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In physics, de Sitter relativity is a modification to the theory of special relativity which may be more accurate in the realm of high-energy particles, near the big-bang and black holes. It may explain dark energy as being at least partly due to spacettime inherently having a de Sitter symmetry group. It may also provide a route to finding a theory of quantum gravity.
Introduction
According to and the references therein, if you take Minkowski's ideas to their logical conclusion then not only are boosts non-commutative but translations are also non-commutative. This means that the symmetry group of spacetime is a de Sitter group rather than the Poincaré group. This results in spacetime being slightly curved even in the absence of matter or energy. This residual curvature is caused by a cosmological constant "Λ" to be determined by observation. Due to the small magnitude of the constant, then special relativity with the Poincaré group is more than accurate enough for all practical purposes, although near the big bang and inflation de Sitter relativity may be more useful due to the cosmological constant being larger back then. It can be considered a new to approach the quantum gravity problem. Note this is not the same thing as solving Einstein's field equations for general relativity to get a de Sitter Universe, rather de Sitter relativity is about getting a de Sitter Group for special relativity which neglects gravity. A modified special relativity means general relativity also needs to be modified.
High energy
The Poincare group generalizes the Galilei group for high-velocity kinematics. The de Sitter group generalizes Poincare for high-energy kinematics. In this theory, the cosmological constant is no longer a free parameter, and can be determined in terms of other quantities. When applied to the whole universe, it is able to predict its value and to explain the cosmic coincidence. When applied to the propagation of ultra-high energy photons, it gives a good estimate of the time delay observed in extragalactic gamma ray flares. More precisely, very-high energy extragalactic gamma-ray flares seem to travel
slower than lower energy ones. If this comes to be confirmed, it will constitute a clear
violation of special relativity.
A large cosmological constant would produce significant changes in the definitions of energy and momentum, as well as in the kinematic relations satisfied by them. These changes could modify significantly the physics that should be applied in the study the early universe. It is conceivable that a high energy experiment could modify the local structure of spacetime from Minkowski space to de Sitter space for a short period of time which could eventually be tested in the existing or planned colliders.
Doubly special relativity
Since the de Sitter group naturally incorporates an invariant length-parameter, de Sitter relativity can be interpreted as an example of the so called doubly special relativity. There is a fundamental difference, though: whereas in all doubly special relativity models the Lorentz symmetry is violated, in de Sitter relativity it remains as a physical symmetry. A drawback of the usual doubly special relativity models is that they are valid only at the
energy scales where ordinary special relativity is supposed to break down, giving rise to a patchwork relativity. On the other hand, de Sitter relativity is found to be invariant
under a simultaneous re-scaling of mass, energy and momentum, and is consequently
valid at all energy scales.
De Sitter general relativity
A modified special relativity means general relativity also needs to be modified.
In ordinary general relativity, the Einstein equation appears as an equality between two covariantly-conserved quantities: the purely geometrical Einstein tensor — divergenceless by the second Bianchi identity — and the source energy-momentum tensor — divergenceless by
Noether's theorem. Consistency with de Sitter special relativity requires that the Einstein equation be generalized, and this results in the cosmological constant no longer being constant
Einstein equation, which is consistent with ordinary (Poincare) special relativity.
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