One of the most intriguing things about the universe, which probably cannot be explained by scientific investigations, is that it exists and we, who are a part of the universe, are able to contemplate and study it.
Indeed, it is not clear whether it is meaningful to talk about 'after' the big crunch, just as it is not clear whether it is meaningful to talk about what happened 'before' the big bang. These questions are not necessarily meaningless, but the fact is we simply do not know.
One way in which a recurrence of life can occur is in the event that the cycle of the big bang and final collapse is repeated, and if galaxies are born again and again conditions for the existence of life may develop in some regions. Whether or not this can happen (assuming that the universe is closed) is, of course, not known.
If the standard model is correct, the universe started in a state of high density and temperature, with all matter and radiation forming one great continuous mass. It is very remarkable that this undifferentiated soup should have the intrinsic property that in due course of time it develops into galaxies of which at least one creates life with such staggering complexity, subtlety and diversity and often such stunning beauty. It also creates thinking and feeling beings which in turn can contemplate the universe and study its properties and which can love and hate.
It is possible that those strange sentient beings of the far-future cold universe will find contemplating a warm universe such as ours not very pleasant, much as a nocturnal creature shuns daylight. But the more speculative amongst them may look back to our universe and to the Earth as an ideal world full of sunshine and a supply of adequate energy to last for billions of years, a dream world which will have passed away never to return. And what do we human beings do with this ideal dream world of ours? We oppress each other, build nuclear weapons for each other's destruction, and plunder the resources of the Earth!
The study of the universe as a whole is a unique enterprise. At least in one sense one is seeking to understand the totality of things. We, as thinking beings, are as much a part of the universe as are neutron stars and white dwarfs and our destiny is inextricably bound up with that of the universe.