De Sitter space

In mathematics and physics, a de Sitter space is the analog in Minkowski space, or spacetime, of a sphere in ordinary, Euclidean space. The n-dimensional de Sitter space, denoted dS_n, is the Lorentzian manifold analog of an n-sphere (with its canonical Riemannian metric); it is maximally symmetric, has constant positive curvature, and is simply connected for n at least 3. De Sitter space and anti-de Sitter space are named after Willem de Sitter (1872–1934), professor of astronomy at Leiden University and director of the Leiden Observatory. Willem de Sitter and Albert Einstein worked in the 1920s in Leiden closely together on the spacetime structure of our universe.

In the language of general relativity, de Sitter space is the maximally symmetric vacuum solution of Einstein's field equations with a positive cosmological constant $\Lambda$ (corresponding to a positive vacuum energy density and negative pressure). When n = 4 (3 space dimensions plus time), it is a cosmological model for the physical universe; see de Sitter universe.