  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 introduce 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 domain wall of zero
size, followed by its growth by quantum tunnelling and its collision with the
first wall, annihilating both. The barrier factor for this quantum tunneling is
calculated by guessing and verifying a Euclidean instanton for the two-wall
system. We also discuss the classical origin and evolution of closed,
topologically spherical domain walls in the early universe, through a
"budding-off" process involving closed domain walls larger than the Hubble
radius. This paper is the first of a series on this subject.
