Universal velocity addition formulas analogous to the well-known formula in special relativity are found for four geometrically defined relative velocities in a large class of Robertson-Walker spacetimes. Explicit examples are given. The special relativity result is recovered as a special case, and it is shown that the spectroscopic relative velocity, in contrast to three other geometric relative velocities, follows the same addition law as in special relativity for comoving observers in Robertson-Walker cosmologies.
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In Sec. V the symbol t will denote the time coordinate in optical coordinates which is different from the Fermi time coordinate τ. However, these two coordinate times are identical along the path β0 where they are both proper time.
21.
The case α = 1 gives the Milne universe.
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