On what does not expand in an expanding universe: a very simple model

TL;DR

This paper demonstrates through a simple harmonic oscillator model that most bound systems do not expand with the universe, highlighting the role of characteristic time scales in their dynamical behavior.

Contribution

It provides an elementary quantum mechanical analysis showing that bound structures remain unaffected by cosmic expansion based on their intrinsic time scales.

Findings

Bound systems do not expand with the universe

The dynamics depend on the characteristic time scale

Most structures are unaffected by cosmic expansion

Abstract

As the separation between galaxies increases owing to the expansion of the universe, galaxies themselves and smaller bound structures do not grow. An accurate description of the dynamics of cosmic structures requires the full apparatus of general relativity. In order to gain a fairly satisfactory understanding of what does not expand in an expanding universe, however, it suffices to take the harmonic oscillator as prototype of a bound system. More precisely, we show that a study of the quantum dynamics of a nonrelativistic harmonic oscillator in an expanding universe makes it clear that most bound systems do not take part in the overall cosmic expansion. The analysis is elementary and indicates that whether a bound structure partakes in the expansion partially or not at all is essentially determined by a characteristic time scale associated with it.