The nearly flat universe

TL;DR

This paper explores the concept of a nearly flat universe, defining it through density, geometry, and dynamics, and uses observational data to constrain its flatness parameter, discussing implications for cosmology.

Contribution

It introduces a unified flatness parameter epsilon and analyzes observational constraints, providing a comprehensive understanding of near-flatness in cosmology.

Findings

Upper limit on the flatness parameter epsilon

Universe could be infinite with k=-1 or finite with k=1

Discussion on naturalness of near-flatness

Abstract

We study here what it means for the Universe to be nearly flat, as opposed to exactly flat. We give three definitions of nearly flat, based on density, geometry and dynamics; all three definitions are equivalent and depend on a single constant flatness parameter epsilon that quantifies the notion of nearly flat. Observations can only place an upper limit on epsilon, and always allow the possibility that the Universe is infinite with k=-1 or finite with k=1. We use current observational data to obtain a numerical upper limit on the flatness parameter and discuss its implications, in particular the "naturalness" of the nearly flat Universe.