Thus the [lambda]-field generating the de Sitter space
(30) is equivalent to the substance described by the energy-impulse tensor
It is also well known that the geometry of the inflationary period of our universe is described with great accuracy by the de Sitter space
1] (c) be an (n + 1)-dimensional Lorentzian space form with constant sectional curvature c, we separately call it de Sitter space
Furthermore, Zheng  studied spacelike hypersurfaces in the de Sitter space
Our expanding universe is contained in some sort of wider space (whether a Minkowski space as in the Brout, Englert, Gunzig model or a curved de Sitter space
as in Gott's model) in which the quantum fluctuations occur in the spacetime geometry which 'pull' particles into existence out of the energy locked up in empty space.
They conjectured that the laws of physics are invariant under the symmetry group of de Sitter space
(maximally symmetric space-time), rather than the Poincare group of special relativity.
Aiyama  had proved that a compact spacelike submanifold with parallel mean curvature vector and flat normal bundle in de Sitter space
That emptiness, Carroll suggests, would be a high-entropy environment technically known as de Sitter space
n] be a complete spacelike hypersurface immersed into de Sitter space
An example of the Casimir effect in curved spacetime has been considered for spherical geometries  in de Sitter space
 and in the background of static domain wall .
We define the (n + 1)-dimensional de Sitter space
4] of 4 complex dimensions is an 8 real-dim Hyperboloid of constant negative scalar curvature that can be identified with the conformal relativistic curved phase space associated with the electron (a particle) moving in a 4D Anti de Sitter space