Does gravity prefer the Poincare dodecahedral space?

TL;DR

This paper investigates whether gravity dynamics favor the Poincare dodecahedral space as a model of the universe, finding it to be significantly more balanced in residual gravity effects than other topologies.

Contribution

It demonstrates that the Poincare space exhibits a much weaker residual gravity effect, suggesting a natural selection of this topology by gravitational considerations.

Findings

Residual gravity effect is about a million times weaker in well-proportioned spaces.

In the Poincare space, the effect is 10,000 times weaker than in other well-proportioned spaces.

The Poincare space is approximately 10^{10} times better balanced in residual gravity effects.

Abstract

The missing fluctuations problem in cosmic microwave background observations is naturally explained by well-proportioned small universe models. Among the well-proportioned models, the Poincare dodecahedral space is empirically favoured. Does gravity favour this space? The residual gravity effect is the residual acceleration induced by weak limit gravity from multiple topological images of a massive object on a nearby negligible mass test object. At the present epoch, the residual gravity effect is about a million times weaker in three of the well-proportioned spaces than in ill-proportioned spaces. However, in the Poincare space, the effect is 10,000 times weaker still, i.e. the Poincare space is about 10^{10} times "better balanced" than ill-proportioned spaces. Both observations and weak limit dynamics select the Poincare space to be special.