Pure and Applied Mathematics Quarterly

Volume 15 (2019)

Number 3

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

DOI: https://dx.doi.org/10.4310/PAMQ.2019.v15.n3.a7


Vincent Moncrief (Departments of Physics and Mathematics, Yale University, New Haven, Connecticut, U.S.A.)

Puskar Mondal (Department of Geophysics, Yale University, New Haven, Connecticut, U.S.A.)


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 [1]. 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