Hello
Is it true that the expansion of the universe will slow down and stop. Then the universe will begin to contract. A contracting universe will shrink smaller and smaller, getting hotter and denser, eventually ending in a fabulously compact inferno, a sort of reverse Big Bang known as the Big Crunch.
This is a challenging question.
Mathematically, a big crunch is possible. We consider the deformation retraction of the geometric shape of the universe (viewed as a sphere or a torus) to a shape that is the skeleton of the original shape of the universe. The assumption made here is the universe is an ever-changing bounded region with a nonempty interior containing one or more strands [called braids] (paths formed by connected [colliding] particles). A deformation retraction would map the contour of the outer surface of the universe to an interior skeleton, which is one of the interior braids. For more about deformation retraction, see Allan Hatcher's book:
https://www.math.cornell.edu/~hatcher/AT/AT.pdf
The attached image from page 1 in chapter 0 of Allan Hatcher's book illustrates a number of simple deformation retractions of shapes to their interior skeletons.
For a good introduction to the boundary conditions of the universe, see
Article The boundary conditions of the universe
More to the point, a big crunch is possible, if we consider an oscillating theory of the universe, which can be viewed as periodic expansions and deformation retractions. See, for example,
Article Oscillating Theory of the Universe
Dear Professor James F Peters,
Thank you very much for your attention and your detailed answer.
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