  The Raychaudhuri equation for null rays is a powerful tool for finding
consistent embeddings of cosmological bubbles into a background spacetime in a
way that is largely independent of the matter content. We find that spatially
flat or positively curved thin wall bubbles surrounded by a cosmological
background must have a Hubble expansion that is either contracting or expanding
slower than the background, which are more stringent constraints than those
obtained by the usual Israel thin-wall formalism. Similarly, a cosmological
bubble surrounded by Schwarzschild space, occasionally used as a simple "swiss
cheese" model of inhomogenities in an expanding universe, must be contracting
(for spatially flat and positively curved bubbles) and bounded in size by the
apparent horizon.
