Why is it interesting?

The simple existence of a non-vanishing cosmological constant in the universe means that Poincare is no longer the kinematic group of spacetime; this is a largely overlooked point.

To the extent that* ~$74 \simeq 100$ %, we can say that our universe is observed to be almost maximally symmetric and de Sitter.(*Dark energy amounts to ~74% of the universe […]). [..] Our universe might very well be described by $dS^4$ to a good approximation, as discussed in chapter VIII.2 and in the preceding section.

Einstein Gravity in a Nutshell - A. Zee

We will confront certain recent astronomical observations suggesting that, even in an empty universe, the event world may possess properties not reflected in the structure of Minkowski spacetime, at least on the cosmological scale. Remarkably, there is a viable alternative the deSitter spacetime, nearly 100 years old, that has precisely these properties and we will devote a little time to becoming acquainted with it.

The Geometry of Minkowski Spacetime - Naber

The present experimental value for the cosmological constant is tiny, but nonzero: $\Lambda \approx 1.19·10^{-52}$ $1/m^2$.

With such a formulation of symmetry, the fact that $Λ \neq 0$ means not that the space-time background is curved (since the notion of the space-time background is not physical) but that the symmetry algebra is the de Sitter algebra rather than the Poincare one. In particular, there is no need to involve dark energy or other fields for explaining this fact. As a consequence, instead of the cosmological constant problem we have a problem why nowadays Poincare symmetry is so good approximate symmetry. This is rather a problem of cosmology but not fundamental quantum physics.

https://arxiv.org/pdf/1004.1861.pdf

The theories in which the kinematic invariance group is not the Poincare group but one of the de Sitter groups SO(1,4) or S0(2,3) have been considered by many physicists. From the group-theoretical and aesthetic points of view, the de Sitter invariance looks much more attractive than the Poincare invariance. However, recently the de Sitter invariance has been studied less intensively, since in the currently popular superstring theories the flatness of the spacetime is supposed from the beginning.

Some group-theoretical aspects of the SO,( 1,4)-invariant theory by F M Lev

Layman

Student

The de Sitter space is the curved space-time which has been most studied by quantum field theorists because it and the anti-de Sitter space are the unique maximally symmetric curved spacetimes Weinberg, 1972). Dirac Wave Equation in the de Sitter Universe E. A. Notte Cuello

Researcher

For the representations of the De Sitter group, see 249. Gürsey, F.: Introduction to the De Sitter Group. In: Gürsey, F. (ed.) Group Theoretical Concepts and Methods in Elementary Particle Physics. Gordon and Breach, New York (1965

and "Positive Cosmological Constant and Quantum Theory" by Lev, Felix M.

"Gürsey (1963) presented the Casimir operators for the de Sitter group and concluded by showing that a particle in a de Sitter universe does not have a definite mass and spin, but definite eigenvalues of the two Casimir invariant operators of the group."Dirac Wave Equation in the de Sitter Universe E. A. Notte Cuello et. al.

Common Question 1

Common Question 2

Examples

Example1

Example2:

History