Decay of acoustic turbulence in two dimensions and implications for cosmological gravitational waves

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Gravitational waves from a phase transition associated with the generation of the masses of elementary particles are within the reach of future space-based detectors such as LISA. A key determinant of the resulting power spectrum, not previously studied, is the lifetime of the acoustic turbulence which follows. We study decaying acoustic turbulence using numerical simulations of a relativistic fluid in two dimensions. Working in the limit of nonrelativistic bulk velocities, with an ultrarelativistic equation of state, we find that the energy spectrum evolves toward a self-similar broken power law, with a high wave number behavior of k−2.08±0.08, cut off at very high k by the inverse width of the shock waves. Our model for the decay of acoustic turbulence can be extended to three dimensions using the universality of the high-k power law and the evolution laws for the kinetic energy and the integral length scale. It is used to build an estimate for the gravitational wave power spectrum resulting from a collection of shock waves, as might be found in the aftermath of a strong first order phase transition in the early universe. The power spectrum has a peak wave number set by the initial length scale of the acoustic waves, and a new secondary scale at a lower wave number set by the integral scale after a Hubble time. Between these scales a distinctive new power law appears. Our results allow more accurate predictions of the gravitational wave power spectrum for a wide range of early universe phase transition scenarios.
Original languageEnglish
Article number063511
JournalPhysical Review D
Issue number6
Number of pages22
Publication statusPublished - 12 Sept 2022
MoE publication typeA1 Journal article-refereed

Fields of Science

  • 114 Physical sciences

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