Pure and Applied Mathematics Quarterly
Volume 15 (2019)
Special Issue: In Honor of Robert Bartnik (Part 2 of 2)
Guest Editors: Piotr T. Chruściel, Greg Galloway, Jim Isenberg, Pengzi Miao, Mu-Tao Wang, and Shing-Tung Yau
Could the universe have an exotic topology?
Pages: 921 – 966
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 at all will nevertheless evolve, under Einsteinian evolution, in such a way as to be asymptotically compatible with the observed, approximate, spatial homogeneity and isotropy of the universe . Since this previous article, however, ignored the potential influence of 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 positive cosmological constant—the simplest viable model for dark energy.
Moncrief is grateful to Robert Bartnik for making possible his two, very enriching professional visits to Australia and for conveying to him numerous valuable insights into the properties of CMC slicings of Einsteinian spacetimes. This article is dedicated to Bartnik on the occasion of his 60th birthday.
Received 26 February 2019
Received revised 6 June 2019
Accepted 15 June 2019
Published 2 January 2020