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Some Implications of the Cosmological Constant to Fundamental Physics
In the presence of a cosmological constant, ordinary Poincare' special
relativity is no longer valid and must be replaced by a de Sitter special
relativity, in which Minkowski space is replaced by a de Sitter spacetime. In
consequence, the ordinary notions of energy and momentum change, and will
satisfy a different kinematic relation. Such a theory is a different kind of a
doubly special relativity. Since the only difference between the Poincare' and
the de Sitter groups is the replacement of translations by certain linear
combinations of translations and proper conformal transformations, the net
result of this change is ultimately the breakdown of ordinary translational
invariance. From the experimental point of view, therefore, a de Sitter special
relativity might be probed by looking for possible violations of translational
invariance. If we assume the existence of a connection between the energy scale
of an experiment and the local value of the cosmological constant, there would
be changes in the kinematics of massive particles which could hopefully be
detected in high-energy experiments. Furthermore, due to the presence of a
horizon, the usual causal structure of spacetime would be significantly
modified at the Planck scale.Comment: 15 pages, lecture presented at the "XIIth Brazilian School of
Cosmology and Gravitation", Mangaratiba, Rio de Janeiro, September 10-23,
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