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Gravity waves generated by sounds from big bang phase transitions

Tigran Kalaydzhyan, Edward Shuryak

TL;DR

This work analyzes gravitational-wave production from hydrodynamic sounds generated during cosmological QCD and EW phase transitions, highlighting a potential inverse acoustic cascade that concentrates sound energy at IR momenta to enhance GW emission. It develops a kinetic treatment of acoustic turbulence, deriving stationary spectra for weak turbulence and outlining possible strong-turbulence indices, including $s_{weak}=4$ and potentially $s_{strong}\approx6$, which would dramatically boost $n_k$ at small $k$. The GW rate is computed from a one-loop stress-tensor correlator with on-shell sound modes, showing the yield scales with the square of the sound occupation numbers and is amplified if the inverse cascade shifts power to IR. The paper also discusses QCD-transition uncertainties, possible out-of-equilibrium sources near $T_c$, and observational prospects, noting current pulsar timing bounds and the potential reach of future detectors to probe this mechanism.

Abstract

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. that the sounds produce gravity waves (GW) 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.

Gravity waves generated by sounds from big bang phase transitions

TL;DR

This work analyzes gravitational-wave production from hydrodynamic sounds generated during cosmological QCD and EW phase transitions, highlighting a potential inverse acoustic cascade that concentrates sound energy at IR momenta to enhance GW emission. It develops a kinetic treatment of acoustic turbulence, deriving stationary spectra for weak turbulence and outlining possible strong-turbulence indices, including and potentially , which would dramatically boost at small . The GW rate is computed from a one-loop stress-tensor correlator with on-shell sound modes, showing the yield scales with the square of the sound occupation numbers and is amplified if the inverse cascade shifts power to IR. The paper also discusses QCD-transition uncertainties, possible out-of-equilibrium sources near , and observational prospects, noting current pulsar timing bounds and the potential reach of future detectors to probe this mechanism.

Abstract

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. that the sounds produce gravity waves (GW) 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.

Paper Structure

This paper contains 14 sections, 65 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Frequencies, observational methods and experimental limits on the cosmic gravity waves
  3. Preliminary discussion of sound-to-GW transition
  4. Acoustic turbulence
  5. Scenario 1: Binary decays allowed
  6. Scenario 2: Four-wave interactions
  7. Scenario 2: Strong turbulence
  8. Scenario 2: Time evolution
  9. Generation of gravity waves
  10. The spectral density of the stress tensor correlator
  11. Sounds to GW: Kinematics
  12. GW generation rate
  13. The QCD phase transition and out-of equilibrium sounds
  14. Summary and discussion

Figures (3)

  • Figure 1: Forward scattering diagrams corresponding to the (a) quartic and (b) sextic terms in the Hamiltonian (\ref{['eqn_Hc']}).
  • Figure 2: (From Ref. Hindmarsh:2013xza) Power spectrum of the velocity squared versus the (log of) the wave number $k$. The grey upper curves are for sounds, from bottom to top as time progresses, $t=600, 800, 1000, 1200, 1400\, T_c^{-1}$. The black curves in the bottom are for rotational excitations.
  • Figure 3: (a) Sketch of the collision of two sound waves (b) The diagram and the cut described in the text. External legs are gravity waves (gravitons), and the sounds (phonons) are in the loop.