Bubble wall perturbations coupled with gravitational waves

We study a coupled system of gravitational waves and a domain wall which is the boundary of a vacuum bubble in de Sitter spacetime. To treat the system, we use the metric junction formalism of Israel. We show that the dynamical degree of the bubble wall is lost and the bubble wall can oscillate only while the gravitational waves go across it. It means that the gravitational backreaction on the motion of the bubble wall can not be ignored.