Consistent Cosmic Bubble Embeddings

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 be either contracting or expanding slower than the background, presenting an obstacle for models of local inflation or false vacuum bubble embeddings. Similarly, a cosmological bubble surrounded by Schwarzschild space must either be contracting (for spatially flat and positively curved bubbles) or bounded in size by the apparent horizon, presenting an obstacle for embedding cosmic bubbles into a background Universe.