \phi^4$, initialized with a Bose-Einstein thermal spectrum at temperatures $T_i = 1.1 M$ to $1.4 M$ and then evolved as an isolated classical field in a non-expanding Minkowski spacetime using a second-order leap-frog integration scheme. The bubble identification algorithm uses primary and secondary detection points to distinguish newly nucleated bubbles from the expansion of existing ones. The false vacuum fraction $h(t) = \exp(-\exp(\beta(t - t_f)))$ and the nucleation rate $p(t) = p_f \exp(\beta(t - t_f))$ are extracted from the simulation data and fitted to the theory.

What would settle it

Run the same lattice simulation with the field coupled to a Langevin thermostat that keeps the temperature at $T_i$ throughout the evolution; if bubbles no longer appear automatically near $T_i = 1.1$–$1.4\,M$, or the false vacuum fraction departs from $\exp(-\exp(\beta(t - t_f)))$, then the isolated-initial-condition setup is the load-bearing ingredient rather than thermal fluctuation itself.

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Extended reading notes

Core claim

On the paper's own terms, the discovery is that the first-order phase transition can occur via thermal fluctuation: starting from a hot scalar field in a false vacuum, the simulation shows that the field spontaneously produces oscillons, which act as precursors to vacuum bubbles. The bubbles expand and collide, completing the transition without any nucleation events being inserted by hand. The paper further establishes that the resulting false vacuum fraction and bubble number density agree with the standard nucleation theory, with the nucleation rate $p(t) = p_f \exp(\beta(t - t_f))$ and $p_f / M^4 \approx (\beta / M)^{2.44}$. The gravitational wave spectrum from the bubble collisions has peak amplitude of order $(H R_* \Omega_{\rm vac})^2$, the same scaling found in quantum-tunneling simulations of first-order phase transitions.

Load-bearing premise

The thermal bath is only realized as the initial condition: after that, the field evolves in isolation with no heat bath and no Hubble expansion, so thermal fluctuations are not continuously regenerated as they would be in the early universe.

Editorial extensions

If this is right

  • Thermal fluctuations alone can complete a first-order phase transition, so gravitational-wave simulations need not inject bubble profiles or nucleation rates by hand.
  • The transition proceeds through four stages: oscillon formation, bubble nucleation, bubble expansion, and bubble collision, providing a concrete microscopic sequence.
  • The false vacuum fraction follows the standard double-exponential form, so the same phenomenological fitting parameters ($\beta$ and $t_f$) apply to thermal-fluctuation-driven transitions.
  • The gravitational wave amplitude from the thermal route is comparable to the quantum-tunneling route, scaling as $(H R_* \Omega_{\rm vac})^2$.
  • Higher initial temperatures shorten the transition and create more oscillons and bubbles, which raises the gravitational wave peak and changes its duration.

Reading between the lines

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

  • In a realistic early-universe setting the plasma would keep re-thermalizing the field; the same simulations run with a dynamical heat bath would show whether the oscillon-bubble sequence survives continuous thermal noise.
  • The oscillon-bubble link may be generic for barrier potentials: oscillons localize energy and can serve as nucleation seeds, so models with different barrier shapes might exhibit the same precursor dynamics.
  • Adding Hubble expansion via a friction term $3H \dot{\phi}$ would test whether the transition completes when $H$ is not negligible compared to $M$, connecting the proof-of-principle to inflation-era or electroweak-scale conditions.
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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

4 major / 5 minor

Summary. The paper reports (3+1)-dimensional lattice simulations of a real scalar field with a cubic-plus-quartic potential in Minkowski spacetime, starting from thermal (Bose-Einstein) initial field configurations at temperatures T_i = 1.1–1.4 M. The authors observe that oscillons form first and then trigger expanding bubble-like regions that collide and complete the transition from the false vacuum. They extract the false-vacuum fraction h(t), fit it to exp(-exp(beta(t-t_f))), count bubbles with a detection algorithm, fit the bubble number density to an integral of p(t) = p_f exp(beta(t-t_f)), and report a power-law relation p_f/M^4 ≈ (beta/M)^2.44. They also compute gravitational-wave spectra and quote an amplitude Ω_GW ≈ O(10^-3)(H R_* Ω_vac)^2. The central qualitative claim is that thermally induced fluctuations alone can spontaneously produce bubble nucleation in this model without externally placed seeds.

Significance. If the central claim were established, the paper would provide the first (3+1)-dimensional demonstration that a first-order phase transition can be completed by thermal fluctuations alone, with a clear oscillon-precursor stage, and would connect that dynamics to a phenomenological false-vacuum-fraction formula and to gravitational-wave amplitudes. The use of open-source CosmoLattice and the direct visualization of oscillons-before-bubbles in 3D snapshots (Fig. S3) are strengths. However, the quantitative conclusions currently rest on several fitted functional forms and on a one-time thermal initial condition, so the significance is contingent on additional control tests.

major comments (4)
  1. [Supplemental Material, Eq. (S4) and Eq. (S5); Simulation framework] The simulation has no heat bath: thermal fluctuations enter only as the initial Gaussian/Bose-Einstein spectrum (Eq. S5), after which the field evolves deterministically under Eq. (S4) in a non-expanding box. In a real cosmological plasma, thermal fluctuations are continuously regenerated by interactions with the plasma. The observed oscillon-bubble sequence may therefore be generic nonlinear relaxation from a large initial fluctuation rather than thermally activated escape. The authors should add a Langevin-type simulation with explicit noise and dissipation (or otherwise couple to a thermal bath) and show that the false-vacuum fraction, nucleation rate, and GW spectrum are unchanged. This is a load-bearing point because the manuscript's central claim is that the transition occurs 'through thermal fluctuation' in the early universe.
  2. [Numerical results, Figs. 3–5] The 'precise agreement' with first-order nucleation theory is partly a consistency check of fits: h(t)=exp(-exp(beta(t-t_f))) is fitted with free beta and t_f, the nucleation rate p(t)=p_f exp(beta(t-t_f)) is assumed to share the same beta, and the p_f versus beta power law is then fitted to the extracted values. The reader should be told explicitly which quantities are predicted and which are fitted, and the goodness of fit should be quantified (e.g., chi-square or residual plots) rather than asserted. Otherwise the p_f ∝ beta^2.44 result could absorb the assumed functional forms.
  3. [Numerical results, Fig. 6] Fig. 6 shows that the beta and t_f extracted from h(t) and from the bubble-count fit n_b(t) disagree increasingly as T_i grows. The text attributes this to 'bubble collision dynamics and the thermal fluctuation effects' without a quantitative test. Since the manuscript claims a 'well-defined functional' and 'precise agreement' with nucleation theory, this discrepancy must be quantified and either explained or used to bound the regime of validity of the Gumbel-form fit.
  4. [Supplemental Material, Bubble identification algorithm] The bubble number density n_b(t) — and hence p_f and the GW normalization R_* — depends on the detection parameters R, phi_1 ~ 0.9 v, and phi_2 ~ 0.1 v. No convergence or robustness study is shown. The authors should demonstrate that the extracted beta, p_f, and R_* are insensitive to reasonable variations in R and the thresholds, especially because the linear relation in Fig. 2 and the power law in Fig. 5 are based entirely on this algorithm.
minor comments (5)
  1. [Abstract and Introduction] The phrase 'appear proceeded by oscillons' should be 'appear preceded by oscillons'; the typo appears in the abstract and introduction.
  2. [Simulation framework] 'Minkovsky space-time' should be 'Minkowski spacetime'; also the rescaled variables introduced in the main text (δ̃x, δ̃t) are not defined before first use.
  3. [Numerical results, Fig. 3 caption] The caption states 'The vertical dotted line corresponds to the time t=t_f and the horizontal dotted line corresponds to h=1/e', but the figure uses multiple curves; please clarify which curve the dotted lines refer to or indicate that they apply to each curve.
  4. [Numerical results, Fig. 6] The figure legend and text do not specify whether the error bars are statistical or systematic; please add a definition.
  5. [Supplemental Material, Initial conditions] Eq. (S5) uses both a physical frequency w_k and a rescaled lattice variable; the rescaling convention for k and T_i in the lattice code should be stated explicitly so the reported T_i = 1.1–1.4 M can be reproduced.

Circularity Check

1 steps flagged · score 4.0 of 10

Fit-consistency circularity in the 'precise agreement' claim; central oscillon-to-bubble simulation is independent.

  1. fitted input called prediction [Numerical results (false vacuum fraction fit, Fig. 3) and Conclusion and discussion]
    "Like the quantum tunneling case [35], we use the typical function h^th_FV = exp(−exp(β(t−t_f ))) (the dashed line in Fig. 3) to fit the false vacuum fraction of the thermal fluctuation one ... we have quantitatively established that the false vacuum fraction follows a well-defined functional which depends on the PT duration parameter β, and is in precise agreement with theoretical predictions from the first-order PT nucleation theory."

    The double-exponential form is the theoretical prediction for a false-vacuum fraction under an exponentially growing nucleation rate, but the paper inserts it as the fitting ansatz and lets β and t_f be free parameters from the very simulation data it then claims to confirm. The reported 'precise agreement' therefore measures how well a two-parameter fit describes h_sim, not an independent prediction of the nucleation theory. The same ansatz is reused for the bubble count n_b(t)=∫p(t')h(t')dt' with p(t)=p_f exp[β(t−t_f)], and the p_f–β relation is a power-law fit to the extracted values; these quantitative outputs are fit-consistency results rather than predictions forced by the simulation alone.

full rationale

The central visual and numerical result—spontaneous formation of oscillon-like precursors from the initial thermal spectrum, followed by expanding true-vacuum bubbles that collide—is a direct simulation output that does not reduce to any fitted input or self-citation. The bubble detection algorithm is independent of the Gumbel fit. No load-bearing uniqueness theorem or prior-work ansatz is imported from the authors; references [12–21, 28–32] supply simulation methods and potential forms, not the claimed result. The main qualification is that 'thermal fluctuation' is implemented only as a one-time Bose-Einstein initial condition (Eq. S5), followed by deterministic Minkowski evolution (Eq. S4) with no coupling to an external heat bath; this is a physical limitation that should be scored as correctness/falsifiability risk, not circularity, because the simulation does not define thermal fluctuation in terms of the observed bubbles. The h(t) and p(t) analyses do contain a fitted-input element: the double-exponential form is assumed and then reported as 'precise agreement,' so the quantitative theory-agreement claim is partly self-consistent rather than independently predictive. On the 0–10 scale this warrants a moderate score of 4.

Assumptions & free parameters 5 free parameters · 7 assumptions · 0 invented entities

The quantitative results rest on fitted parameters (beta, t_f, p_f, power-law exponent) and hand-chosen bubble-detection thresholds, plus the modeling assumption that an isolated initial thermal spectrum in Minkowski space represents cosmological thermal fluctuations. No new particles, forces, or conserved quantities are introduced; the oscillons are a known phenomenon from the cited literature.

free parameters (5)
  • beta (transition duration parameter) = Not quoted; varies with T_i, shown in Fig. 6
    Free parameter in the assumed fit h(t)=exp(-exp(beta(t-tf))); extracted from both h(t) and n_b(t). The paper calls it the PT duration parameter.
  • t_f (transition end time) = Not quoted; varies with T_i, defined by h=1/e
    Free parameter in the same h(t) fit, marking the time at which the false vacuum fraction reaches 1/e.
  • p_f (nucleation rate amplitude) = Not quoted; extracted from n_b(t) fits, shown in Fig. 5
    Free amplitude in the assumed nucleation rate p(t)=p_f exp[beta(t-tf)]; used to define the false vacuum decay rate.
  • Power-law exponent in p_f vs beta relation = 2.44
    Obtained by fitting p_f/M^4 against beta/M in Fig. 5; no error bars and no derivation from first principles.
  • Bubble detection parameters R, phi1, phi2 = R comparable to bubble radius; phi1~0.9v; phi2~0.1v
    Hand-chosen thresholds in the bubble-counting algorithm; no sensitivity check, so derived bubble densities and rates may depend on these values.
assumptions (7)
  • domain assumption The scalar potential V(phi)=1/2 M^2 phi^2 + 1/3 delta phi^3 + 1/4 lambda phi^4 with delta=-1.632 and lambda=0.5 is a representative model for a cosmological first-order phase transition.
    The potential is taken from Refs. [15,17,28-32]; the transition dynamics and GW spectrum depend on this specific shape and barrier.
  • domain assumption Equation S5 Bose-Einstein spectrum at initial temperature T_i, evolved in isolation, represents thermal fluctuations during the phase transition.
    The thermal bath is not sustained during evolution; there is no stochastic noise or friction in the equation of motion. The limitation is not addressed.
  • domain assumption The effective mass m_eff in the thermal spectrum (S5) is known, presumably m_eff=M, though not stated.
    Equation S5 defines w_k=sqrt(k^2+m_eff^2), but the paper never specifies m_eff; the initial fluctuation spectrum, and hence nucleation, depends on this choice.
  • domain assumption Minkowski spacetime and M^-1 << H^-1 justify neglecting Hubble expansion.
    The simulation is in a non-expanding background; the validity condition is asserted but not checked quantitatively.
  • ad hoc to paper The false vacuum fraction is described by h(t)=exp(-exp(beta(t-tf))).
    This functional form is assumed and fitted; it is not derived from the potential or thermal spectrum.
  • ad hoc to paper The bubble nucleation rate has the form p(t)=p_f exp[beta(t-tf)].
    Standard exponential nucleation parameterization used to fit n_b(t); both parameters are fitted to the simulation data.
  • ad hoc to paper The bubble-detection algorithm with thresholds phi1~0.9v, phi2~0.1v and spacing R correctly identifies new nucleation sites.
    The algorithm is described in detail, but its accuracy is not validated against a known configuration or tested for threshold sensitivity.

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Cite this review

Pith. "Pith review of Numerical simulations on First-order phase transition through thermal fluctuation." pith.science (2026). https://pith.science/paper/K3MXX6AP

@misc{pith2026250515360,
  author       = {Pith},
  title        = {Pith review of: Numerical simulations on First-order phase transition through thermal fluctuation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/K3MXX6AP}},
  note         = {Machine review of arXiv:2505.15360}
}
read the original abstract

In this Letter, we numerically present the possibility of the first-order phase transition occurring through the thermal fluctuation in the early universe. We find that when the temperature is slightly higher than the mass scale of the background field, the bubble-like field configurations appear proceeded by oscillons, which expand and collide to finish the phase transition. We provide the false vacuum decay rate and the accompanied gravitational waves. We also present the vacuum phase transition comparison of the quantum tunneling case and thermal fluctuation case.

Figures

Figures reproduced from arXiv: 2505.15360 by the authors.

Figure 2
Figure 2. FIG. 2. Bubble number density versus initial energy density [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 1
Figure 1. FIG. 1. The slices along the [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 4
Figure 4. FIG. 4. The temporal evolution of bubble number density [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗
Figures from the paper (3 more)
Figure 5
Figure 5. Figure 5: and fit it using the power law relation pf /M4 ≈ (β/M) 2.44. It can be seen that both pf and β exhibit growth with increasing Ti . The expressions for h(t) and nb(t) both have parameters β and pf , so we can extract these parameters from two different fits and compare …
Figure 7
Figure 7. Figure 7: FIG. 7. The power spectrum of the scalar field under the ini [PITH_FULL_IMAGE:figures/full_fig_p003_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. The power spectrum of GWs in early time [PITH_FULL_IMAGE:figures/full_fig_p004_8.png]

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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. Dynamics of nucleation in thermal phase transitions

    hep-th 2026-07 conditional novelty 7.0 of 10

    The thermal nucleation rate is the transition-state estimate multiplied by one minus the re-crossing probability, and oscillons make that correction large.

Reference graph

Works this paper leans on

35 extracted references · 3 canonical work pages · cited by 1 Pith paper

  1. [1]

    Athron, C

    P. Athron, C. Bal´ azs, A. Fowlie, L. Morris, and L. Wu, Prog. Part. Nucl. Phys.135, 104094 (2024), arXiv:2305.02357 [hep-ph]

    arXiv 2024

  2. [2]

    Arkani-Hamed, T

    N. Arkani-Hamed, T. Han, M. Mangano, and L.-T. Wang, Phys. Rept.652, 1 (2016), arXiv:1511.06495 [hep- ph]

    arXiv 2016

  3. [3]

    D. E. Morrissey and M. J. Ramsey-Musolf, New J. Phys. 14, 125003 (2012), arXiv:1206.2942 [hep-ph]

    arXiv 2012

  4. [4]

    Witten, Phys

    E. Witten, Phys. Rev. D30, 272 (1984)

    1984

  5. [5]

    C. J. Hogan, Mon. Not. Roy. Astron. Soc.218, 629 (1986)

    1986

  6. [6]

    Amaro-Seoaneet al.(LISA), (2017), arXiv:1702.00786 [astro-ph.IM]

    P. Amaro-Seoaneet al.(LISA), (2017), arXiv:1702.00786 [astro-ph.IM]

    arXiv 2017

  7. [7]

    Luoet al., Classical and Quantum Gravity33, 035010 (2016)

    J. Luoet al., Classical and Quantum Gravity33, 035010 (2016)

    work page 2016

  8. [8]

    Ruan, Z.-K

    W.-H. Ruan, Z.-K. Guo, R.-G. Cai, and Y.-Z. Zhang, International Journal of Modern Physics A35, 2050075 (2020), https://doi.org/10.1142/S0217751X2050075X

    doi:10.1142/s0217751x2050075x 2020

Show all 35 references
  1. [9]

    S. R. Coleman, Phys. Rev. D15, 2929 (1977), [Erratum: Phys.Rev.D 16, 1248 (1977)]

    1977

  2. [10]

    C. G. Callan, Jr. and S. R. Coleman, Phys. Rev. D16, 1762 (1977)

    1977

  3. [11]

    A. D. Linde, Nucl. Phys. B216, 421 (1983), [Erratum: Nucl.Phys.B 223, 544 (1983)]

    1983

  4. [12]

    Y. Li, Y. Jia, and L. Bian, JCAP02, 038 (2025), arXiv:2304.05220 [hep-ph]

    2025 arXiv

  5. [13]

    Y. Di, J. Wang, R. Zhou, L. Bian, R.-G. Cai, and J. Liu, Phys. Rev. Lett.126, 251102 (2021), arXiv:2012.15625 [astro-ph.CO]

    2021 arXiv

  6. [14]

    Z. Zhao, Y. Di, L. Bian, and R.-G. Cai, JHEP10, 158 (2023), arXiv:2204.04427 [hep-ph]

    2023 arXiv

  7. [15]

    Cutting, M

    D. Cutting, M. Hindmarsh, and D. J. Weir, Phys. Rev. D97, 123513 (2018), arXiv:1802.05712 [astro-ph.CO]

    2018 arXiv

  8. [16]

    Cutting, M

    D. Cutting, M. Hindmarsh, and D. J. Weir, Phys. Rev. Lett.125, 021302 (2020), arXiv:1906.00480 [hep-ph]

    2020 arXiv

  9. [17]

    Cutting, E

    D. Cutting, E. G. Escartin, M. Hindmarsh, and D. J. Weir, Phys. Rev. D103, 023531 (2021), arXiv:2005.13537 [astro-ph.CO]

    2021 arXiv

  10. [18]

    Cutting, E

    D. Cutting, E. Vilhonen, and D. J. Weir, Phys. Rev. D 106, 103524 (2022), arXiv:2204.03396 [astro-ph.CO]

    2022 arXiv

  11. [19]

    Hindmarsh, S

    M. Hindmarsh, S. J. Huber, K. Rummukainen, and D. J. Weir, Phys. Rev. Lett.112, 041301 (2014), arXiv:1304.2433 [hep-ph]

    2014 arXiv

  12. [20]

    Hindmarsh, S

    M. Hindmarsh, S. J. Huber, K. Rummukainen, and D. J. Weir, Phys. Rev. D92, 123009 (2015), arXiv:1504.03291 [astro-ph.CO]

    2015 arXiv

  13. [21]

    Hindmarsh, S

    M. Hindmarsh, S. J. Huber, K. Rummukainen, and D. J. Weir, Phys. Rev. D96, 103520 (2017), [Erra- tum: Phys.Rev.D 101, 089902 (2020)], arXiv:1704.05871 [astro-ph.CO]. 5

    2017 arXiv

  14. [22]

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

    1995 arXiv

  15. [23]

    Gleiser and R

    M. Gleiser and R. M. Haas, Phys. Rev. D54, 1626 (1996), arXiv:hep-ph/9602282

    1996 arXiv

  16. [24]

    Gleiser, Phys

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

    1994

  17. [25]

    Gleiser and R

    M. Gleiser and R. C. Howell, Phys. Rev. Lett.94, 151601 (2005), arXiv:hep-ph/0409179

    2005 arXiv

  18. [26]

    Gleiser, B

    M. Gleiser, B. Rogers, and J. Thorarinson, Phys. Rev. D77, 023513 (2008), arXiv:0708.3844 [hep-th]

    2008 arXiv

  19. [27]

    P ˆ ırvu, M

    D. P ˆ ırvu, M. C. Johnson, and S. Sibiryakov, JHEP11, 064 (2024), arXiv:2312.13364 [hep-th]

    2024 arXiv

  20. [28]

    G. V. Dunne and H. Min, Phys. Rev. D72, 125004 (2005), arXiv:hep-th/0511156

    2005 arXiv

  21. [29]

    Baacke and G

    J. Baacke and G. Lavrelashvili, Phys. Rev. D69, 025009 (2004), arXiv:hep-th/0307202

    2004 arXiv

  22. [30]

    J. T. Giblin, Jr. and J. B. Mertens, JHEP12, 042 (2013), arXiv:1310.2948 [hep-th]

    2013 arXiv

  23. [31]

    H. L. Child and J. T. Giblin, Jr., JCAP10, 001 (2012), arXiv:1207.6408 [astro-ph.CO]

    2012 arXiv

  24. [32]

    J. T. Giblin and J. B. Mertens, Phys. Rev. D90, 023532 (2014), arXiv:1405.4005 [astro-ph.CO]

    2014 arXiv

  25. [33]

    D. G. Figueroa, A. Florio, F. Torrenti, and W. Valken- burg, JCAP04, 035 (2021), arXiv:2006.15122 [astro- ph.CO]

    2021 arXiv

  26. [34]

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

    2023 arXiv

  27. [35]

    M. A. Ajmi and M. Hindmarsh, Phys. Rev. D106, 023505 (2022), arXiv:2205.04097 [gr-qc]. 1 Supplemental Material This supplemental material includes the details of our simulation and explanations of the results presented in the main text, as well as some extra results. We begin ...

    2022 arXiv

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