Gravitational Wave Production by Collisions: More Bubbles

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Abstract

We reexamine the production of gravitational waves by bubble collisions during a first-order phase transition. The spectrum of the gravitational radiation is determined by numerical simulations using the "envelope approximation". We find that the spectrum rises as f^3.0 for small frequencies and decreases as f^-1.0 for high frequencies. Thus, the fall-off at high frequencies is significantly slower than previously stated in the literature. This result has direct impact on detection prospects for gravity waves originating from a strong first-order electroweak phase transition at space-based interferometers, such as LISA or BBO. In addition, we observe a slight dependence of the peak frequency on the bubble wall velocity.

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Most cited references 18

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Gravitational radiation from colliding vacuum bubbles

Arthur Kosowsky, Michael Turner, Richard Watkins (1992)

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Gravitational waves from first-order cosmological phase transitions

Michael Turner, Richard Watkins, Arthur Kosowsky (1992)

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Is Open Access

Gravitational Radiation from First-Order Phase Transitions

Michael Turner, Marc Kamionkowski, Arthur Kosowsky (1993)

We consider the stochastic background of gravity waves produced by first-order cosmological phase transitions from two types of sources: colliding bubbles and hydrodynamic turbulence. First we discuss the fluid mechanics of relativistic spherical combustion. We then numerically collide many bubbles expanding at a velocity \(v\) and calculate the resulting spectrum of gravitational radiation in the linearized gravity approximation. Our results are expressed as simple functions of the mean bubble separation, the bubble expansion velocity, the latent heat, and the efficiency of converting latent heat to kinetic energy of the bubble walls. We also estimate the gravity waves produced by a Kolmogoroff spectrum of turbulence and find that the characteristic amplitude of gravity waves produced is comparable to that from bubble collisions. Finally, we apply these results to the electroweak transition. Using the one-loop effective potential for the minimal electroweak model, the characteristic amplitude of gravity waves produced is \(h\simeq 1.5\times 10^{-27}\) at a characteristic frequency of \(4.1\times 10^{-3} \,\rm Hz\) corresponding to \(\Omega \sim10^{-22}\) in gravity waves, far too small for detection. Gravity waves from more strongly first-order phase transitions, including the electroweak transition in non-minimal models, have better prospects for detection, though probably not by LIGO.