Perturbations of the expanding-bubble solution in scalar field theory: Four-dimensional case

The perturbations of Coleman's bubble, considered as an accelerating wall of classical field in real time, are studied in 3+1 dimensions. A retarded Green's function is constructed for linear perturbations around the ''bounce'' solution. We find a power-law growth, in time, of fields and energies in a significant space-time region, for perturbations of arbitrary spatial multipolarity, l. The quantum field fluctuation energy grows accordingly. Applications to phase transitions in the early universe are briefly discussed