Analog model for an expanding universe

Abstract

Over the last few years numerous papers concerning analog models for gravity have been published. It was shown that the dynamical equation of several systems (e.g. Bose-Einstein condensates with a sink or a vortex) have the same wave equation as light in a curved-space (e.g. black holes). In the last few months several papers were released which deal with simulations of the universe. In this article the de-Sitter universe will be compared with a freely expanding three-dimensional spherical Bose-Einstein condensate. Initially the condensate is in a harmonic trap, which suddenly will be switched off. At the same time a small perturbation will be injected in the center of the condensate cloud. The motion of the perturbation in the expanding condensate will be discussed, and after some transformations the similarity to an expanding universe will be shown.