Gravitational waves from first order cosmological phase transitions in the Sound Shell Model

We calculate gravitational wave power spectra from first order early Universe phase transitions using the Sound Shell Model. The model predicts that the power spectrum depends on the mean bubble separation, the phase transition strength, the phase boundary speed, with the overall frequency scale set by the nucleation temperature. There is also a dependence on the time evolution of the bubble nucleation rate. The gravitational wave peak power and frequency are in good agreement with published numerical simulations, where bubbles are nucleated simultaneously. Agreement is particularly good for detonations, but the total power for deflagrations is predicted higher than numerical simulations show, indicating refinement of the model of the transfer of energy to the fluid is needed for accurate computations. We show how the time-dependence of the bubble nucleation rate affects the shape of the power spectrum: an exponentially rising nucleation rate produces higher amplitude gravitational waves at a longer wavelength than simultaneous nucleation. We present an improved fit for the predicted gravitational wave power spectrum in the form of a double broken power law, where the two breaks in the slope happen at wavenumber corresponding to the mean bubble separation and the thickness of the fluid shell surrounding the expanding bubbles, which in turn is related to the difference of the phase boundary speed from the speed of sound.