Time travel in space?

i've been looking at pictures online of the possible ways of the universe's expansion and apparently our solar system's located in the "present" and that there is a "future" far far away part of our universe (as well as a past) if we are stuck in the present then is the future part of our universe that is very far away also several years ahead as if they have a sort of time lapse because i have heard of how time can warp or possibly end in space