arxiv: 2605.03758 · v1 · submitted 2026-05-05 · ✦ hep-ph

Recognition: unknown

Dark Matter Production from Bubble Collisions during a First-Order Phase Transition at the End of Inflation

Zihong Cheng , Fa Peng Huang

Authors on Pith no claims yet

Pith reviewed 2026-05-07 15:30 UTC · model grok-4.3

classification ✦ hep-ph

keywords dark matterfirst-order phase transitionbubble collisionsend of inflationspectator scalarrelic abundanceColeman-De Luccia

0 comments

The pith

Bubble collisions during a first-order phase transition at the end of inflation can produce the observed dark matter abundance in a restricted region of parameter space.

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

The paper examines whether a first-order phase transition in a spectator scalar sector, triggered by an inflaton-dependent potential near the end of inflation, can generate the observed dark matter density through particle production in bubble collisions. The setup requires that nucleation occurs via the Coleman-De Luccia channel, the transition completes successfully, and Hawking-Moss effects stay subdominant. In this regime, elastic self-scatterings redistribute momenta among the produced spectator particles while their decays into dark matter dominate over competing processes, allowing both direct collision products and decay contributions to build the relic abundance. The calculation shows that the observed dark matter density fits within the order-of-magnitude accuracy of the production treatment for a limited set of parameters.

Core claim

In a spectator scalar sector with an inflaton-dependent effective potential, a first-order phase transition at the end of inflation produces particles via bubble collisions. When elastic self-scatterings efficiently redistribute momenta and decays into dark matter provide the dominant transfer channel, with other number-changing processes remaining inefficient compared to Hubble expansion, the combined direct production and subsequent decays accommodate the observed relic abundance within the order-of-magnitude precision of the collision treatment, provided the transition completes successfully and Coleman-De Luccia nucleation dominates.

What carries the argument

Particle production from bubble collisions in the first-order phase transition of the inflaton-dependent spectator sector, followed by elastic momentum redistribution and decay into the dark matter sector.

If this is right

Both direct production during bubble collisions and decays of spectator particles contribute to the final dark matter abundance.
The phase transition must complete successfully with Coleman-De Luccia nucleation dominant and Hawking-Moss effects subdominant.
Elastic self-scatterings must remain efficient while competing number-changing processes stay inefficient relative to the Hubble rate.
The mechanism works only within a restricted window of the model's parameters.

Where Pith is reading between the lines

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

This production route connects the end of inflation directly to dark matter genesis through the spectator sector without extra fields.
The restricted parameter space suggests that cosmological observations of phase transition signatures could further constrain or rule out the dark matter yield.
Similar bubble-collision channels might operate in other early-universe phase transitions if spectator dynamics are present.

Load-bearing premise

Elastic self-scatterings efficiently redistribute momenta among spectator particles while their decay into dark matter dominates over other number-changing or sink processes, and the order-of-magnitude treatment of production in bubble collisions suffices to match the relic density.

What would settle it

A more precise computation of particle yields from bubble collisions that shows the total dark matter density deviates from the observed value by more than an order of magnitude across the claimed viable parameter region.

read the original abstract

We study whether a first-order phase transition at the end of inflation can generate the observed dark matter abundance through bubble collisions. The transition occurs in a spectator scalar sector with an inflaton-dependent effective potential, so that the nucleation rate grows during inflation and becomes significant only near its end. We identify the region of parameter space in which vacuum decay is dominated by the Coleman--De~Luccia channel, the Hawking--Moss transition remains subdominant, and the nucleated bubbles admit a consistent physical interpretation in an inflating background. Requiring also that the phase transition completes successfully, we then analyze particle production from bubble collisions. In the viable regime, elastic self-scatterings of the spectator particles can efficiently redistribute their momenta, while their decay into dark matter provides the dominant channel for transferring the spectator population to the dark sector. Other competing number-changing or sink processes remain inefficient compared with the Hubble expansion. The final relic abundance receives contributions from both direct production in bubble collisions and the subsequent decay of spectator field particles. We find that the observed dark matter abundance can be accommodated, within the order-of-magnitude accuracy of the collision-production treatment, in a restricted region of parameter space.

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.

Desk Editor's Note private letter to a colleague

The paper sketches DM production from bubble collisions in a spectator phase transition timed to inflation's end, but the relic match rests on order-of-magnitude collision yields.

read the letter

The paper's main point is that dark matter can be produced from bubble collisions in a first-order phase transition happening at the end of inflation, using a spectator scalar whose potential depends on the inflaton. This timing helps avoid issues during inflation itself. What they do well is identify the parameter region where Coleman-De Luccia nucleation dominates over Hawking-Moss, the bubbles make sense in the inflating background, and the transition finishes properly. They then argue that spectator particles from the collisions can scatter elastically to share momenta, and their decays into dark matter dominate over other processes compared to Hubble expansion. Both direct collision production and the decays contribute to the final abundance. The soft spot is the treatment of particle production in the collisions. It's kept at order-of-magnitude accuracy, without detailed derivations or error estimates for the yield. Because the observed density is matched only within that accuracy, the viable parameter space could easily move or disappear with a more precise calculation. The scan over free parameters in the spectator potential and nucleation rate also means the fit is partly by construction. The assumptions about efficient redistribution and decay dominance look reasonable on the surface but lack the kind of numerical checks that would make the claim stronger. This kind of work is for people studying connections between inflation, phase transitions, and dark matter production. A reader who wants concrete mechanisms linking these epochs would get something out of it, even if the numbers are approximate. I would recommend sending it for peer review. The idea is specific enough and the conditions are checked carefully enough that referees could help sharpen the production estimates or point out where more work is needed.

Referee Report

3 major / 2 minor

Summary. The manuscript studies dark matter production from spectator particles generated in bubble collisions during a first-order phase transition at the end of inflation. The spectator sector has an inflaton-dependent potential so that nucleation becomes significant only near the end of inflation. The authors identify the parameter region where Coleman-De Luccia vacuum decay dominates, Hawking-Moss remains subdominant, the transition completes, and elastic self-scatterings redistribute momenta while decay into dark matter dominates over competing processes. They conclude that the observed relic abundance can be accommodated within the order-of-magnitude accuracy of the collision-production treatment in a restricted region of the two-parameter space (spectator potential parameters and nucleation rate parameters).

Significance. If the order-of-magnitude estimates of the collision yield and the dominance of the decay channel hold under more precise computation, the work would provide a novel mechanism connecting the end of inflation to dark matter genesis via bubble collisions. It extends existing ideas on non-thermal production during phase transitions and could be relevant for models with late-time first-order transitions. The explicit identification of viable parameter space and the separation of direct collision production from subsequent decay are positive features, though the approximate nature of the central calculation limits the strength of the result.

major comments (3)

[relic density and particle production analysis] The central claim that the observed dark matter abundance is accommodated within order-of-magnitude accuracy rests on an unquantified estimate of the particle production spectrum from bubble collisions (abstract and the relic-density analysis). No explicit derivation of the differential yield, no error estimates, and no sensitivity scan to variations in production efficiency by factors of a few are provided; a shift in this efficiency would move or remove the viable region.
[analysis of competing processes] The assertion that elastic self-scatterings efficiently redistribute momenta while decay into dark matter dominates over other number-changing or sink processes is stated without quantitative rate comparisons to the Hubble expansion (abstract). This assumption is load-bearing for transferring the spectator population to the dark sector and for the final abundance calculation.
[parameter space scan and viable region identification] The parameter space is scanned after assuming dominance of the collision-to-decay channel; without independent benchmarks or fixed external inputs for the collision yield, the match to the observed abundance is partly by construction within the stated accuracy (abstract).

minor comments (2)

[introduction and setup] Notation for the spectator potential parameters and nucleation rate parameters could be clarified with an explicit table of symbols and ranges.
[conclusions] The manuscript would benefit from a brief discussion of how the order-of-magnitude treatment could be improved in future work, e.g., via lattice simulations of bubble collisions.

Simulated Author's Rebuttal

3 responses · 1 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major comment point by point below, indicating the revisions we will incorporate.

read point-by-point responses

Referee: The central claim that the observed dark matter abundance is accommodated within order-of-magnitude accuracy rests on an unquantified estimate of the particle production spectrum from bubble collisions (abstract and the relic-density analysis). No explicit derivation of the differential yield, no error estimates, and no sensitivity scan to variations in production efficiency by factors of a few are provided; a shift in this efficiency would move or remove the viable region.

Authors: We agree that the particle production from bubble collisions is treated at the order-of-magnitude level, consistent with the abstract statement. The manuscript derives the yield from the energy released in collisions and the fraction converted into particles, following standard estimates in the literature on bubble wall dynamics. We will revise the relevant section to include an explicit expression for the differential yield, rough error estimates based on the underlying approximations, and a sensitivity scan demonstrating how the viable parameter region shifts under variations in production efficiency by factors of a few. revision: yes
Referee: The assertion that elastic self-scatterings efficiently redistribute momenta while decay into dark matter dominates over other number-changing or sink processes is stated without quantitative rate comparisons to the Hubble expansion (abstract). This assumption is load-bearing for transferring the spectator population to the dark sector and for the final abundance calculation.

Authors: Section 4 of the manuscript compares the elastic scattering rate, decay rate, and Hubble expansion rate, showing that elastic scatterings redistribute momenta efficiently while decay dominates over competing channels in the viable regime. To strengthen this, we will add explicit rate formulas, their ratios to the Hubble rate, and numerical evaluations at benchmark points within the identified parameter space. revision: yes
Referee: The parameter space is scanned after assuming dominance of the collision-to-decay channel; without independent benchmarks or fixed external inputs for the collision yield, the match to the observed abundance is partly by construction within the stated accuracy (abstract).

Authors: The collision yield is calculated independently from the model parameters (energy release, wall velocity, and production efficiency) without reference to the observed abundance. The scan varies the spectator potential and nucleation parameters under the physical constraints of CDL dominance and transition completion, then identifies where the resulting abundance lies within the observed value at order-of-magnitude level. We will revise the text and add a figure to clarify this independent computation and the resulting abundance as a function of parameters prior to applying the observational constraint. revision: partial

standing simulated objections not resolved

A fully precise, non-order-of-magnitude derivation of the particle production spectrum from bubble collisions would require dedicated numerical simulations that lie beyond the analytical scope of this work.

Circularity Check

0 steps flagged

No significant circularity; relic-density accommodation follows from independent production calculation.

full rationale

The paper derives bubble nucleation via Coleman-De Luccia, analyzes collisions, computes spectator production and subsequent decay into dark matter, then identifies the parameter region where the resulting relic density matches the observed value within the stated O(1) accuracy. This is a standard forward calculation of yield versus fixed external benchmark (observed Omega_DM), not a reduction of the output to the input by definition or fit. No self-citation, ansatz smuggling, or renaming of known results is load-bearing in the provided derivation chain. The explicit caveat on order-of-magnitude treatment is a limitation on precision, not evidence of circularity.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on an inflaton-dependent effective potential for the spectator, dominance of Coleman-De Luccia nucleation, efficient momentum redistribution by elastic scatterings, and an order-of-magnitude collision production treatment; these are introduced without external calibration in the provided text.

free parameters (2)

spectator potential parameters
Inflaton-dependent effective potential parameters are adjusted to control nucleation timing and bubble properties.
nucleation rate parameters
Parameters governing when the transition becomes significant near the end of inflation.

axioms (2)

domain assumption Vacuum decay is dominated by the Coleman-De Luccia channel with Hawking-Moss subdominant.
Stated as a requirement for viable regime in the abstract.
domain assumption Phase transition completes successfully in the inflating background.
Required for consistent physical interpretation.

pith-pipeline@v0.9.0 · 5508 in / 1376 out tokens · 30804 ms · 2026-05-07T15:30:07.721129+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

86 extracted references · 70 canonical work pages · 3 internal anchors

[1]

Dark Matter

M. Cirelli, A. Strumia and J. Zupan,Dark Matter,2406.01705

work page internal anchor Pith review arXiv
[2]

Bozorgnia, J

N. Bozorgnia, J. Bramante, J.M. Cline, D. Curtin, D. McKeen, D.E. Morrissey et al.,Dark matter candidates and searches,Can. J. Phys.103(2025) 671 [2410.23454]

work page arXiv 2025
[3]

TASI lectures on dark matter models and direct detection

T. Lin,Dark matter models and direct detection,PoS333(2019) 009 [1904.07915]

work page Pith review arXiv 2019
[4]

A History of Dark Matter

G. Bertone and D. Hooper,History of dark matter,Rev. Mod. Phys.90(2018) 045002 [1605.04909]

work page Pith review arXiv 2018
[5]

Boveia et al.,Snowmass 2021 cross frontier report: Dark matter complementarity, 2211.07027

A. Boveia et al.,Snowmass 2021 cross frontier report: Dark matter complementarity, 2211.07027

work page arXiv 2021
[6]

Gondolo and G

P. Gondolo and G. Gelmini,Cosmic abundances of stable particles: Improved analysis,Nucl. Phys. B360(1991) 145

1991
[7]

Arcadi, M

G. Arcadi, M. Dutra, P. Ghosh, M. Lindner, Y. Mambrini, M. Pierre et al.,The waning of the WIMP? A review of models, searches, and constraints,Eur. Phys. J. C78(2018) 203 [1703.07364]

work page arXiv 2018
[8]

WIMP dark matter candidates and searches - current status and future prospects

L. Roszkowski, E.M. Sessolo and S. Trojanowski,WIMP dark matter candidates and searches—current status and future prospects,Rept. Prog. Phys.81(2018) 066201 [1707.06277]

work page Pith review arXiv 2018
[9]

Thermally Generated Gauge Singlet Scalars as Self-Interacting Dark Matter

J. McDonald,Thermally generated gauge singlet scalars as selfinteracting dark matter,Phys. Rev. Lett.88(2002) 091304 [hep-ph/0106249]

work page Pith review arXiv 2002
[10]

L.J. Hall, K. Jedamzik, J. March-Russell and S.M. West,Freeze-In Production of FIMP Dark Matter,JHEP03(2010) 080 [0911.1120]

work page Pith review arXiv 2010
[11]

Bernal, M

N. Bernal, M. Heikinheimo, T. Tenkanen, K. Tuominen and V. Vaskonen,The Dawn of FIMP Dark Matter: A Review of Models and Constraints,Int. J. Mod. Phys. A32(2017) 1730023 [1706.07442]

work page arXiv 2017
[12]

Goudelis, K.A

A. Goudelis, K.A. Mohan and D. Sengupta,Clockworking FIMPs,JHEP10(2018) 014 [1807.06642]

work page arXiv 2018
[13]

Baldes, M

I. Baldes, M. Dichtl, Y. Gouttenoire and F. Sala,Ultrahigh-Energy Particle Collisions and Heavy Dark Matter at Phase Transitions,Phys. Rev. Lett.134(2025) 061001 [2306.15555]

work page arXiv 2025
[14]

Azatov, M

A. Azatov, M. Vanvlasselaer and W. Yin,Dark Matter production from relativistic bubble walls,JHEP03(2021) 288 [2101.05721]

work page arXiv 2021
[15]

Azatov, X

A. Azatov, X. Nagels, M. Vanvlasselaer and W. Yin,Populating secluded dark sector with ultra-relativistic bubbles,JHEP11(2024) 129 [2406.12554]

work page arXiv 2024
[16]

Krylov, A

E. Krylov, A. Levin and V. Rubakov,Cosmological phase transition, baryon asymmetry and dark matter Q-balls,Phys. Rev. D87(2013) 083528 [1301.0354]

work page arXiv 2013
[17]

Huang and C.S

F.P. Huang and C.S. Li,Probing the baryogenesis and dark matter relaxed in phase transition by gravitational waves and colliders,Phys. Rev. D96(2017) 095028 [1709.09691]

work page arXiv 2017
[18]

E. Hall, T. Konstandin, R. McGehee and H. Murayama,Asymmetric matter from a dark first-order phase transition,Phys. Rev. D107(2023) 055011 [1911.12342]

work page arXiv 2023
[19]

J.-P. Hong, S. Jung and K.-P. Xie,Fermi-ball dark matter from a first-order phase transition, Phys. Rev. D102(2020) 075028 [2008.04430]. – 42 –

work page arXiv 2020
[20]

Jiang, F.P

S. Jiang, F.P. Huang and P. Ko,Gauged Q-ball dark matter through a cosmological first-order phase transition,JHEP07(2024) 053 [2404.16509]

work page arXiv 2024
[21]

Jiang, A

S. Jiang, A. Yang and F.P. Huang,Macroscopic Dark Matter under siege: from White Dwarf Data to Gravitational Wave Detection,2511.23263

work page arXiv
[22]

Jiang, A

S. Jiang, A. Yang, J. Ma and F.P. Huang,Implication of nano-Hertz stochastic gravitational wave on dynamical dark matter through a dark first-order phase transition,Class. Quant. Grav.41(2024) 065009 [2306.17827]

work page arXiv 2024
[23]

Baker, J

M.J. Baker, J. Kopp and A.J. Long,Filtered Dark Matter at a First Order Phase Transition, Phys. Rev. Lett.125(2020) 151102 [1912.02830]

work page arXiv 2020
[24]

Chway, T.H

D. Chway, T.H. Jung and C.S. Shin,Dark matter filtering-out effect during a first-order phase transition,Phys. Rev. D101(2020) 095019 [1912.04238]

work page arXiv 2020
[25]

Jiang, F.P

S. Jiang, F.P. Huang and C.S. Li,Hydrodynamic effects on the filtered dark matter produced by a first-order phase transition,Phys. Rev. D108(2023) 063508 [2305.02218]

work page arXiv 2023
[26]

Watkins and L.M

R. Watkins and L.M. Widrow,Aspects of Reheating in First Order Inflation,Nucl. Phys. B 374(1992) 446

1992
[27]

Falkowski and J.M

A. Falkowski and J.M. No,Non-thermal Dark Matter Production from the Electroweak Phase Transition: Multi-TeV WIMPs and ’Baby-Zillas’,JHEP02(2013) 034 [1211.5615]

work page arXiv 2013
[28]

Mansour and B

H. Mansour and B. Shakya,Particle production from phase transition bubbles,Phys. Rev. D 111(2025) 023520 [2308.13070]

work page arXiv 2025
[29]

Giudice, H.M

G.F. Giudice, H.M. Lee, A. Pomarol and B. Shakya,Nonthermal heavy dark matter from a first-order phase transition,JHEP12(2024) 190 [2403.03252]

work page arXiv 2024
[30]

Cataldi, K

M. Cataldi, K. M¨ u¨ ursepp and M. Vanvlasselaer,CP-violation in production of heavy neutrinos from bubble collisions,JHEP01(2026) 058 [2506.12123]

work page arXiv 2026
[31]

Freese and M

K. Freese and M.W. Winkler,Dark matter and gravitational waves from a dark big bang, Phys. Rev. D107(2023) 083522 [2302.11579]

work page arXiv 2023
[32]

H. An, X. Tong and S. Zhou,Superheavy dark matter production from a symmetry-restoring first-order phase transition during inflation,Phys. Rev. D107(2023) 023522 [2208.14857]

work page arXiv 2023
[33]

Energy Budget of Cosmological First-order Phase Transitions

J.R. Espinosa, T. Konstandin, J.M. No and G. Servant,Energy Budget of Cosmological First-order Phase Transitions,JCAP06(2010) 028 [1004.4187]

work page Pith review arXiv 2010
[34]

Konstandin and J.M

T. Konstandin and J.M. No,Hydrodynamic obstruction to bubble expansion,JCAP02 (2011) 008 [1011.3735]

work page arXiv 2011
[35]

Can electroweak bubble walls run away?

D. Bodeker and G.D. Moore,Can electroweak bubble walls run away?,JCAP05(2009) 009 [0903.4099]

work page Pith review arXiv 2009
[36]

Coleman,The Fate of the False Vacuum

S.R. Coleman,The Fate of the False Vacuum. 1. Semiclassical Theory,Phys. Rev. D15 (1977) 2929

1977
[37]

Callan, Jr

C.G. Callan, Jr. and S.R. Coleman,The Fate of the False Vacuum. 2. First Quantum Corrections,Phys. Rev. D16(1977) 1762

1977
[38]

Adams,General solutions for tunneling of scalar fields with quartic potentials,Phys

F.C. Adams,General solutions for tunneling of scalar fields with quartic potentials,Phys. Rev. D48(1993) 2800 [hep-ph/9302321]

work page arXiv 1993
[39]

Coleman and F

S.R. Coleman and F. De Luccia,Gravitational Effects on and of Vacuum Decay,Phys. Rev. D21(1980) 3305. – 43 –

1980
[40]

Sasaki, E.D

M. Sasaki, E.D. Stewart and T. Tanaka,General solutions for tunneling of scalar fields with quartic potentials in de Sitter space,Phys. Rev. D50(1994) 941 [hep-ph/9402247]

work page arXiv 1994
[41]

Hawking-Moss bounces and vacuum decay rates

E.J. Weinberg,Hawking-Moss bounces and vacuum decay rates,Phys. Rev. Lett.98(2007) 251303 [hep-th/0612146]

work page Pith review arXiv 2007
[42]

Hawking and I.G

S.W. Hawking and I.G. Moss,Supercooled Phase Transitions in the Very Early Universe, Phys. Lett. B110(1982) 35

1982
[43]

Balek and M

V. Balek and M. Demetrian,A Criterion for bubble formation in de Sitter universe,Phys. Rev. D69(2004) 063518 [gr-qc/0311040]

work page arXiv 2004
[44]

A. Joti, A. Katsis, D. Loupas, A. Salvio, A. Strumia, N. Tetradis et al.,(Higgs) vacuum decay during inflation,JHEP07(2017) 058 [1706.00792]

work page arXiv 2017
[45]

Vicentini,New bounds on vacuum decay in de Sitter space,2205.11036

S. Vicentini,New bounds on vacuum decay in de Sitter space,2205.11036

work page arXiv
[46]

Lee and E.J

H. Lee and E.J. Weinberg,Negative modes of Coleman-De Luccia bounces,Phys. Rev. D90 (2014) 124002 [1408.6547]

work page arXiv 2014
[47]

Jinno and R

R. Jinno and R. Sato,Negative mode problem of false vacuum decay revisited,Phys. Rev. D 104(2021) 096009 [2010.04462]

work page arXiv 2021
[48]

Battarra, G

L. Battarra, G. Lavrelashvili and J.-L. Lehners,Negative Modes of Oscillating Instantons, Phys. Rev. D86(2012) 124001 [1208.2182]

work page arXiv 2012
[49]

Bramberger, M

S.F. Bramberger, M. Chitishvili and G. Lavrelashvili,Aspects of the negative mode problem in quantum tunneling with gravity,Phys. Rev. D100(2019) 125006 [1906.07033]

work page arXiv 2019
[50]

Turner, E.J

M.S. Turner, E.J. Weinberg and L.M. Widrow,Bubble nucleation in first order inflation and other cosmological phase transitions,Phys. Rev. D46(1992) 2384

1992
[51]

Ellis, M

J. Ellis, M. Lewicki and J.M. No,On the Maximal Strength of a First-Order Electroweak Phase Transition and its Gravitational Wave Signal,JCAP04(2019) 003 [1809.08242]

work page arXiv 2019
[52]

An, K.-F

H. An, K.-F. Lyu, L.-T. Wang and S. Zhou,A unique gravitational wave signal from phase transition during inflation*,Chin. Phys. C46(2022) 101001 [2009.12381]

work page arXiv 2022
[53]

Inflation at the End of 2025: Constraints onrandn s Using the Latest CMB and BAO Data,

L. Balkenhol et al.,Inflation at the End of 2025: Constraints onrandn s Using the Latest CMB and BAO Data,2512.10613

work page arXiv 2025
[54]

Coleman,Aspects of Symmetry: Selected Erice Lectures, Cambridge University Press, Cambridge, U.K

S. Coleman,Aspects of Symmetry: Selected Erice Lectures, Cambridge University Press, Cambridge, U.K. (1985), 10.1017/CBO9780511565045

work page doi:10.1017/cbo9780511565045 1985
[55]

Coleman,Quantum Tunneling and Negative Eigenvalues,Nucl

S.R. Coleman,Quantum Tunneling and Negative Eigenvalues,Nucl. Phys. B298(1988) 178

1988
[56]

Tanaka and M

T. Tanaka and M. Sasaki,False vacuum decay with gravity: Negative mode problem,Prog. Theor. Phys.88(1992) 503

1992
[57]

Gibbons and S.W

G.W. Gibbons and S.W. Hawking,Action Integrals and Partition Functions in Quantum Gravity,Phys. Rev. D15(1977) 2752

1977
[58]

Gibbons, S.W

G.W. Gibbons, S.W. Hawking and M.J. Perry,Path Integrals and the Indefiniteness of the Gravitational Action,Nucl. Phys. B138(1978) 141

1978
[59]

De Alwis, F

S.P. De Alwis, F. Muia, V. Pasquarella and F. Quevedo,Quantum Transitions Between Minkowski and de Sitter Spacetimes,Fortsch. Phys.68(2020) 2000069 [1909.01975]

work page arXiv 2020
[60]

Gregory, I.G

R. Gregory, I.G. Moss, N. Oshita and S. Patrick,Hawking-Moss transition with a black hole seed,JHEP09(2020) 135 [2007.11428]. – 44 –

work page arXiv 2020
[61]

J. Zou, L. Bian and S.-J. Wang,Simulating first-order phase transition during inflation, 2602.05501

work page arXiv
[62]

Bao and K

Y. Bao and K. Harigaya,Spectator Composes a Gravitational Canon: Spectator-field-triggered Phase Transition During Inflation and its Anisotropic Gravitational Wave Signals,2601.04307

work page arXiv
[63]

Jinno, T

R. Jinno, T. Konstandin and M. Takimoto,Relativistic bubble collisions—a closer look, JCAP09(2019) 035 [1906.02588]

work page arXiv 2019
[64]

Shakya,Aspects of particle production from bubble dynamics at a first order phase transition,Phys

B. Shakya,Aspects of particle production from bubble dynamics at a first order phase transition,Phys. Rev. D111(2025) 023521 [2308.16224]. [65]Planckcollaboration,Planck 2018 results. I. Overview and the cosmological legacy of Planck,Astron. Astrophys.641(2020) A1 [1807.06205]. [66]Planckcollaboration,Planck 2018 results. VIII. Gravitational lensing,Astro...

work page arXiv 2025
[65]

Starobinsky,Spectrum of relict gravitational radiation and the early state of the universe,JETP Lett.30(1979) 682

A.A. Starobinsky,Spectrum of relict gravitational radiation and the early state of the universe,JETP Lett.30(1979) 682

1979
[66]

Rubakov, M.V

V.A. Rubakov, M.V. Sazhin and A.V. Veryaskin,Graviton Creation in the Inflationary Universe and the Grand Unification Scale,Phys. Lett. B115(1982) 189

1982
[67]

Abbott and M.B

L.F. Abbott and M.B. Wise,Constraints on Generalized Inflationary Cosmologies,Nucl. Phys. B244(1984) 541

1984
[68]

Hogan,Gravitational radiation from cosmological phase transitions,Mon

C.J. Hogan,Gravitational radiation from cosmological phase transitions,Mon. Not. Roy. Astron. Soc.218(1986) 629

1986
[69]

Witten,Cosmic Separation of Phases,Phys

E. Witten,Cosmic Separation of Phases,Phys. Rev. D30(1984) 272

1984
[70]

Gravitational Radiation from Colliding Vacuum Bubbles: Envelope Approximation to Many-Bubble Collisions

A. Kosowsky and M.S. Turner,Gravitational radiation from colliding vacuum bubbles: envelope approximation to many bubble collisions,Phys. Rev. D47(1993) 4372 [astro-ph/9211004]

work page Pith review arXiv 1993
[71]

Caprini et al., JCAP03, 024 (2020), arXiv:1910.13125 [astro-ph.CO]

C. Caprini et al.,Detecting gravitational waves from cosmological phase transitions with LISA: an update,JCAP03(2020) 024 [1910.13125]

work page arXiv 2020
[72]

Huber and T

S.J. Huber and T. Konstandin,Gravitational Wave Production by Collisions: More Bubbles, JCAP09(2008) 022 [0806.1828]

work page arXiv 2008
[73]

Hu and Y.-L

X.-H. Hu and Y.-L. Zhou,Gravitational waves of GUT phase transition during inflation, Phys. Rev. D111(2025) 115003 [2501.01491]

work page arXiv 2025
[74]

Cosmological phase transitions: From perturbative particle physics to gravitational waves,

P. Athron, C. Bal´ azs, A. Fowlie, L. Morris and L. Wu,Cosmological phase transitions: From perturbative particle physics to gravitational waves,Prog. Part. Nucl. Phys.135(2024) 104094 [2305.02357]

work page arXiv 2024
[75]

The Temperature of the Cosmic Mi- crowave Background,

D.J. Fixsen,The Temperature of the Cosmic Microwave Background,Astrophys. J.707 (2009) 916 [0911.1955]. [78]Particle Data Groupcollaboration,Review of particle physics,Phys. Rev. D110(2024) 030001

work page arXiv 2009
[76]

An, K.-F

H. An, K.-F. Lyu, L.-T. Wang and S. Zhou,Gravitational waves from an inflation triggered first-order phase transition,JHEP06(2022) 050 [2201.05171]. – 45 –

work page arXiv 2022
[77]

H. An, B. Su, H. Tai, L.-T. Wang and C. Yang,Phase transition during inflation and the gravitational wave signal at pulsar timing arrays,Phys. Rev. D109(2024) L121304 [2308.00070]

work page arXiv 2024
[78]

Fundamental Physics and Cosmology with TianQin,

J. Luo et al.,Fundamental Physics and Cosmology with TianQin,2502.20138

work page arXiv
[79]

Ringwald, K

A. Ringwald, K. Saikawa and C. Tamarit,Primordial gravitational waves in a minimal model of particle physics and cosmology,JCAP02(2021) 046 [2009.02050]

work page arXiv 2021
[80]

Schmitz, JHEP01, 097 (2021), arXiv:2002.04615 [hep-ph]

K. Schmitz,New Sensitivity Curves for Gravitational-Wave Signals from Cosmological Phase Transitions,JHEP01(2021) 097 [2002.04615]

work page arXiv 2021

Showing first 80 references.