Recently, I read a science fiction by Cixin Liu. In that novel, when the universe begin to collapse, the direction of time is reversed. People become younger and younger... That is science fiction. But, this makes me wondering what physics laws may really change in a collapsing universe.
* Certainly the Hubble's law of red shift will change to blue shift.
* I think the thermodynamics laws may also change, especially the second law, which determines that heat will transfer naturally from high temperature object to low temperature object. Maybe it will be reversed.
* And what about the direction of time flow, will it really be reversed?
* How about the electrodynamics and quantum physics, will the speed of light in the vacuum be changed also?
The key word in your question is clearly "begin''.
As long as we are considering weak gravitational fields, the expansion and/or collapse of the universe is well described in the frame of the theory of general relativity (GR), and no new physics is needed to describe its evolution if and when it "begins to collapse". Neither the statistical laws of thermodynamic, the velocity of light in vacuum, nor any quantum considerations would thus be modified in such a model.
On the other hand, we don't know much about strong gravitational fields, and we don't have much experimental data to discriminate between the various theories of gravitation (which are all basically equivalent in the linear, weak field approximation) in this limit. On the contrary, we know that they mostly are not compatible with usual quantum theories, so we might be in for some surprises.
And no, while the definition of time flow might be more metaphysical than physical, I can see is no reason to think that it would be changed by the end of the expansion of the universe. But if you are curious about this kind of wild speculations, I'd recommand Greg Egan's Orthogonal (hard..) SF trilogy: The Clockwork Rocket (2011), The Eternal Flame (2012) & The Arrows of Time (2013).
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