The Copernican Principle in Compact Spacetimes

TL;DR

This paper explores how finite, topologically identified universes influence our understanding of the Copernican principle, revealing a preferred frame that aligns with the comoving frame in homogeneous, isotropic cosmologies.

Contribution

It demonstrates that in finite, topologically identified universes, the preferred frame coincides with the comoving frame, extending the Copernican principle to such topologies.

Findings

The preferred topological frame is the same as the comoving frame.

Finite topologies introduce a preferred frame in cosmology.

Implications of topologically identifying time are discussed.

Abstract

Copernicus realised we were not at the centre of the universe. A universe made finite by topological identifications introduces a new Copernican consideration: while we may not be at the geometric centre of the universe, some galaxy could be. A finite universe also picks out a preferred frame: the frame in which the universe is smallest. Although we are not likely to be at the centre of the universe, we must live in the preferred frame (if we are at rest with respect to the cosmological expansion). We show that the preferred topological frame must also be the comoving frame in a homogeneous and isotropic cosmological spacetime. Some implications of topologically identifying time are also discussed.