The Topology and Size of the Universe from the Cosmic Microwave Background

TL;DR

This paper investigates the universe's topology using WMAP data, constraining the size of possible compact topologies and finding the most probable topology to be T^2 x R^1 with a size near 1.9 times the distance to the last scattering surface.

Contribution

It provides new constraints on the universe's topology and size using seven-year WMAP data, and identifies the most probable topology among several candidates.

Findings

Compact topologies have size constraints between 1.2 and 2.1 times the last scattering distance.

An infinite universe is compatible with data at 4.3 sigma.

Most probable topology is T^2 x R^1 with size 1.9 times the last scattering distance.

Abstract

We study the possibility that the universe has compact topologies T^3, T^2 x R^1, or S^1 x R^2 using the seven-year WMAP data. The maximum likelihood 95% confidence intervals for the size L of the compact direction are 1.7 < L/L_0 < 2.1, 1.8 < L/L_0 < 2.0, 1.2 < L/L_0 < 2.1 for the three cases, respectively, where L_0=14.4 Gpc is the distance to the last scattering surface. An infinite universe is compatible with the data at 4.3 sigma. We find using a Bayesian analysis that the most probable universe has topology T^2 x R^1, with L/L_0=1.9.