A Quasilocal Test of the Finiteness of the Universe

TL;DR

This paper proposes a new quasilocal method to determine whether the universe is finite or infinite by measuring the expansion rate of light rays from a surface, bypassing the need for global energy density measurements.

Contribution

It introduces a novel approach to test the universe's finiteness using local measurements of light-ray expansion, avoiding the intractable global energy density determination.

Findings

The method could potentially determine the universe's finiteness without global energy density data.

It provides a way to infer the universe's global geometry through local light-ray expansion measurements.

Abstract

The Cosmological Principle states that the universe is both homogeneous and isotropic. This, alone, is not enough to specify the global geometry of the spacetime. If we were able to measure both the Hubble constant and the energy density we could determine whether the universe is open or closed. Unfortunately, while some agreement exists on the value of the Hubble constant, the question of the energy density seems quite intractable. This Letter describes a possible way of avoiding this difficulty and shows that if one could measure the rate at which light-rays emerging from a surface expand, one might well be able to deduce whether the universe is closed.