The Universe is Expanding

Anti-de Sitter spaceAnti-de Sitter Space (Λ < 0)A spacetime with a negative cosmological constant, shaped like a saddle rather than a sphere. It requires a boundary to define sensible physics, so the theory is not fully self-contained under Einstein's relativity principle. Beloved in string theory for its mathematical tractability, but ruled out as our universe by observation.. Requires boundary conditions from outside itself.

Minkowski spaceMinkowski Space (Λ = 0)Perfectly flat spacetime with no cosmological constant, the playground of special relativity. Named after mathematician Hermann Minkowski, who in 1908 reframed Einstein's 1905 relativity in the language of four-dimensional geometry. In a Minkowski universe, there is no natural scale of length or time, so the metric's ruler is not fixed from within the framework.. Cannot determine its own scale. Needs an external ruler.

De Sitter spacede Sitter Space (Λ > 0)A spacetime with a positive cosmological constant, the geometry of our actual universe on the largest scales. Imagine the surface of a four-dimensional sphere stretching outward in every direction at once. Named after Dutch astronomer Willem de Sitter (1872–1934), who found this solution to Einstein's equations in 1917.. Self-contained, globally hyperbolicGlobal HyperbolicityA technical requirement for a spacetime to have consistent, deterministic physics. A globally hyperbolic spacetime is one where, given initial conditions on a single moment of time (a 'Cauchy surface'), the entire future and past of the universe can in principle be calculated without needing information from some external boundary. Our universe is believed to be globally hyperbolic. Anti-de Sitter space is not, it has a boundary at spatial infinity that can send signals back inward.. Metric fully determined.