First proposed by Luigi Fantappiè in 1954, the theory remained obscure until it was rediscovered in 1968 by Henri Bacry and Jean-Marc Lévy-Leblond.
In 1972, Freeman Dyson popularized it as a hypothetical road by which mathematicians could have guessed part of the structure of general relativity before it was discovered.
[1] The discovery of the accelerating expansion of the universe has led to a revival of interest in de Sitter invariant theories, in conjunction with other speculative proposals for new physics, like doubly special relativity.
De Sitter suggested that spacetime curvature might not be due solely to gravity[2] but he did not give any mathematical details of how this could be accomplished.
[3] Later, Freeman Dyson[1] advocated this as an approach to making the mathematical structure of general relativity more self-evident.
The symmetry group of this pancake world is then SO(2) semidirect product with R2, meaning that a two-dimensional rotation plus two extra parameters, the x-tilt and the y-tilt.
In relativity, if translations mix up nontrivially with rotations, but the universe is still homogeneous and isotropic, the only option is that spacetime has a uniform scalar curvature.
Due to the small magnitude of the constant, special relativity with its Poincaré group is indistinguishable from de Sitter space for most practical purposes.
Modern proponents of this idea, such as S. Cacciatori, V. Gorini and A. Kamenshchik,[4] have reinterpreted this theory as physics, not just mathematics.
This means that the theory of de Sitter relativity might be able to provide insight on the value of the cosmological constant, perhaps explaining the cosmic coincidence.
When a cosmological constant is viewed as a kinematic parameter, the definitions of energy and momentum must be changed from those of special relativity.
These changes could significantly modify the physics of the early universe if the cosmological constant was greater back then.
Some speculate that a high energy experiment could modify the local structure of spacetime from Minkowski space to de Sitter space with a large cosmological constant for a short period of time, and this might eventually be tested in the existing or planned particle collider.
[13] At distances comparable to the radius of the space, objects feel an additional linear repulsion from the center of coordinates.