Consider the following model: we have a rocket-like particle (system) that moves with relativistic speed.

  1. How do we account for the effect that it were moving in an expanding Universe?

  2. How could we compute the same time computations we do with a uniformly accelerating relativistic rocket in special relativity but now taking also into account the expansion of the Universe?

Example of what I am trying to calculate: Suppose a relativistic rocket uniformly accelerating until relativistic speeds, in an expanding Universe with constant $H_0$.

  1. How do we calculate the time to arrive at the edge of the universe, supposing it is the Hubble horizon?
  • $\begingroup$ This is not an answer, just a suggestion, but would the ant on a rubber rope analysis help here? en.wikipedia.org/wiki/Ant_on_a_rubber_rope. Except with the hyperbolic distance/time/speed relationships for the ant. $\endgroup$ – m4r35n357 Jan 9 '18 at 22:03
  • $\begingroup$ It seems tbe kind of question that those who know don't answer while those who answer don't really know. Good luck! $\endgroup$ – safesphere Jan 10 '18 at 3:24

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