GRAVITATIONAL-RADIATION FROM 1ST-ORDER PHASE-TRANSITIONS

We consider the stochastic background of gravity waves produced by fir st-order cosmological phase transitions from two types of sources: col liding bubbles and hydrodynamic turbulence. First we discuss the fluid mechanics of relativistic spherical combustion. We then numerically c ollide many bubbles expanding at a velocity v and calculate the result ing spectrum of gravitational radiation in the linearized gravity appr oximation. Our results are expressed as simple functions of the mean b ubble separation, the bubble expansion velocity, the latent heat, and the efficiency of converting latent heat to kinetic energy of the bubb le walls. A first-order phase transition is also likely to excite a Ko lmogoroff spectrum of turbulence. We estimate the gravity waves produc ed by such a spectrum of turbulence and find that the characteristic a mplitude of the gravity waves produced is comparable to that from bubb le collisions. Finally, we apply these results to the electroweak tran sition. Using the one-loop effective potential for the minimal electro weak model, the characteristic amplitude of the gravity waves produced is h congruent-to 1.5 x 10(-27) at a characteristic frequency of 4.1 x 10(-3) Hz corresponding to OMEGA approximately 10(-22) in gravity wa ves, far too small for detection. Gravity waves from more strongly fir st-order phase transitions, including the electroweak transition in no nminimal models, have better prospects for detection, though probably not by LIGO.