Question some of you might be able to answer

[TheDesertFox]

Some of this doesn't have much to do with time travel, but I figure people with a knowledge of time travel might also know about this:

Okay, the universe is expanding and collapsing. Most scientists believe this. We'll assume there is only one universe for this. Most universes created don't even have star creation. Anyway, through the infinite length of time, are we "doomed" (although I don't want to sound negative) to live our lives over and over and over again? Eventually, though randomness, will a universe exactly like this be created, even if it is some 10000000000000000000000^10000000000000000000 years later?

 

[RenUnconscious]

Okay, the universe is expanding and collapsing.

Expanding yes (and faster than before, but slower than the initial Big Bang explosion). Collapsing? There is actually no proof of this, the so called, Big Crunch. As we have almost no understanding of Dark Matter and Dark Energy, the mass of 90% of our Universe that cannot even be Seen.

Anyway, through the infinite length of time, are we "doomed" (although I don't want to sound negative) to live our lives over and over and over again?

Time is just a measurement, one that has no meaning if we do end up back in the Big Crunch. I would not say we are doomed, because of Chaos theory, the set of circumstances that made You or I, is so extremely unlikely to happen again, that, your consciousness would be altered were there to be another You in another Universe. but are you talking one every expanding/contracting univerese or multi-dimensional universes?

Eventually, though randomness, will a universe exactly like this be created, even if it is some 10000000000000000000000^10000000000000000000 years later?

I would say this question deals more with a Creator than that of the randomness of mathematics and numbers. Is the universe truly random, is there an underlying Order to the Chaos? Is there a reason?