Sound shell model for acoustic gravitational wave production at a first-order phase transition in the early Universe

Abstract

A model for the acoustic production of gravitational waves at a first order phase transition is presented. The source of gravitational radiation is the sound waves generated by the explosive growth of bubbles of the stable phase. The model assumes that the sound waves are linear and that their power spectrum is determined by the characteristic form of the sound shell around the expanding bubble. The predicted power spectrum has two length scales, the average bubble separation and the sound shell width when the bubbles collide. The peak of the power spectrum is at wavenumbers set by the sound shell width. For higher wavenumber $k$, the power spectrum decreases as $k^{-3}$. At wavenumbers below the inverse bubble separation, the power spectrum goes as $k^5$. For bubble wall speeds near the speed of sound where these two length scales are distinguished, there is an intermediate $k^{1}$ power law. The detailed dependence of the power spectrum on the wall speed and the other parameters of the phase transition raises the possibility of their constraint or measurement at a future space-based gravitational wave observatory such as eLISA.