An observer moves with uniform acceleration within a de Sitter spacetime with Hubble constant . The journey can be divided into three stages. In the first stage, the observer accelerates by in the positive direction; in the second stage, acceleration is in the negative direction; and in the third stage, acceleration is again in the positive direction. The proper times of the two acceleration changes are denoted by and .
Round trips are only possible for . At , the observer has reached the turning point, which is located at . The journey ends at , but note that, in general, the observer must have a nonvanishing velocity.
A detailed description of this topic can be found in S. Boblest, T. Müller, and G. Wunner, "Twin Paradox in de Sitter Spacetime," arXiv:1009.3427v1 [gr-qc].