Gravity waves generated by sounds from big bang phase transitions

Inhomogeneities associated with the cosmological QCD and electroweak phase transitions produce hydrodynamical perturbations, longitudinal sounds and rotations. It has been demonstrated by Hindmarsh et al. [Phys. Rev. Lett. 112, 041301 (2014)] that the sounds produce gravity waves well after the phase transition is over. We further argue that, under certain conditions, an inverse acoustic cascade may occur and move sound perturbations from the (UV) momentum scale at which the sound is originally produced to much smaller (IR) momenta. The weak turbulence regime of this cascade is studied via the Boltzmann equation, possessing stationary power and time-dependent self-similar solutions. We suggest certain indices for the strong turbulence regime as well, into which the cascade eventually proceeds. Finally, we point out that two on-shell sound waves can produce one on-shell gravity wave, and we evaluate the rate of the process using a standard sound loop diagram.