Is the generally accepted belief in the science community, that if one sits in a spaceship and move away from Earth where r (distance between earth and my ship) is continuously increasing, can one keep going forever?

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    $\begingroup$ The point that that is mind blowing but other scenario are mind blowing as well. $\endgroup$ – Alchimista Mar 19 '18 at 11:50

Yes. There are no edges of the universe that have been observed.

The standard cosmological models favoured by observations (open or flat universes) allow you to move outwards indefinitely. Closed universes are like the surface of a sphere, and you would eventually return to Earth unless the expansion was too fast; the same is true for the models with nontrivial topologies - but these have no evidence at present.

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  • $\begingroup$ I think it's only fair to say that we don't know whether the universe is open or closed. It's possible it's closed, in which case one would eventually end up back at the Earth (or where the Earth used to be, since it would move around the Sun which moves around the Milky Way center which is also moving etc). $\endgroup$ – Allure Mar 19 '18 at 9:41
  • $\begingroup$ Your answer does not discuss the effect of cosmic expansion and what a traveler would be able to see and reach due to that. E.g. can a traveler ever reach the galaxies we see now at the edge of the observed universe ? $\endgroup$ – StephenG Mar 19 '18 at 12:01
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    $\begingroup$ @Allure - yes, we do not know. But getting a closed universe to also expand in accelerating manner requires a bit of extra work, so there is a simplicity prior here. $\endgroup$ – Anders Sandberg Mar 19 '18 at 12:04
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    $\begingroup$ @StephenG - Yes, the acceleration does prevent you from reaching many galaxies we can currently see. We can only travel to galaxies currently within distance ~4.9 Gpc. Those beyond will recede too fast to catch up. But this event horizon (in comoving coordinates) doesn't stop you from travelling straight ahead, it is just going to be less and less stuff to encounter in the far future. $\endgroup$ – Anders Sandberg Mar 19 '18 at 12:06

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