(ed.). Gravitational waves (IOP, 2001)(422s).

First-order phase transitions 2358070Ω=10 −960ln(η s/η 1)5040Ω=10−830Ω=10−720100.00 0.05 0.10 0.15 0.20βFigure 13.8. The forbidden region in the parameter space is the shaded area. Along thechain line ≡ h 2 0 gw(1 kHz) = 10 −7 , along the dotted line = 10 −8 and along thedashed line = 10 −9 (from [58]).The maximum value obtained for gw is still below the experimental plannedsensibility of VIRGO and LIGO, but hopefully within the planned sensitivity ofthe advanced projects.13.4 First-order phase transitionsFirst-order phase transitions are thought to have occurred in the early stage of theexpansion of the universe, each time its temperature dropped sufficiently belowthe critical temperature T c of a transition. Candidates for such a phase transitioninclude GUT-symmetry breaking (T c = 10 15±1 GeV), electroweak-symmetrybreaking (T c ∼ 200 GeV), and phase transitions yet to be discussed.In a first-order phase transition, the universe starts in a metastable (highenergy-density)false-vacuum state. If the energy barrier separating this stateto the (low-energy-density) true-vacuum state is sufficiently large, significantsupercooling occurs and the transition between these two states proceeds vianucleation [59] of bubbles of true vacuum within the false vacuum phase [60].Once nucleated, each bubble larger than a critical size begins to expand, beingdriven by the energy difference (latent heat) between its true-vacuum interiorand the false-vacuum exterior. This energy difference is converted into kineticenergy of the bubble wall, which become thinner and more energetic as thebubble expands, and rapidly approaches a velocity near the speed of light. As