Quantum Decay of Domain Walls in Cosmology II: Hamiltonian Approach

This paper studies the decay of a large, closed domain wall in a closed universe. Such walls can form in the presence of a broken, discrete symmetry. We study a novel process of quantum decay for such a wall, in which the vacuum fluctuates from one discrete state to another throughout one half of the universe, so that the wall decays into pure field energy. Equivalently, the fluctuation can be thought of as the nucleation of a second closed domain wall of zero size, followed by its growth by quantum tunnelling and its collision with the first wall, annihilating both. We therefore study the 2-wall system coupled to a spherically symmetric gravitational field. We derive a simple form of the 2-wall action, use Dirac quantization, obtain the 2-wall wave function for annihilation, find from it the barrier factor for this quantum tunneling, and thereby get the decay probability. This is the second paper of a series.