  A special relativity based on the de Sitter group is introduced, which is the
theory that might hold up in the presence of a non-vanishing cosmological
constant. Like ordinary special relativity, it retains the quotient character
of spacetime, and a notion of homogeneity. As a consequence, the underlying
spacetime will be a de Sitter spacetime, whose associated kinematics will
differ from that of ordinary special relativity. The corresponding modified
notions of energy and momentum are obtained, and the exact relationship between
them, which is invariant under a re-scaling of the involved quantities,
explicitly exhibited. Since the de Sitter group can be considered a particular
deformation of the Poincar\'e group, this theory turns out to be a specific
kind of deformed (or doubly) special relativity. Some experimental
consequences, as well as the causal structure of spacetime--modified by the
presence of the de Sitter horizon--are briefly discussed.
