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