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arxiv: 2606.27775 · v1 · pith:UBHSTSLLnew · submitted 2026-06-26 · ✦ hep-ph · astro-ph.CO

HydroGrav: Precise hydrodynamics and gravitational waves for cosmological phase transitions

Flynn Linton , William Searle , Xiao Wang , Csaba Bal\'azs This is my paper

Pith reviewed 2026-06-29 04:17 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.CO
keywords hydrodynamicsgravitational wavesfirst-order phase transitionselectroweak symmetry breakingsound shell modelequation of stateLISA
0
0 comments X

The pith

HydroGrav computes gravitational wave spectra from first-order phase transitions using the exact equation of state from the effective potential rather than bag or μν approximations.

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

HydroGrav is a code that constructs self-similar fluid profiles directly from the exact equation of state obtained from a model's effective potential. It feeds those profiles into the sound shell model to produce gravitational wave spectra and also supports the simpler bag and μν equations of state. When applied to a Z2-symmetric extension of the Standard Model, the exact equation of state yields fluid profiles that differ from the approximations, resulting in shifts in the peak amplitude and overall shape of the gravitational wave spectrum. A scan of the model's parameter space locates the regions where these differences are pronounced. The code further quantifies how the choice of equation of state changes the expected signal-to-noise ratio for LISA after a four-year observation.

Core claim

HydroGrav builds self-similar hydrodynamic fluid profiles from the exact equation of state taken directly from the effective potential and inserts them into the sound shell model to obtain gravitational wave spectra. For a Z2-symmetric extension of the Standard Model the resulting profiles and spectra differ from those generated by the bag and μν equations of state both in peak amplitude and in spectral shape. Parameter-space scans identify the regions where the discrepancies are largest, and the consequent change in LISA signal-to-noise ratio after four years is estimated.

What carries the argument

Self-similar fluid profiles generated from the exact equation of state of the effective potential, which replace bag and μν approximations inside the sound shell model for gravitational wave spectrum computation.

If this is right

  • Fluid profiles differ between the exact equation of state and the bag or μν approximations in the Z2 model.
  • Gravitational wave spectra obtained via the sound shell model show shifts in peak amplitude and spectral shape.
  • Certain regions of the model's parameter space exhibit the largest discrepancies between exact and approximate equations of state.
  • LISA signal-to-noise ratios after four years change when the exact equation of state is used instead of simplified approximations.

Where Pith is reading between the lines

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

  • The HydroGrav method can be applied to additional particle-physics models to test whether simplified equations of state remain adequate.
  • If the reported differences persist across models, existing gravitational-wave forecasts for phase transitions may require systematic revision.
  • Direct comparison of HydroGrav outputs against full 3D simulations would provide an independent check on the self-similar assumption.

Load-bearing premise

The self-similar hydrodynamic profiles obtained from the exact equation of state remain valid representations of the bubble-wall dynamics throughout the transition, and the sound-shell model correctly maps those profiles onto the gravitational-wave spectrum without additional model-dependent corrections.

What would settle it

A three-dimensional numerical hydrodynamic simulation of bubble expansion in the same Z2-symmetric model that produces fluid velocity and enthalpy profiles inconsistent with HydroGrav's self-similar exact-EOS solutions would falsify the claimed mapping to gravitational wave spectra.

read the original abstract

We present HydroGrav, a C++ code used to construct self-similar fluid profiles, using the exact equation of state determined directly from the effective potential, for any particle physics model capable of producing a first-order electroweak phase transition. HydroGrav also supports the bag and $\mu\nu$ (or improved bag) equations of state and includes an implementation of the sound shell model for computing the corresponding gravitational wave spectra. Using this framework, we compare the fluid profiles and gravitational wave spectra for the simplified (bag and $\mu\nu$) and exact equations of state for a $\mathbb{Z}_2$-symmetric extension of the Standard Model. Furthermore, we perform a scan across the parameter space of this model to identify regions where the simplified and exact equations of state differ in peak amplitude and spectral shape. Finally, we estimate the effect of using the exact equation of state on the signal-to-noise ratio across the parameter space, as measured by LISA after a 4-year mission.

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 HydroGrav, a C++ code that constructs self-similar fluid profiles from the exact equation of state derived directly from the effective potential for any model with a first-order electroweak phase transition. The code also implements the bag and μν equations of state and the sound-shell model for gravitational-wave spectra. For a Z2-symmetric extension of the Standard Model the authors compare fluid profiles and GW spectra between the exact and simplified EOS, scan the model parameter space to locate regions of difference in peak amplitude and spectral shape, and estimate the resulting change in LISA signal-to-noise ratio after a 4-year mission.

Significance. If the central comparisons are robust, the work supplies a practical tool for quantifying the systematic error introduced by simplified EOS approximations in GW forecasts from cosmological phase transitions, directly informing the interpretation of LISA data and the design of future detectors.

major comments (1)
  1. [Sound-shell model implementation and results section] The central claim that exact-EOS profiles produce identifiable differences in GW peak amplitude and spectral shape rests on feeding self-similar solutions directly into the sound-shell model. The manuscript provides no quantitative validation (e.g., comparison against 3-D hydrodynamic simulations) that quantifies the modeling error of the sound-shell decomposition when the EOS is non-polytropic and temperature-dependent in a model-specific way; this validation is load-bearing for the reported differences and the LISA SNR estimates.
minor comments (2)
  1. The abstract states that a parameter-space scan was performed but does not report the scanned ranges, the number of points, or the fraction of parameter space where differences exceed a stated threshold; adding these numbers would improve reproducibility.
  2. Notation for the exact EOS (derived from the effective potential) versus the bag and μν cases should be introduced with a single equation or table early in the text to avoid repeated re-definition.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting an important point about the sound-shell model. We respond to the major comment below.

read point-by-point responses

  1. Referee: The central claim that exact-EOS profiles produce identifiable differences in GW peak amplitude and spectral shape rests on feeding self-similar solutions directly into the sound-shell model. The manuscript provides no quantitative validation (e.g., comparison against 3-D hydrodynamic simulations) that quantifies the modeling error of the sound-shell decomposition when the EOS is non-polytropic and temperature-dependent in a model-specific way; this validation is load-bearing for the reported differences and the LISA SNR estimates.

    Authors: We agree that the manuscript does not contain a direct quantitative validation of the sound-shell model via comparison to 3D hydrodynamic simulations for the case of non-polytropic, temperature-dependent EOS derived from a specific effective potential. The sound-shell model is a standard approximation in the literature for computing GW spectra from self-similar fluid profiles (as used in prior works with bag and μ u EOS), and the central contribution of this work is to implement and compare the exact EOS within that established framework. Performing dedicated 3D simulations to quantify the additional modeling error for model-specific EOS lies outside the scope of the present manuscript. We will revise the results section to include an expanded discussion of the assumptions underlying the sound-shell model and its applicability to exact EOS, thereby clarifying the context and limitations of the reported amplitude and shape differences as well as the LISA SNR estimates. revision: yes

Circularity Check

0 steps flagged

No significant circularity; comparisons between independently solved EOS cases

full rationale

The manuscript implements HydroGrav to solve self-similar fluid profiles directly from the exact equation of state extracted from the effective potential, and separately from the bag and μν EOS. These profiles are then fed into the sound-shell model to generate GW spectra for comparison across the Z2 model parameter space. No equation or result reduces by construction to a fitted quantity defined from the same data, no self-citation chain supplies a load-bearing uniqueness theorem, and the central comparisons rest on distinct numerical implementations of the EOS rather than renaming or self-referential prediction. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard domain assumptions of the sound-shell model and self-similar hydrodynamics; no new free parameters or invented entities are introduced in the abstract.

axioms (2)
  • domain assumption The sound shell model maps fluid velocity and enthalpy profiles to the gravitational-wave spectrum without additional model-dependent corrections.
    Invoked to obtain GW spectra from the computed profiles.
  • domain assumption Self-similar solutions accurately capture the late-time hydrodynamic evolution of expanding bubbles.
    Basis for constructing the fluid profiles in HydroGrav.

pith-pipeline@v0.9.1-grok · 5706 in / 1375 out tokens · 37073 ms · 2026-06-29T04:17:59.160961+00:00 · methodology

discussion (0)

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