The nearly flat universe

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.

14 pages, 5 figures

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• The Most Probable Size of the Universe
• Spacetime, Spin and Gravity Probe B
• f(R,T) Gravity Model Behaving as a Dark Energy Source
• Perturbative approach to $f(R)$-gravitation in FLRW cosmology
• Unitarity at Infinity and Topological Holography
• Horizon, homogeneity and flatness problems -- do their resolutions really depend upon inflation?
• Singularities in and Stability of Ooguri-Vafa-Verlinde Cosmologies