On the spacetime connecting two aeons in conformal cyclic cosmology

TL;DR

This paper explores a special conformal invariant spacetime that can connect two aeons in Penrose's conformal cyclic cosmology, providing a geometric framework for the bridging spacetime.

Contribution

It introduces a singular, flat, conformal invariant cone spacetime as a candidate for the connecting spacetime in conformal cyclic cosmology, extending the geometric understanding.

Findings

The spacetime satisfies the Weyl curvature hypothesis.

It emerges as a limit of de Sitter-Cartan geometry with an infinite cosmological term.

It provides a geometric model for connecting two aeons in 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.