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.
