# Consistent Cosmic Bubble Embeddings

## TL;DR

This paper uses the Raychaudhuri equation to derive constraints on the embedding of cosmological bubbles into background spacetimes, revealing more stringent conditions than traditional methods, with implications for cosmic inhomogeneities.

## Contribution

It introduces a novel application of the Raychaudhuri equation to determine consistent bubble embeddings, surpassing the limitations of the Israel thin-wall formalism.

## Key findings

- Flat or positively curved bubbles must expand slower than the background.
- Bubbles in Schwarzschild space must be contracting and limited by the apparent horizon.
- Constraints are more stringent than those from traditional thin-wall approaches.

## Abstract

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.