  The interior of a vacuum bubble in de Sitter space may give an open universe
with sufficient homogeneity to agree with observations. Here, previous work by
Bucher, Goldhaber and Turok is extended to describe a thin bubble wall with
nonzero radius and energy difference across the wall. The vacuum modes present
before formation of the bubble propagate into the interior of open universe and
the power spectrum of the resulting gauge invariant gravitational potential is
calculated. It is found to become scale invariant on small scales, with onset
at about the same scale as that found in the zero radius case. There is
sensitivity to the radius and energy difference at large scales, but it is
expected that they cannot be strongly constrained because of cosmic variance.
As the prediction of a scale invariant spectrum is robust with respect to
variation of these parameters at small scales, it is a generic feature of the
contribution of these modes for these thin wall models.
