Taming singularities and chaos in conformal gravity

TL;DR

This paper demonstrates that in conformal gravity, cosmological singularities like the big bang and big crunch are avoided through conformal transformations, leading to geodesically complete and less chaotic cosmological models.

Contribution

It shows that singularities in Bianchi IX spacetime can be eliminated via conformal frames, providing a new approach to resolving cosmological singularities in conformal gravity.

Findings

Singularities are absent in an infinite class of conformal frames.

Spacetime is geodesically complete for various particle types.

Chaotic behavior near singularities is mitigated by conformal rescaling.

Abstract

We hereby address the cosmological singularity problem in a general gravitational theory invariant under Weyl conformal transformations. In particular, we focus on the Bianchi IX spacetime and we show that both the initial (big bang) and final (big crunch) singularities disappear in an infinite class of conformal frames naturally selected according to analyticity. It turns out that the past and future singularities are both unattainable within a finite affine parameter (for massless particles) or within a finite proper time (for massive and conformally coupled particles). In order to prove such a statement, we show the geodesic completion of the spacetime when probed by massless, massive, and conformally coupled particles. Finally, the chaotic behavior of the spacetime near the singularity is tamed by a conformal rescaling that turns the Bianchi IX metric into a quasi-FLRW spacetime.