Inhomogeneous Anisotropic Cosmology

TL;DR

This paper proves that inhomogeneous and anisotropic cosmologies with certain topologies will inevitably expand forever in some regions, supporting the likelihood of inflation regardless of initial conditions or inhomogeneities.

Contribution

It establishes a universal lower bound on the expansion rate for a broad class of complex cosmological models with various topologies.

Findings

Inhomogeneous, anisotropic universes with 'flat' or 'open' topology expand forever in some regions.

Most 3-manifold topologies lead to eternal expansion, influencing universe fate predictions.

Results support the robustness of inflationary scenarios despite initial inhomogeneities.

Abstract

In homogeneous and isotropic Friedmann-Robertson-Walker cosmology, the topology of the universe determines its ultimate fate. If the Weak Energy Condition is satisfied, open and flat universes must expand forever, while closed cosmologies can recollapse to a Big Crunch. A similar statement holds for homogeneous but anisotropic (Bianchi) universes. Here, we prove that $arbitrarily$ inhomogeneous and anisotropic cosmologies with "flat" (including toroidal) and "open" (including compact hyperbolic) spatial topology that are initially expanding must continue to expand forever at least in some region at a rate bounded from below by a positive number, despite the presence of arbitrarily large density fluctuations and/or the formation of black holes. Because the set of 3-manifold topologies is countable, a single integer determines the ultimate fate of the universe, and, in a specific sense, most 3-manifolds are "flat" or "open". Our result has important implications for inflation: if there is a positive cosmological constant (or suitable inflationary potential) and initial conditions for the inflaton, cosmologies with "flat" or "open" topology must expand forever in some region at least as fast as de Sitter space, and are therefore very likely to begin inflationary expansion eventually, regardless of the scale of the inflationary energy or the spectrum and amplitude of initial inhomogeneities and gravitational waves. Our result is also significant for numerical general relativity, which often makes use of periodic (toroidal) boundary conditions.