de Sitter special relativity

Abstract

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 Poincaré 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.

Dark energy as a kinematic effect

“…Namely, the concomitant replacement of special relativity with an S O(1, 4) invariant special relativity allows for the existence of an invariant length parameter proportional to Λ −2 , while preserving the constancy of the speed of light [5]. Because the cosmological function is not restricted to be constant, its value can evolve with cosmological time, this model may be suitable to describe the evolution of the universe, which requires different values of the cosmological term at different epochs.…”

“…Be that as it may, there is significant evidence that our universe momentarily undergoes accelerated expansion [3,4], which indicates that the large-scale kinematics of spacetime is approximated better by the de Sitter group S O (1,4) [5]. We shall take this evidence to heart and conjecture that local kinematics is regulated by the de Sitter group.…”

Lorentz violation with a universal minimum speed as foundation of de Sitter relativity

“…[14][15][16] Thus, SSR-theory provides an explanation for the effects of dark energy (cosmological anti-gravity) by means of a new kinematics principle (an invariant minimum speed). However, unlike relativity theories based on dS-group, the invariant minimum speed leads to a change on Minkowski metric by means of the introduction of the scale factor depending on velocity, i.e.…”

“…14,15,18 Taking into account the relationship between the vacuum energy density and the cosmological constant, namely,…”

Is Physics Asking for a New Kinematics?

“…On the other hand, de Sitter relativity is found to be invariant under a simultaneous re-scaling of mass, energy and momentum [6], and is consequently valid at all energy scales -it is a "universal" relativity. This is a very important property presented by all fundamental theories, like for example quantum mechanics.…”