Quantum State During and after O(4)-Symmetric Bubble Nucleation with Gravitaional Effects

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We extend our previous analysis of the quantum state during and after O(4)-symmetric bubble nucleation to the case including gravitational effects. We find that there exists a simple relationship between the case with and without gravitational effects. In a special case of a conformally coupled scalar field which is massless except on the bubble wall, the state is found to be conformally equivalent to the case without gravity.