Warning: I'm trying to obfuscate much of this question, and hiding the key elements in spoiler blocks..but some spoilers will probably be inevitable.

At the ending of the book Tau Zero the ending seems odd:

the spaceship, travelling at close to the speed of light, is able to have eons pass by in instants, which allows it to travel far, far into our future. It eventually ends up circling around the eventually collapsing universe, and is able to watch as the universe is reborn in a new big bang.

Now, I'm not asking whether the big-crunch theory is out of date, whether the universe is slated to eventually collapse, or about the relative (no pun intended) likelyhood of the creation of a spaceship that can travel near the speed of light. He makes these assumptions/assertions, backs them up as he sees fit, and moves on.

But I was under the understanding that the matter that takes up space in our universe is inately connected with the space of the universe...that during a big-crunch type event, it would not just be the matter within the universe collapsing, but space itself collapsing to a singularity...which would leave the ending not making any sense. Yet, with the amount of effort he puts into explaining the effects of time dialation and the irrationality of the notion of simultaneity at near-light speeds, it seems odd that something like this would be left hanging.

Is there a solution?