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Apr 16, 2016 at 17:31 comment added pela @RobJeffries: Sorry for misspelling your name. :)
Apr 16, 2016 at 17:29 comment added pela @Jonathan: No, these calculations assume a cosmological constant, i.e. no big rip. But the acceleration still means that the recession velocity of any object not gravitationally bound to us will increase without bounds, eventually making them unreachable.
Apr 16, 2016 at 17:17 comment added ProfRob @Pela this is the answer.
Apr 16, 2016 at 17:10 comment added Jonathan @pela, Does this imply that in 15 billion years (roughly 3 * 5 Gpc = 15 G light years), something like a big rip is going to happen to the universe?
Apr 16, 2016 at 17:00 comment added pela @RobJeffries and Jonathan: But if you take into account expansion, the answer is almost given in the question: You can go no farther than 5 Gpc, which would take $\infty$ as seen from the Earthlings, and only a few years as seen from the traveler, since she very quickly reaches (almost) the speed of light and hence experiences (almost) no time to go anywhere.
Apr 16, 2016 at 16:54 comment added Jonathan Good point, I did not account for the expansion of the universe taking place here. That's why I am looking for additional feedback.
Apr 16, 2016 at 16:04 comment added ProfRob This appears to be a standard twin-paradox solution; but how have you accounted for the expansion of the universe?
Apr 16, 2016 at 15:14 history answered Jonathan CC BY-SA 3.0