Shape of the acoustic gravitational wave power spectrum from a first order phase transition
Abstract
We present results from largescale numerical simulations of a first order thermal phase transition in the early Universe, in order to explore the shape of the acoustic gravitational wave and the velocity power spectra. We compare the results with the predictions of the recently proposed sound shell model. For the gravitational wave power spectrum, we find that the predicted k^{3} behavior, where k is the wave number, emerges clearly for detonations. The power spectra from deflagrations show similar features, but exhibit a steeper highk decay and an extra feature not accounted for in the model. There are two independent length scales: the mean bubble separation and the thickness of the sound shell around the expanding bubble of the low temperature phase. It is the sound shell thickness which sets the position of the peak of the power spectrum. The low wave number behavior of the velocity power spectrum is consistent with a causal k^{3}, except for the thinnest sound shell, where it is steeper. We present parameters for a simple broken power law fit to the gravitational wave power spectrum for wall speeds well away from the speed of sound where this form can be usefully applied. We examine the prospects for the detection, showing that a LISAlike mission has the sensitivity to detect a gravitational wave signal from sound waves with an RMS fluid velocity of about 0.05 c , produced from bubbles with a mean separation of about 10^{2} of the Hubble radius. The shape of the gravitational wave power spectrum depends on the bubble wall speed, and it may be possible to estimate the wall speed, and constrain other phase transition parameters, with an accurate measurement of a stochastic gravitational wave background.
 Publication:

Physical Review D
 Pub Date:
 November 2017
 DOI:
 10.1103/PhysRevD.96.103520
 arXiv:
 arXiv:1704.05871
 Bibcode:
 2017PhRvD..96j3520H
 Keywords:

 Astrophysics  Cosmology and Nongalactic Astrophysics;
 High Energy Physics  Phenomenology
 EPrint:
 16+1 pages, 9+1 figures