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.

Model-independent features of gravitational waves from bubble collisions

“…The other quantities are introduced by using the relation H 2 = 8πGρ tot /3, assuming that the total energy density can be decomposed into vacuum and radiation energy densities, ρ tot = ρ vac +ρ rad , and assuming that the vacuum energy density coincides with the latent heat released at the phase transition. These approximations can be improved (see [136,137] for recent discussions), but are useful to focus on the calculation of the dimensionless quantity ∆ for a simplified phase transition kinematics and then applying Eq. ( 10) to specific realistic models (see, e.g., [93,114]).…”

Turn up the volume: Listening to phase transitions in hot dark sectors

“…[9] we employ the optimistic estimate turb 10 %. An accurate prediction of the spectrum of GWs generated in a first-order phase transition in the early universe for a given model can be very challenging, requiring numerical methods for the calculation of the effective potential, for the onset and duration of the phase transition, as well as for a description of bubble walls [46]. The focus of the present work is however not on the detailed dynamics of the phase transition itself, but on the cosmological evolution of the dark sector that gives rise to such a phase transition subsequent to the generation of a GW signal.…”

“…A general review of more refined computational approaches than the one used in this work can be found in Ref. [46]. Most importantly, we used the nucleation temperature as a reference scale to define thermodynamic quantities.…”

On the perturbative expansion at high temperature and implications for cosmological phase transitions

“…See also Ref [111]. where the magnitude of various uncertainties due to macroscopic, rather than quantum field theoretic, physics were investigated.…”

“…While certainly important, none of these are quite as severe as those we find here. Our approach to the macroscopic physics can be described as moderately diligent in the language of Ref [111]…”