I found this article very interesting. It claims anything beyond 15 billion light years from earth will be forever out of our reach because the universe is expanding at an accelerating rate. Only three percent of universe would be within our reach if we had the ship capable of traveling at lightspeed.
By observing distant supernovae and measuring how the Universe had expanded over billions of years, astronomers discovered something remarkable, puzzling and entirely unexpected. After maybe seven billion years of the expansion rate slowing down, with gravitation fighting the initial outward push of the Big Bang, distant galaxies stopped slowing down as they receded from us. Instead, they began accelerating, and speeding away faster and faster. This accelerated expansion of the Universe not only has continued ever since, but has allowed us to predict the far future of the distant Universe. It isn’t pretty.
Galaxies that are more distant than about 15 billion light years away are already beyond our reach. The light we’re emitting right now, 13.8 billion years after the Big Bang, will never reach them, and the light they’re emitting will never reach us. If you were to survey the entire observable Universe, you’d find that approximately 97% of all the galaxies in it have already reached this point. They are forever unreachable by us, even if we left today, even at the speed of light.
That’s the way it looks to us now, but if we can survive this tricky time in our history, perhaps new technological solutions as yet unimagined will appear. Wormholes, faster than light travel, time shifting ships?