Relevance of the Snyder–de Sitter algebra to low-energy quantum gravity

Determine whether the Snyder–de Sitter algebra is relevant to the low-energy behavior of quantum gravity in the presence of a nonzero cosmological constant.

Background

The Snyder–de Sitter algebra is a Lorentz-covariant deformation of phase-space geometry involving a curvature parameter α and a noncommutativity parameter β. Its β → 0 limit gives the de Sitter phase-space algebra, while its α → 0 limit gives the Snyder algebra. Because the algebra incorporates both curvature and noncommutativity and possesses Born reciprocity, the paper notes a conjecture that it may describe aspects of quantum gravity with a nonzero cosmological constant.