The long-term future of space travel

The fact that we apparently live in an accelerating universe places limitations on where humans might visit. If the current energy density of the universe is dominated by a cosmological constant, a rocket could reach a galaxy observed today at a redshift of 1.7 on a one-way journey or merely 0.65 on a round trip. Unfortunately these maximal trips are impractical as they require an infinite proper time to traverse. However, calculating the rocket trajectory in detail shows that a rocketeer could nearly reach such galaxies within a lifetime (a long lifetime admittedly—about 100 years). For less negative values of $w$ the maximal redshift increases becoming infinite for $w\ge -1/3$.

Figure 1

Three possible paths (bold curves) for the rocketeer for de Sitter space and the light cones that these curves asymptotically approach. On the lowermost path, the rocket is constantly accelerating and sends a signal back to Earth that arrives on Earth after an infinite time. The middle path shows a rocket that decelerates and stops relative to the comoving material and sends a signal back to Earth and the uppermost path shows a rocketeer that returns to Earth albeit after an infinite proper time.

Figure 2

The currently observed redshift (upper set of curves) and age of galaxies (lower set of curves) located at the maximal comoving distances that can be achieved on a one-way (outer curves) and round-trip journeys (inner curves).

Figure 3

The upper panel shows the duration of the journey according to the rocketeer The upper curves are for the round-trip journey lasting 99% and 90% of the remaining conformal time. The lower curves show the currently observed value of redshift at the far end of the journey. The upper set is for one-way trips, and the lower set is for round trips.