Cosmological acceleration is difficult to accommodate in theories of
fundamental interactions involving supergravity and superstrings. An
alternative is that the acceleration is not universal but happens in a large
localized region, which is possible in theories admitting regular black holes
with de Sitter-like interiors. We point out that, given a global anti-de Sitter
background, the formation of such ‘de Sitter bubbles’ will be enhanced by
mechanisms analogous to the Bizon-Rostworowski instability in general
relativity. This opens an arena for discussing the production of multiple
accelerating universes from anti-de Sitter fluctuations. We demonstrate such
collapse enhancement by explicit numerical work in the context of a simple
two-dimensional dilaton-gravity model that mimics the spherically symmetric
sector of higher-dimensional gravities.