Is the universe an anti de Sitter space?
It acts like the 4D hypersurface of a 5D hypersphere, in a sense, where the curvature everywhere on the hypersurface is the same. * Thus, de Sitter space is maximally symmetric. Because de Sitter space has no mass-energy in it, but our universe does, one should not say ours is a de Sitter universe.
What is de Sitter solution?
The de Sitter space is the simplest solution of Einstein’s equation with a positive cosmological constant. It is spherically symmetric and it has a cosmological horizon surrounding any observer, and describes an inflating universe.
Is de Sitter space maximally symmetric?
In mathematical physics, n-dimensional de Sitter space (often abbreviated to dSn) is a maximally symmetric Lorentzian manifold with constant positive scalar curvature.
Why was the de Sitter model unusual?
De Sitter’s concept of the universe differed in some respects from that of Einstein. Einstein’s relativistic conception of curved space led him to envision the universe as static and unchanging in size, but de Sitter maintained that relativity actually implied that the universe was constantly…
What was Einstein’s theory of the universe?
Einstein was the first to apply his ideas of space and time plasticity to the universe as a whole. In 1919, he devised a model for the entire universe: a static, spherical, perfectly symmetric cosmos, with matter homogeneously distributed everywhere, reflecting a mix of Platonic perfection and of Ockham’s Razor.
What is anti-de Sitter space in general relativity?
An anti-de Sitter space in general relativity is similar to a de Sitter space, except with the sign of the spacetime curvature changed. In anti-de Sitter space, in the absence of matter or energy, the curvature of spacelike sections is negative, corresponding to a hyperbolic geometry, and initially parallel timelike geodesics eventually intersect.
What is the metric on anti-de Sitter space?
The metric on anti-de Sitter space is that induced from the ambient metric. It is nondegenerate and, in the case of q = 1 has Lorentzian signature. When q = 0, this construction gives a standard hyperbolic space. The remainder of the discussion applies when q ≥ 1 .
What is anti-de-Sitter space?
In anti-de Sitter space, in the absence of matter or energy, the curvature of spacelike sections is negative, corresponding to a hyperbolic geometry, and initially parallel timelike geodesics eventually intersect.
Was the early universe a de Sitter space?
Many cosmologists believe that the very early universe was close to being a de Sitter space. The far future may also be de Sitter-like because of cosmic acceleration. Conversely, the simplest negatively curved spacetime is called anti-de Sitter space.