An expanding balloon: a small universe

Abstract

Cosmic expansion is an important concept in astronomy. For ease of understanding, astronomers generally draw an analogy between cosmic expansion and the expansion of a spherical surface in 3D space. This study theoretically and experimentally investigates the laws governing the motion of particles on the surface of a balloon during expansion. Firstly, the relevance of Hubble’s law to the movement of the surface particles is analyzed. The results of this analysis show that the receding velocity of a particle relative to another particle is proportional to the arc length between the two particles. Secondly, variation in the Hubble constant with time is examined and thirdly, the variation in arc length between two particles with time during balloon expansion is investigated. Finally, the peculiar motion of a small object on the surface of an expanding balloon is investigated. The experimental data are in good agreement with the results of the theoretical analysis. This comparison between cosmic expansion and the expansion of a balloon suggests that these two processes exhibit essential differences but that the expansion of a balloon can be regarded as an appropriate metaphor for cosmic expansion. The experiment described here requires only simple materials, making it convenient for the in-class exploration of cosmic expansion by middle-school students or junior undergraduates.