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Models of particle physics that feature phase transitions typically providepredictions for stochastic gravitational wave signals at future detectors andsuch predictions are used to delineate portions of the model parameter spacethat can be constrained. The question is: how precise are such predictions?Uncertainties enter in the calculation of the macroscopic thermal parametersand the dynamics of the phase transition itself. We calculate suchuncertainties with increasing levels of sophistication in treating the phasetransition dynamics. Currently, the highest level of diligence corresponds tocareful treatments of the source lifetime; mean bubble separation; going beyondthe bag model approximation in solving the hydrodynamics equations andexplicitly calculating the fraction of energy in the fluid from these equationsrather than using a fit; and including fits for the energy lost to vorticitymodes and reheating effects. The lowest level of diligence incorporates none ofthese effects. We compute the percolation and nucleation temperatures, the meanbubble separation, the fluid velocity, and ultimately the gravitational wavespectrum corresponding to the level of highest diligence for three explicitexamples: SMEFT, a dark sector Higgs model, and the real singlet-extendedStandard Model (xSM). In each model, we contrast different levels of diligencein the calculation and find that the difference in the final predicted signalcan be several orders of magnitude. Our results indicate that calculating thegravitational wave spectrum for particle physics models and deducing preciseconstraints on the parameter space of such models continues to remain very mucha work in progress and warrants care.

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