Does Kinney et al.'s extension of the BGV theorem require a cosmic singularity?

[Luis Mijares]

TL;DR

I was wondering if someone could explain this paper to me

I was wondering if anyone has read this new paper (link provided) one of the authors Will Kinney, seems very sure it forecloses on any cosmological model with no singularities. Can anyone speak about the limitations of the paper or if it does definitively prove a singular beginning in space? https://arxiv.org/abs/2307.10958

Reference: https://www.physicsforums.com/forums/cosmology.69/post-thread

 

[member 673059]

It only talks about net expanding metrics on a locally de Sitter space in a time interval, so while it would apply to cosmological models using the standard FLRW metric and related expanding metrics like the LTB metric, as well as the metrics used in Penrose's Cyclic Cosmology, it wouldn't apply to any cosmological model which doesn't have a net expanding metric on a locally de Sitter space in a time interval. For example, one class of conformal metrics talked about in Lucas Lombriser's recent paper "Cosmology in Minkowski space" occurs in static Minkowski space and thus is not net expanding or in locally de Sitter space, and wouldn't be affected by the result in the paper.

 

[ohwilleke]

FWIW, BGV is a reference to the Borde-Guth-Vilenkin (BGV) theorem which states that any spacetime with net positive expansion must be geodesically incomplete. The paper and its abstract are as follows:

[Submitted on 20 Jul 2023]

The Borde-Guth-Vilenkin Theorem in extended de Sitter spaces​

William H. Kinney (Univ. at Buffalo, SUNY, USA), Suvashis Maity, L. Sriramkumar (Indian Insitute of Technology, Madras, India)

The Borde-Guth-Vilenkin (BGV) theorem states that any spacetime with net positive expansion must be geodesically incomplete. We derive a new version of the theorem using the fluid flow formalism of General Relativity.

The theorem is purely kinematic, depending on the local expansion properties of geodesics, and makes no assumptions about energy conditions. We discuss the physical interpretation of this result in terms of coordinate patches on de Sitter space, and apply the theorem to Penrose's model of Conformal Cyclic Cosmology. We argue that the Conformal Cyclic extension of an asymptotically de Sitter universe is geodesically incomplete.