De Sitter space

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In mathematical physics, n-dimensional de Sitter space (often denoted dS_n) is a maximally symmetric Lorentzian manifold with constant positive scalar curvature. It is the Lorentzian^{[further explanation needed]} analogue of an n-sphere (with its canonical Riemannian metric).

The main application of de Sitter space is its use in general relativity, where it serves as one of the simplest mathematical models of the universe consistent with the observed accelerating expansion of the universe. More specifically, de Sitter space is the maximally symmetric vacuum solution of Einstein's field equations with a positive cosmological constant ${\displaystyle \Lambda }$ (corresponding to a positive vacuum energy density and negative pressure).

De Sitter space and anti-de Sitter space are named after Willem de Sitter (1872–1934),^[1][2] professor of astronomy at Leiden University and director of the Leiden Observatory. Willem de Sitter and Albert Einstein worked closely together in Leiden in the 1920s on the spacetime structure of our universe. De Sitter space was also discovered, independently, and about the same time, by Tullio Levi-Civita.^[3]