# Could the Universe have an Exotic Topology?

## TL;DR

This paper investigates whether the universe's topology could be exotic by analyzing how a positive cosmological constant influences the evolution of closed 3-manifolds under Einstein's equations, potentially leading to observed homogeneity.

## Contribution

It extends previous work by incorporating dark energy effects into the analysis of universe topology evolution under Einsteinian dynamics.

## Key findings

- Dark energy modifies the evolution of universe topologies.
- Closed 3-manifolds can evolve towards homogeneity even if initially inhomogeneous.
- Positive cosmological constant influences the asymptotic behavior of the universe.

## Abstract

A recent article uncovered a surprising dynamical mechanism at work within the (vacuum) Einstein `flow' that strongly suggests that many closed 3-manifolds that do not admit a locally homogeneous and isotropic metric \textit{at all} will nevertheless evolve, under Einsteinian evolution, in such a way as to be \textit{asymptotically} compatible with the observed, approximate, spatial homogeneity and isotropy of the universe \cite{Moncrief:2015}. Since this previous article, however, ignored the potential influence of \textit{dark-energy} and its correspondent accelerated expansion upon the conclusions drawn, we analyze herein the modifications to the foregoing argument necessitated by the inclusion of a \textit{positive} cosmological constant --- the simplest viable model for dark energy.