On the spacetime connecting two aeons in conformal cyclic cosmology

Abstract

As quotient spaces, Minkowski and de Sitter are fundamental, non-gravitational spacetimes for the construction of physical theories. When general relativity is constructed on a de Sitter spacetime, the usual Riemannian structure is replaced by a more general structure called de Sitter-Cartan geometry. In the contraction limit of an infinite cosmological term, the de Sitter-Cartan spacetime reduces to a singular, flat, conformal invariant four-dimensional cone spacetime, in which our ordinary notions of time interval and space distance are absent. It is shown that such spacetime satisfies all properties, including the Weyl curvature hypothesis, necessary to play the role of the bridging spacetime connecting two aeons in Penrose's conformal cyclic cosmology.

15 pages. V2: presentation changes aiming at clarifying the text, matches published version

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• de Sitter special relativity
• Special Relativity in the 21${}^{\mathrm{st}}$ century
• Snyder's Model -- de Sitter Special Relativity Duality and de Sitter Gravity
• A note on spin two fields in curved backgrounds
• Higher spin $m\ne 0$ excitations on curved backgrounds and cosmological supergravity
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• de Sitter invariant special relativity and galaxy rotation curves
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• The generalized holographic $c$-function for regular AdS black holes
• An Improved Framework for Quantum Gravity
• De Sitter-Invariant Black Holes