A Has anyone read this new paper on extending the BGV?

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The recent paper by Will Kinney and colleagues extends the Borde-Guth-Vilenkin (BGV) theorem, asserting that any cosmological model with net positive expansion must be geodesically incomplete. It specifically applies to models using standard FLRW and related metrics, but does not encompass models lacking net expansion, such as those in static Minkowski space. The authors emphasize that their findings are kinematic and independent of energy conditions, focusing on the local expansion properties of geodesics. They also discuss implications for Penrose's Conformal Cyclic Cosmology, suggesting it is geodesically incomplete under their new framework. Overall, the paper raises important questions about the nature of singularities in cosmological models.
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I was wondering if someone could explain this paper to me
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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.
 
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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.
 
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