Quantum State during and after Nucleation of an O(4)-Symmetric Bubble

We investigate the quantum state of a scalar field interacting with another field whose false vacuum decays through a Euclidean O(4)-symmetric bubble. We apply the field theoretical formulation of the multi-dimensional WKB tunneling wave function to the system and construct appropriate mode functions which describe the quantum state during and after the false vacuum decay. We find that the quantum state inside the nucleated bubble is Lorentz-invariant but very different from the Minkowski vacuum, containing field excitations which behave like thermal radiation at late times. Implications of the result are discussed; in particular, in connection with the Lorentz invariance of the resulting state, the possibility of creating an open universe through nucleation of an O(4)-symmetric bubble is mentioned.