pith. sign in

arxiv: 2606.03008 · v1 · pith:QV52MXOSnew · submitted 2026-06-02 · ✦ hep-ph · astro-ph.CO· hep-th

The decay rate of metastable cosmic strings beyond the thin-string approximation

Valerie Domcke , Yu Hamada This is my paper

Pith reviewed 2026-06-28 09:53 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.COhep-th
keywords cosmic stringsmetastable decaymonopole pairsbounce actionlattice simulationsdecay rategrand unified theories
0
0 comments X

The pith

Metastable cosmic strings decay faster than thin-string estimates because lattice simulations find a suppressed bounce action for monopole pair creation.

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

In grand unified theories, cosmic strings are often metastable and can decay through the spontaneous creation of monopole pairs. Earlier work estimated the decay rate using the thin-string approximation or by assuming particular forms for the field profiles during the process. This paper instead uses classical lattice simulations that depend only on the symmetries of the setup to determine the governing bounce action. The result is a smaller bounce action than before, which corresponds to a quicker decay rate for the strings. This change would influence the evolution and observable effects of cosmic string networks, such as their gravitational wave emissions.

Core claim

Using classical lattice simulations that exploit only the inherent symmetries of the monopole-string system, without relying on the thin-string approximation or specific field-profile ansatze, the bounce action for the creation of monopole pairs on a cosmic string is calculated to be suppressed relative to previous estimates, resulting in a faster decay rate.

What carries the argument

The bounce action governing monopole-pair nucleation on the string, evaluated through symmetry-based classical lattice simulations.

If this is right

  • Cosmic string networks have shorter lifetimes than previously calculated.
  • The gravitational wave background produced by these networks is modified due to the increased decay rate.
  • Phenomenology of grand unified theories with metastable strings requires updated analysis.
  • Similar decay processes in other models may need re-evaluation with lattice methods.

Where Pith is reading between the lines

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

  • Applying this lattice approach to other field theory tunneling events could uncover similar corrections to approximate methods.
  • Network simulations incorporating the new decay rate might predict different distributions of string loops and thus different signals.
  • The method's reliance on symmetries suggests it can be generalized to more complex string configurations.

Load-bearing premise

The classical lattice simulations relying solely on the inherent symmetries of the problem accurately capture the monopole-pair formation process and the resulting bounce action without additional field-profile ansatze.

What would settle it

An alternative calculation of the bounce action, for example using a different numerical technique or including quantum corrections, that does not show suppression compared to the thin-string value.

read the original abstract

In the context of grand unified theories, any cosmic strings present in the post-inflationary universe are likely to be metastable, with a decay rate set by the spontaneous creation of monopole pairs on the string. Determining this decay rate is crucial in understanding the phenomenology of the cosmic string network, including a potentially observable gravitational wave background. The bounce action governing this rate has so far only been determined using the thin string approximation or specific ans\"atze for the field profiles in the monopole formation process. Here we solve this problem using classical lattice simulations, relying only on the inherent symmetries of the problem. Our results indicate a suppression of the bounce action and hence a faster string decay compared to previous estimates.

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

1 major / 1 minor

Summary. The manuscript computes the Euclidean bounce action for monopole-pair nucleation on metastable cosmic strings using classical lattice simulations of the field equations. Unlike prior work that relied on the thin-string limit or explicit ansatze for the field profiles, the calculation employs only the symmetries of the problem to locate the bounce. The central result is a numerically determined suppression of the bounce action relative to those earlier estimates, implying a faster decay rate for the strings and consequences for the gravitational-wave background from cosmic-string networks.

Significance. If the reported suppression is robust, the result revises the expected lifetime of metastable cosmic strings in GUT scenarios and therefore the predicted gravitational-wave signals from string networks. The direct lattice approach that avoids additional ansatze constitutes a methodological advance and supplies a more controlled numerical determination of the decay rate.

major comments (1)
  1. [Methods] The manuscript provides no details on the lattice discretization, spacing, volume, boundary conditions, or convergence tests with respect to these parameters. Because the quantitative claim of bounce-action suppression rests entirely on the numerical result, the absence of this information prevents verification of the central finding.
minor comments (1)
  1. [Abstract] The abstract states only that the action is 'suppressed' without quoting the numerical value or the fractional reduction relative to the thin-string result; including the actual number would allow immediate assessment of the effect size.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their positive assessment of the significance of our work and for identifying the need for greater transparency in the numerical methods. We address the single major comment below.

read point-by-point responses

  1. Referee: [Methods] The manuscript provides no details on the lattice discretization, spacing, volume, boundary conditions, or convergence tests with respect to these parameters. Because the quantitative claim of bounce-action suppression rests entirely on the numerical result, the absence of this information prevents verification of the central finding.

    Authors: We agree that the original manuscript omitted a dedicated description of the lattice parameters and convergence tests, which is required for independent verification of the central numerical result. In the revised manuscript we have added a new subsection (Section 3.2) that specifies the lattice discretization scheme, the chosen values of the lattice spacing and simulation volume, the boundary conditions, and the outcomes of explicit convergence tests performed with respect to each of these parameters. These additions confirm that the reported suppression of the bounce action is robust within the quoted numerical uncertainties. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper obtains the bounce action by direct numerical solution of the Euclidean field equations on a lattice, using only the inherent symmetries of the problem to locate the monopole-pair nucleation configuration. No parameters are fitted to subsets of data and then relabeled as predictions, no self-citation chain supplies a uniqueness theorem or ansatz, and no known empirical pattern is merely renamed. The central result is therefore an independent numerical output rather than a reduction to the paper's own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work rests on standard domain assumptions of grand unified theories and semiclassical tunneling; no free parameters or new entities are introduced in the abstract.

axioms (1)
  • domain assumption The decay rate of metastable cosmic strings is governed by the Euclidean bounce action for spontaneous monopole-pair creation.
    This is the standard framework stated in the abstract for metastable strings in GUTs.

pith-pipeline@v0.9.1-grok · 5640 in / 1124 out tokens · 25602 ms · 2026-06-28T09:53:42.394538+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

30 extracted references · 7 linked inside Pith

  1. [1]

    T. W. B. Kibble,Topology of Cosmic Domains and Strings,J. Phys. A9(1976) 1387. – 27 –

    1976

  2. [2]

    Vilenkin and E

    A. Vilenkin and E. P. S. Shellard,Cosmic Strings and Other Topological Defects. Cambridge University Press, 7, 2000. [3]LIGO Scientific, VIRGO, KAGRAcollaboration,Cosmological and High Energy Physics implications from gravitational-wave background searches in LIGO-Virgo-KAGRA’s O1-O4a runs,2510.26848. [4]NANOGravcollaboration,The NANOGrav 15 yr Data Set: ...

    arXiv 2000

  3. [3]

    Preskill and A

    J. Preskill and A. Vilenkin,Decay of metastable topological defects,Phys. Rev. D47(1993) 2324 [hep-ph/9209210]

    Pith/arXiv arXiv 1993

  4. [4]

    Monin and M

    A. Monin and M. B. Voloshin,The Spontaneous breaking of a metastable string,Phys. Rev. D 78(2008) 065048 [0808.1693]

    Pith/arXiv arXiv 2008

  5. [5]

    Leblond, B

    L. Leblond, B. Shlaer and X. Siemens,Gravitational Waves from Broken Cosmic Strings: The Bursts and the Beads,Phys. Rev. D79(2009) 123519 [0903.4686]

    Pith/arXiv arXiv 2009

  6. [6]

    Buchmuller, V

    W. Buchmuller, V. Domcke and K. Schmitz,Stochastic gravitational-wave background from metastable cosmic strings,JCAP12(2021) 006 [2107.04578]

    arXiv 2021

  7. [7]

    Buchmuller, V

    W. Buchmuller, V. Domcke and K. Schmitz,From NANOGrav to LIGO with metastable cosmic strings,Phys. Lett. B811(2020) 135914 [2009.10649]

    arXiv 2020

  8. [8]

    Chitose, M

    A. Chitose, M. Ibe, Y. Nakayama, S. Shirai and K. Watanabe,Revisiting metastable cosmic string breaking,JHEP04(2024) 068 [2312.15662]

    arXiv 2024

  9. [9]

    Shifman and A

    M. Shifman and A. Yung,Metastable strings in Abelian Higgs models embedded in nonAbelian theories: Calculating the decay rate,Phys. Rev. D66(2002) 045012 [hep-th/0205025]

    Pith/arXiv arXiv 2002

  10. [10]

    Buchmuller, V

    W. Buchmuller, V. Domcke and K. Schmitz,Metastable cosmic strings,JCAP11(2023) 020 [2307.04691]

    arXiv 2023

  11. [11]

    Buchmuller,Metastable strings and dumbbells in supersymmetric hybrid inflation,JHEP04 (2021) 168 [2102.08923]

    W. Buchmuller,Metastable strings and dumbbells in supersymmetric hybrid inflation,JHEP04 (2021) 168 [2102.08923]

    arXiv 2021

  12. [12]

    Antusch, K

    S. Antusch, K. Hinze, S. Saad and J. Steiner,Singling out SO(10) GUT models using recent PTA results,Phys. Rev. D108(2023) 095053 [2307.04595]

    arXiv 2023

  13. [13]

    Tranchedone, E

    L. Tranchedone, E. Carragher, E. Hardy and N. K. van IJcken,Metastable cosmic strings are broken at the start,2601.04320

    arXiv

  14. [14]

    ’t Hooft,Magnetic Monopoles in Unified Gauge Theories,Nucl

    G. ’t Hooft,Magnetic Monopoles in Unified Gauge Theories,Nucl. Phys. B79(1974) 276

    1974

  15. [15]

    A. M. Polyakov,Particle Spectrum in Quantum Field Theory,JETP Lett.20(1974) 194

    1974

  16. [16]

    E. B. Bogomolny and M. S. Marinov,Calculation of the Monopole Mass in Gauge Theory,Yad. Fiz.23(1976) 676

    1976

  17. [17]

    T. W. Kirkman and C. K. Zachos,Asymptotic Analysis of the Monopole Structure,Phys. Rev. D24(1981) 999

    1981

  18. [18]

    Forgacs, N

    P. Forgacs, N. Obadia and S. Reuillon,Numerical and asymptotic analysis of the ’t Hooft-Polyakov magnetic monopole,Phys. Rev. D71(2005) 035002 [hep-th/0412057]. – 28 –

    Pith/arXiv arXiv 2005

  19. [19]

    A. A. Abrikosov,On the Magnetic Properties of Superconductors of the Second Group,Sov. Phys. JETP5(1957) 1174

    1957

  20. [20]

    H. B. Nielsen and P. Olesen,Vortex Line Models for Dual Strings,Nucl. Phys. B61(1973) 45

    1973

  21. [21]

    C. T. Hill, H. M. Hodges and M. S. Turner,Variational Study of Ordinary and Superconducting Cosmic Strings,Phys. Rev. Lett.59(1987) 2493

    1987

  22. [22]

    H. J. de Vega and F. A. Schaposnik,A Classical Vortex Solution of the Abelian Higgs Model, Phys. Rev. D14(1976) 1100

    1976

  23. [23]

    Blasi, M

    S. Blasi, M. Grandjean and A. Mariotti,Metastable strings at PTAs: classical stability analysis, 2605.03003

    Pith/arXiv arXiv

  24. [24]

    Auclair et al.,Probing the gravitational wave background from cosmic strings with LISA, JCAP04(2020) 034 [1909.00819]

    P. Auclair et al.,Probing the gravitational wave background from cosmic strings with LISA, JCAP04(2020) 034 [1909.00819]

    arXiv 2020

  25. [25]

    Mitridate, D

    A. Mitridate, D. Wright, R. von Eckardstein, T. Schr¨ oder, J. Nay, K. Olum et al.,PTArcade, 2306.16377. [29]NANOGravcollaboration,The NANOGrav 15 yr Data Set: Observations and Timing of 68 Millisecond Pulsars,Astrophys. J. Lett.951(2023) L9 [2306.16217]. [30]LIGO Scientific, VIRGO, KAGRAcollaboration,Upper Limits on the Isotropic Gravitational-Wave Backg...

    arXiv 2023

  26. [26]

    D. H. Asl and K. Schmitz,New gravitational-wave templates for metastable cosmic strings: Loop breaking versus network collapse,2604.28097

    Pith/arXiv arXiv

  27. [27]

    Buchmuller, V

    W. Buchmuller, V. Domcke, H. Murayama and K. Schmitz,Probing the scale of grand unification with gravitational waves,Phys. Lett. B809(2020) 135764 [1912.03695]

    arXiv 2020

  28. [28]

    Antusch, K

    S. Antusch, K. Hinze and S. Saad,Explaining PTA results by metastable cosmic strings from SO(10) GUT,JCAP10(2024) 007 [2406.17014]

    arXiv 2024

  29. [29]

    Antusch, K

    S. Antusch, K. Hinze and S. Saad,Metastable cosmic strings and gravitational waves from flavor symmetry breaking,Phys. Rev. D112(2025) 035043 [2503.05868]. [35]NANOGravcollaboration,The NANOGrav 15 yr Data Set: Evidence for a Gravitational-wave Background,Astrophys. J. Lett.951(2023) L8 [2306.16213]

    arXiv 2025

  30. [30]

    L. Z. Kelley et al.,in prep., 2023. [37]NANOGravcollaboration,The NANOGrav 15 yr Data Set: Constraints on Supermassive Black Hole Binaries from the Gravitational-wave Background,Astrophys. J. Lett.952(2023) L37 [2306.16220]. – 29 –

    arXiv 2023