The observable universe is limited by a cosmic horizon. Galaxies beyond the horizon move away from us faster than light, so we cannot see them. Imagine a spaceship in the vicinity of our horizon. If the ship is stationary relative to the local galaxies there, we would see it moving away from us near the speed of light due to the space expansion.
Now the ship takes off in the direction away from us with a relativistic speed relative to the local galaxies there. What would be its speed relative to us? Would the ship cross the horizon and disappear from our view even though the ship still is not as far away from us as the actual horizon? Or would the relativistic speed addition apply allowing us to still see the ship (albeit deeply redshifted)?
