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De Sitter space
Maximally symmetric Lorentzian manifold with a positive cosmological constant
De Sitter space
In mathematical physics, n-dimensional de Sitter space (often denoted dSn) is a maximally symmetric Lorentzian manifold with constant positive scalar curvature. It is analogue of an n-sphere, with a Lorentzian metric in place of the Riemannian metric of the latter. 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 in which the cosmological constant Λ {\displaystyle \Lambda } is positive (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), professor of astronomy at Leiden University and director of the Leiden Observatory. Willem de Sitter and Albert Einstein worked...
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