Août 6 2020
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E. Calabi, S.Y. Of course, we find it most convenient to discuss cosmology in the (Friedmann, Robertson-Walker) coordinates that exploit the natural homogeneity and isotropy of the relevant matter sources. Definition of de Sitter space : the simplest hypothetical space-time that has positive curvature Those clues, in particular, may be applied to the most symmetric solution of Einstein's equations with positive cosmological constant and no matter— de Sitter space . de Sitter space involves a variation of general relativity in which spacetime is slightly curved in the absence of matter or energy. A sketch by Xi Dong of the cutting, warping and gluing procedure that he and his colleagues used to construct a hologram of a de Sitter universe.The fabric of space and time is widely believed by physicists to be emergent, The space-time filling the region inside the bottle — a continuum that bends and undulates, producing the force called gravity — exactly maps to a network of quantum particles living on the bottle’s rigid, gravity-free surface. The physicists could then do the obvious thing: “glue” the two bowls together along their rims. This space is still approximated by a CFT that lives on its boundary, but the boundary is now a finite distance away.Next, Dong and co-authors added ingredients from string theory to two of these theoretical Randall-Sundrum throats to energize them and give them positive curvature. Pink shows a collapsing universe, with six times the critical density of matter. One is free to transform coordinates as much as one likes, but there will no longer be any choices in which the metric is static! This procedure, called “uplifting,” turned the two saddle-shaped AdS spaces into bowl-shaped dS spaces. In de Sitter space-time, where the cosmological constant has a positive value, the universe is shaped like a sphere. The space of special relativity (Negative curvature means curved hyperbolically, like a General relativity is a theory of the nature of time, space and gravity in which gravity is a curvature of space and time that results from the presence of matter or energy.
In mathematics and physics, n-dimensional anti-de Sitter space (AdSn) is a maximally symmetric Lorentzian manifold with constant negative scalar curvature. As noted above, the analogy used above describes curvature of a two-dimensional space caused by gravity in general relativity in a three-dimensional embedding space that is flat, like the Minkowski space of special relativity. Different directions on the saddle curve in opposite ways, with one direction curving up and the other curving down. Green shows a model favoured until 1998, with exactly the critical density and a universe 100 percent matter. That is a crucial difference between these two spaces. Much as spherical and hyperbolic spaces can be visualized by an The metric on anti-de Sitter space is that induced from the The unproven 'AdS instability conjecture' states that arbitrarily small perturbations to certain configurations of AdS lead to the formation of black holes. This corresponds to the vacuum having an energy density and pressure. Cheng and S.T. A key feature of general relativity is that it describes gravity not as a conventional force like electromagnetism, but as a change in the geometry of spacetime that results from the presence of matter or energy. The CFTs describing both hemispheres become coupled with each other, forming a single quantum system that is holographically dual to the entire spherical de Sitter space.“The resulting space-time has no boundary, but by construction it is dual to two CFTs,” Dong said. Like the AdS/CFT correspondence, theirs is also a toy model, but some of the principles of its construction may extend to more realistic space-time holograms.
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