Signature for the Shape of the Universe

TL;DR

This paper introduces a statistical method to detect the universe's topology by identifying correlated images of cosmic objects, using simulations across different RW spacetime models.

Contribution

It proposes a new statistical quantity for revealing the universe's topology and demonstrates its effectiveness through computer simulations.

Findings

The method can identify topological signatures in flat, elliptic, and hyperbolic universes.

Simulations show the statistical quantity successfully detects nontrivial topologies.

The approach provides a new tool for understanding the universe's shape.

Abstract

If the universe has a nontrivial shape (topology) the sky may show multiple correlated images of cosmic objects. These correlations can be couched in terms of distance correlations. We propose a statistical quantity which can be used to reveal the topological signature of any Robertson-Walker (RW) spacetime with nontrivial topology. We also show through computer-aided simulations how one can extract the topological signatures of flat, elliptic, and hyperbolic RW universes with nontrivial topology.