Is The Universe Infinite Or Is It Just Really Big?

Abstract

The global geometry of the universe is in principle as observable an attribute as local curvature. Previous studies have established that if the universe is wrapped into a flat hypertorus, the simplest compact space, then the fundamental domain must be at least 0.4 times the diameter of the observable universe. Despite a standard lore that the other five compact, orientable flat spaces are more weakly constrained, we find the same bound holds for all. Our analysis provides the first limits on compact cosmologies built from the identifications of hexagonal prisms.

4 pages LaTeX

References in corpus (5)

• Can COBE see the shape of the universe?
• Flat Spots: topological signatures of an open universe in COBE sky maps
• How the Universe got its Spots
• The closet non-Gaussianity of anisotropic Gaussian fluctuations
• Geodesics in Open Universes

Cited by in corpus (33)

• Topology and the Cosmic Microwave Background
• The Cosmic Microwave Background and Particle Physics
• Planck 2013 results. XXVI. Background geometry and topology of the Universe
• Phase Correlations in Cosmic Microwave Background Temperature Maps
• Eigenmodes of 3-dimensional spherical spaces and their application to cosmology
• Do we Live in a "Small Universe"?
• The Degree of Fine-Tuning in our Universe -- and Others
• Well-proportioned universes suppress CMB quadrupole
• The twin paradox in compact spaces
• Detecting Topology in a Nearly Flat Spherical Universe
• The Cosmic Microwave Background for a Nearly Flat Compact Hyperbolic Universe
• How the Universe got its Spots
• A Topological Signature in Cosmic Topology
• Nonperturbative effects in the Standard Model with gauged 1-form symmetry
• The Fluctuations of the Cosmic Microwave Background for a Compact Hyperbolic Universe
• Non-Random Phases in Non-Trivial Topologies
• COBE and Global Topology: An Example of the Application of the Identified Circles Principle
• A Counterexample to Claimed COBE Constraints on Compact Toroidal Universe Models
• Temperature correlations in a compact hyperbolic universe
• Topology beyond the horizon: how far can it be probed?
• COBE Constraints on a Compact Toroidal Low-density Universe
• Topological signatures in CMB temperature anisotropy maps
• Detectability of Cosmic Topology in Flat Universes
• How large is our universe?
• Topology of the universe from COBE-DMR; a wavelet approach
• Distinguishing Marks of Simply-connected Universes
• Ghosts of the Milky Way: a search for topology in new quasar catalogues
• Cosmic microwave anisotropies in an inhomogeneous compact flat universe
• The Hantzsche-Wendt Manifold in Cosmic Topology
• Geometric Gaussianity and Non-Gaussianity in the Cosmic Microwave Background
• Path Integrals on Euclidean Space Forms
• Dark energy as a spatial continuity condition
• Holomorphic Path Integrals in Tangent Space for Flat Manifolds