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arxiv: 2605.15259 · v1 · submitted 2026-05-14 · ✦ hep-ph · astro-ph.CO

TransitionListener v2.0 -- Robust gravitational wave predictions for cosmological phase transitions

Jonas Matuszak , Carlo Tasillo This is my paper

Pith reviewed 2026-05-19 16:00 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.CO
keywords cosmological phase transitionsgravitational wavesbubble dynamicsreheatingmean bubble separationLISApulsar timing arraysscalar potential
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0 comments X p. Extension

The pith

TransitionListener v2.0 tracks the true-vacuum fraction and mean bubble separation to produce consistent gravitational wave predictions from phase transitions.

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

The paper presents an updated software framework that calculates gravitational wave signals from first-order cosmological phase transitions by following the full dynamics of the transition rather than relying on simplified approximations. It follows how the fraction of space in the true vacuum grows over time, how that growth slows the overall expansion of the universe, and how energy is released as heat when bubbles fill the space. A direct calculation of the typical distance between bubbles then feeds into established templates for the three main sources of gravitational waves: bubble collisions, sound waves, and turbulence. This approach matters because the strongest signals are expected from very slow or supercooled transitions where older methods lose accuracy.

Core claim

Version 2 introduces a self-consistent treatment of the transition dynamics, including the evolution of the true-vacuum fraction and its backreaction on the Hubble expansion, as well as a consistent description of reheating during percolation, and computes the mean bubble separation directly to map onto gravitational wave templates from bubble collisions, sound waves, and turbulence.

What carries the argument

self-consistent evolution of the true-vacuum fraction together with direct computation of mean bubble separation

If this is right

  • Numerical stability improves for transitions that are strongly supercooled or ultraslow.
  • Large parameter scans can now be performed with consistent physical modeling of the expansion history and reheating.
  • Signal-to-noise ratios for detectors such as LISA and pulsar timing arrays become more reliable across a wider range of models.
  • Built-in interfaces support Bayesian inference on the underlying scalar potential parameters.

Where Pith is reading between the lines

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

  • If the new predictions differ noticeably from older codes in the supercooled regime, existing upper limits from pulsar timing arrays may need re-evaluation.
  • The reheating description could be tested by checking whether the predicted peak frequency and amplitude line up with future LISA data for a given model.
  • Users could extend the framework to include additional sources such as magnetohydrodynamic turbulence once the core dynamics are validated.

Load-bearing premise

The templates derived from existing simulations of bubble collisions, sound waves, and turbulence remain accurate when applied to the strongly supercooled and ultraslow regimes targeted by the new code.

What would settle it

A direct numerical simulation of bubble nucleation and expansion in a strongly supercooled model whose gravitational wave spectrum is then compared to the spectrum predicted by TransitionListener v2.0 using the same input potential.

Figures

Figures reproduced from arXiv: 2605.15259 by Carlo Tasillo, Jonas Matuszak.

Figure 1
Figure 1. Figure 1: Workflow of the TransitionListener pipeline. Given a user-defined tree-level po￾tential and mass spectrum of a theory, the 1-loop effective potential is constructed, the phase structure is traced and possible first-order transitions are identified. For each possible transition, the nucleation history and the evolution of the true-vacuum fraction is computed. Using this, the percolation and reheating temper… view at source ↗
Figure 2
Figure 2. Figure 2: Evolution of the energy densities in the false and true vacuum around the phase [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Numerical validation of the f 1/3 perc correction relating RH with β/H, based on a line scan over the quartic coupling λ in the dark Abelian Higgs model (g = 1, v = 100 MeV), defined in appendix A. Left: Three different definitions of β/H. The factor f 1/3 perc is needed to achieve consistency, see also appendix C for a derivation. Middle: For ultraslow transitions, the conventional definition of (β/H)S3 ,… view at source ↗
Figure 4
Figure 4. Figure 4: Left: Reheating temperature and its approximation T approx perc = Tperc (1 + α) 1/4 as a function of the gauge coupling g in the conformal U(1)′ model (y = 0.01, v = 140 MeV). Right: Comparison of the self-consistent and approximate (¯ρ = ρf) solution of the percolation integral Pt(T) = 1−exp {−I[H[Pt]](T)} for an ultraslow transition with (β/H)RH = 3.5 featured in the dark Abelian Higgs model (λ = 0.018, … view at source ↗
Figure 5
Figure 5. Figure 5: Gravitational wave spectra for the four benchmark points listed in table [PITH_FULL_IMAGE:figures/full_fig_p020_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Module dependencies inside TransitionListener. evolution described by the effective degrees of freedom g ext eff and h ext eff , cf. eq. (2.11). Helper functions (visualised in green in fig. 6) for the bookkeeping of different types of particles are implemented in particles.py, degrees of freedom are computed via the methods implemented in thermodynamics.py, the Jb and Jf integrals are found in finiteT.py,… view at source ↗
Figure 7
Figure 7. Figure 7: Flowchart showing the structure of the percolation algorithm. [PITH_FULL_IMAGE:figures/full_fig_p030_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Compilation of the output plots using the [PITH_FULL_IMAGE:figures/full_fig_p036_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Output of the action plot option for the dark flipflop benchmark point 2 from table 1. Upper panel: Bounce action S3/T in dependence of temperature. Lower panel: Corresponding bubble nucleation rate Γ in units of H4 . 100 101 102 Bubble radius / GeV−1 0 2 4 φi / GeV φ0 φ1 [PITH_FULL_IMAGE:figures/full_fig_p037_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Bubble profile at nucleation for the dark flipflop benchmark point 2 from table [PITH_FULL_IMAGE:figures/full_fig_p037_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: True-vacuum fraction evolution of the conformal dark [PITH_FULL_IMAGE:figures/full_fig_p038_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Overview plot of the example line scan based on the conformal model near the [PITH_FULL_IMAGE:figures/full_fig_p039_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Overview plot of the example grid scan for the Abelian dark Higgs model from [PITH_FULL_IMAGE:figures/full_fig_p040_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Posterior distributions in the α–(β/H)RH plane for the three dark sector models described in appendix A. Left: Generic model predictions generated based on flat and log priors using TransitionListener’s random scan method. Right: Parameter regions favoured by the individual models when requiring a fit to the NANOGrav 15 yr data set, produced using the UltraNest backend in TransitionListener. This figure w… view at source ↗
Figure 15
Figure 15. Figure 15: Comparison of a 2HDM benchmark scan between [PITH_FULL_IMAGE:figures/full_fig_p043_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Relative differences between the BSMPT and TL curves shown in fig. 15. Dotted vertical lines indicate points which we manually identified as unflagged BSMPT errors, which we excluded from this comparison. Note that BSMPT does not automatically flag these points as invalid or numerically questionable. as Tperc = −1 GeV, negative Treh and α ∼ 107 . Further, for λ3 at the borders of the scanned region, BSMPT… view at source ↗
read the original abstract

Gravitational wave backgrounds from strong first-order cosmological phase transitions are key observational targets predicted by many SM extensions and might be observed by current and future observatories like LISA, the Einstein Telescope or pulsar timing arrays (PTAs). Still, their precise forecast given a specific model remains a challenge. In this article, we present TransitionListener v2.0, a Python framework for precision studies of cosmological phase transitions and their associated gravitational wave (GW) signals. The code provides an end-to-end pipeline from a user-defined scalar potential to GW spectra and signal-to-noise ratios, enabling both benchmark studies and large-scale parameter scans. Version 2 introduces a self-consistent treatment of the transition dynamics, including the evolution of the true-vacuum fraction and its backreaction on the Hubble expansion, as well as a consistent description of reheating during percolation. A direct computation of the mean bubble separation allows to faithfully map to the GW spectral templates from bubble collisions, sound waves, and turbulence stemming from state-of-the-art simulations. TransitionListener includes built-in sensitivity curves for space- and ground-based detectors and PTAs, interfaces to PTA likelihoods, and wrappers for Bayesian model inference and high-dimensional parameter scans. Compared to existing public tools, TransitionListener v2.0 improves the physical consistency and numerical stability of GW predictions across a wide range of models, with particular emphasis on the strongly supercooled and ultraslow transition regime where conventional approximations break down and the most promising GW signals are expected.

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 / 2 minor

Summary. The manuscript presents TransitionListener v2.0, a Python framework providing an end-to-end pipeline from a user-defined scalar potential to gravitational wave (GW) spectra and signal-to-noise ratios for cosmological phase transitions. Version 2 introduces self-consistent treatment of transition dynamics, including evolution of the true-vacuum fraction with backreaction on Hubble expansion, consistent reheating during percolation, and direct computation of mean bubble separation to map onto spectral templates for bubble collisions, sound waves, and turbulence. The code includes built-in sensitivity curves for LISA, Einstein Telescope, and PTAs, interfaces to PTA likelihoods, and wrappers for Bayesian inference and parameter scans, with emphasis on the strongly supercooled and ultraslow regime.

Significance. If the self-consistent dynamics and mapping procedure hold under scrutiny, the package would offer a useful advance for precision GW forecasts in models predicting strong first-order transitions. The focus on regimes where conventional approximations break down aligns with the parameter space expected to yield the most detectable signals at LISA and PTAs. Explicit support for reproducible scans and likelihood interfaces strengthens its potential community impact.

major comments (1)
  1. [Abstract and GW spectrum section] Abstract (final paragraph) and the description of the GW mapping procedure: the central claim of 'robust' and 'faithful' predictions rests on applying state-of-the-art simulation templates for bubble collisions, sound waves, and turbulence to the strongly supercooled and ultraslow regimes targeted by the new dynamics. The manuscript does not provide validation, error budgets, or tests demonstrating that the template functional forms and normalizations remain accurate when the altered expansion history modifies wall velocities, sound-wave lifetimes, and turbulence injection scales. This assumption is load-bearing for the robustness claim.
minor comments (2)
  1. Notation for the mean bubble separation and its mapping to the template parameters could be clarified with an explicit equation relating the computed quantity to the peak frequency and amplitude in each channel.
  2. The manuscript would benefit from a dedicated validation subsection comparing v2.0 outputs to known analytic limits or previous codes in the weakly supercooled regime before presenting results in the ultraslow limit.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for recognizing the potential utility of TransitionListener v2.0 for precision GW forecasts in challenging regimes. We address the single major comment below.

read point-by-point responses

  1. Referee: [Abstract and GW spectrum section] Abstract (final paragraph) and the description of the GW mapping procedure: the central claim of 'robust' and 'faithful' predictions rests on applying state-of-the-art simulation templates for bubble collisions, sound waves, and turbulence to the strongly supercooled and ultraslow regimes targeted by the new dynamics. The manuscript does not provide validation, error budgets, or tests demonstrating that the template functional forms and normalizations remain accurate when the altered expansion history modifies wall velocities, sound-wave lifetimes, and turbulence injection scales. This assumption is load-bearing for the robustness claim.

    Authors: We agree that the robustness claim is load-bearing and that the manuscript does not contain dedicated validation or quantitative error budgets for the application of existing simulation templates under the modified expansion histories that arise in strongly supercooled transitions. The new dynamics module computes a self-consistent mean bubble separation and reheating history that serve as improved inputs to the templates, but the functional forms and normalizations themselves originate from simulations performed in standard cosmologies. We will revise the manuscript by adding a dedicated paragraph in the GW spectrum section (and a corresponding note in the abstract) that explicitly states the assumptions inherited from the templates, discusses how altered wall velocities and sound-wave lifetimes could affect the spectra, and provides a qualitative error estimate drawn from the existing literature on non-standard expansion. This will qualify the language of 'robust' and 'faithful' predictions accordingly. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained from user potential

full rationale

The framework computes transition quantities (true-vacuum fraction evolution, Hubble backreaction, reheating, mean bubble separation) directly from a user-defined scalar potential using self-consistent dynamics. These feed into a mapping onto pre-existing GW templates from external state-of-the-art simulations. No self-definitional loops, fitted parameters renamed as predictions, or load-bearing self-citations appear in the derivation chain. The pipeline remains independent of the target GW spectra themselves and is externally falsifiable via the input potential and simulation templates.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Only the abstract is available, so the ledger is necessarily incomplete. The framework relies on standard cosmological assumptions plus external simulation templates whose validity in the target regime is taken as given.

axioms (2)
  • standard math Standard Friedmann-Lemaître-Robertson-Walker cosmology and general relativity govern the background expansion during the transition.
    Invoked implicitly when backreaction on the Hubble rate is discussed.
  • domain assumption Gravitational-wave spectral templates from existing bubble-collision, sound-wave, and turbulence simulations remain applicable in the strongly supercooled and ultraslow regimes.
    Stated in the final paragraph of the abstract as the justification for the direct mean-bubble-separation mapping.

pith-pipeline@v0.9.0 · 5798 in / 1394 out tokens · 43111 ms · 2026-05-19T16:00:55.887132+00:00 · methodology

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