Editing Shape of the universe (section)

==== Universe with zero curvature <span class="anchor" id="Flat universe"></span> ====
In a universe with zero curvature, the local geometry is [[geometrization conjecture#Euclidean geometry E3|flat]]. The most familiar such global structure is that of Euclidean space, which is infinite in extent. Flat universes that are finite in extent include the [[torus]] and [[Klein bottle]]. Moreover, in three dimensions, there are 10 finite closed flat 3-manifolds, of which 6 are orientable and 4 are non-orientable. These are the [[flat manifold|Bieberbach manifolds]]. The most familiar is the aforementioned [[three-torus model of the universe|3-torus universe]].

In the absence of dark energy, a flat universe expands forever but at a continually decelerating rate, with expansion [[asymptote|asymptotically]] approaching zero. With dark energy, the expansion rate of the universe initially slows down, due to the effect of gravity, but eventually increases. The [[ultimate fate of the universe]] is the same as that of an open universe in the sense that space will continue expanding forever.

A flat universe can have [[zero-energy universe|zero total energy]].<ref>{{cite AV media |date=2009 |title=A Universe From Nothing lecture by Lawrence Krauss at AAI |url=https://www.youtube.com/watch?v=7ImvlS8PLIo |url-status=live |archive-url=https://ghostarchive.org/varchive/youtube/20211215/7ImvlS8PLIo |archive-date=2021-12-15 |access-date=17 October 2011 |via=[[YouTube]]}}{{cbignore}}</ref>