Some Implications of the Cosmological Constant to Fundamental Physics

TL;DR

This paper explores how a non-zero cosmological constant leads to a de Sitter special relativity framework, altering fundamental notions of energy, momentum, and spacetime structure, with potential experimental implications.

Contribution

It introduces the concept of de Sitter special relativity replacing Poincare' relativity in the presence of a cosmological constant, highlighting its effects on symmetries and potential experimental tests.

Findings

De Sitter relativity replaces Poincare' relativity with modified symmetries.

Violations of translational invariance could be experimentally detectable.

The causal structure of spacetime is significantly altered at the Planck scale.

Abstract

In the presence of a cosmological constant, ordinary Poincare' special relativity is no longer valid and must be replaced by a de Sitter special relativity, in which Minkowski space is replaced by a de Sitter spacetime.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.