De Sitter Invariant Special Relativity

In mathematical physics, de Sitter invariant special relativity is the speculative idea that the fundamental symmetry group of spacetime is the Indefinite orthogonal group SO(4,1), that of de Sitter space. In the standard theory of General Relativity, de Sitter space is a highly symmetrical special vacuum solution, which requires a cosmological constant or the stress-energy of a constant scalar field to sustain.

The idea of de Sitter invariant relativity is to require that the laws of physics are not fundamentally invariant under the Poincaré group of special relativity, but under the symmetry group of de Sitter space instead. With this assumption, empty space automatically has de Sitter symmetry, and what would normally be called the cosmological constant in General Relativity becomes a fundamental dimensional parameter describing the symmetry structure of space-time.

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. The discovery of the accelerating expansion of the universe has led to a revival of interest in deSitter invariant theories, in conjunction with other speculative proposals for new physics, like doubly special relativity.