Topology and the Cosmic Microwave Background

TL;DR

This paper reviews the mathematical concepts of finite spaces and explores the possibility of observing the universe's finite size through cosmic microwave background radiation, challenging the notion of an infinite universe.

Contribution

It provides a comprehensive overview of finite space mathematics and discusses observational strategies to detect the universe's finite extent.

Findings

Finite space models are mathematically consistent.

Observations of the cosmic microwave background could reveal the universe's finiteness.

Theories beyond general relativity often imply a finite universe.

Abstract

Nature abhors an infinity. The limits of general relativity are often signaled by infinities: infinite curvature as in the center of a black hole, the infinite energy of the singular big bang. We might be inclined to add an infinite universe to the list of intolerable infinities. Theories that move beyond general relativity naturally treat space as finite. In this review we discuss the mathematics of finite spaces and our aspirations to observe the finite extent of the universe in the cosmic background radiation.