Theory of how whole universe moving cosmic space?

“I don’t think the human race will survive the next thousand years, unless we spread into space. There are too many accidents that can befall life on a single planet. But I’m an optimist. We will reach out to the stars.” — Stephen Hawking, theoretical physicist and cosmologist

the Big Bang theory is explain us how our universe in created, our universe birth from a explosion of singularity of dense matter then galaxy ,stars and planets are made .

So i can say that all cosmic objects traveling some distance in this cosmic space fabric , so that way our universe moving or traveling in this cosmic space like caterpillar. this means Big Bang to big crunch.