The Benefits of Diligence: How Precise are Predicted Gravitational Wave Spectra in Models with Phase Transitions?

Abstract

Models of particle physics that feature phase transitions typically provide predictions for stochastic gravitational wave signals at future detectors and such predictions are used to delineate portions of the model parameter space that can be constrained. The question is: how precise are such predictions? Uncertainties enter in the calculation of the macroscopic thermal parameters and the dynamics of the phase transition itself. We calculate such uncertainties with increasing levels of sophistication in treating the phase transition dynamics. Currently, the highest level of diligence corresponds to careful treatments of the source lifetime; mean bubble separation; going beyond the bag model approximation in solving the hydrodynamics equations and explicitly calculating the fraction of energy in the fluid from these equations rather than using a fit; and including fits for the energy lost to vorticity modes and reheating effects. The lowest level of diligence incorporates none of these effects. We compute the percolation and nucleation temperatures, the mean bubble separation, the fluid velocity, and ultimately the gravitational wave spectrum corresponding to the level of highest diligence for three explicit examples: SMEFT, a dark sector Higgs model, and the real singlet-extended Standard Model (xSM). In each model, we contrast different levels of diligence in the calculation and find that the difference in the final predicted signal can be several orders of magnitude. Our results indicate that calculating the gravitational wave spectrum for particle physics models and deducing precise constraints on the parameter space of such models continues to remain very much a work in progress and warrants care.

Probing QCD critical point and induced gravitational wave by black hole physics

“…It has been argued that higherorder corrections prevent true runaway transitions from occurring [60], we will specialize in the case for which the bubble wall terminal velocity v w < 1. For these nonrunway bubbles, the GWs are dominated by sound waves with the energy spectrum [61] h 2 Ω GW (f ) = 8.5 × 10 −6 100 g n…”

Higher-order corrections to the bubble-nucleation rate at finite temperature

“…It is further assumed that β p H (T p ). The percolation temperature is approximately given by [10,22]…”

“…Gravitational waves offer a new way to study primordial phase transitions. And the area is increasingly active [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] after the discovery of gravitational waves by the LIGO collaboration [21]. As such, much work is spent looking at the Electroweak phase transition.…”

“…These considerations take on a new light since higher-order corrections to the nucleation rate is one of the main uncertainties for gravitational wave production [1]. What's more, barring these issues, there are additional uncertainties for predictions of the gravitational wave spectrum [6,10,22,34]. Addressing these issues is vital, for if gravitational waves from a phase transition are discovered, accurate predictions are a must to identify the underlying theory.…”

Exploring the Early Universe with Gaia and THEIA

“…Note that the method we use in this paper is common, but has some non-trivial uncertainties, as it neglects vorticity and reheating effects[25], assumes a bag model[26,27] and is not always an accurate estimate of the nucleation temperature[28] …”