Astronomy and Astrophysics – Astrophysics
Scientific paper
1992-11-07
Phys.Rev.D47:4372-4391,1993
Astronomy and Astrophysics
Astrophysics
In plain TeX, 28 pages (not including 13 figures, available by request). FERMILAB-Pub-92/295-A
Scientific paper
10.1103/PhysRevD.47.4372
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 $E_{\rm GW}/E_{\rm vac} = 0.06(H/\beta)^2$ and the peak of the spectrum occurs at $\omega_{\rm max}=1.6\beta$ ($H^2=8\pi G\rho /3$ 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.
Kosowsky Arthur
Turner Michael S.
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