Gravitational Radiation from Colliding Vacuum Bubbles: Envelope Approximation to Many-Bubble Collisions

Abstract

We introduce an approximation to calculate the gravitational radiation produced by the collision of true-vacuum bubbles that is simple enough to allow the simulation of a phase transition by the collision of hundreds of bubbles. This ``envelope approximation'' neglects the complicated ``overlap'' regions of colliding bubbles and follows only the evolution of the bubble walls. The approximation accurately reproduces previous results for the gravitational radiation from the collision of two scalar-field vacuum bubbles. Using a bubble nucleation rate given by $\Gamma ={\Gamma }_0{e}^{\beta t}$, we simulate a phase transition by colliding 20 to 200 bubbles; the fraction of vacuum energy released into gravity waves is $E_{\mathrm{GW}}/E_{\mathrm{vac}}=0.06(H/\beta {)}^2$ and the peak of the spectrum occurs at ${\omega }_{\max }=1.6\beta$ ($H^2=8\pi G\rho /3$ is the Hubble constant associated with the false-vacuum phase). The spectrum is very similar to that in the two-bubble case, except that the efficiency of gravity-wave generation is about five times higher, presumably due to the fact that a given bubble collides with many others. Finally, we consider two further ``statistical'' approximations, where the gravitational radiation is computed as an incoherent sum over individual bubbles weighted by the distribution of bubble sizes. These approximations provide reasonable estimates of the gravitational-wave spectrum with far less computation.

In plain TeX, 28 pages (not including 13 figures, available by request). FERMILAB-Pub-92/295-A

References in corpus (2)

• Towards the Theory of Cosmological Phase Transitions
• Instability and Subsequent Evolution of Electroweak Bubbles

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