At https://arxiv.org/pdf/1403.1599.pdf, Vilenkin, in 2014, used the Borde-Guth-Vilenkin theorem's premise that the "bouncing" local universes of an expanding or contracting multiverse would necessarily be geodesically incomplete either to the past or to the future unless their expansion would be balanced exactly by contraction, using General Relativity without the one assumption added to it in 1928 by Einstein in collaboration with the mathematician Elie Cartan, which was an assumption that fermions have spatial extent. That extent would be submicroscopic, but nevertheless greater than the Planck length (and thereby not inherently prone to result in the collapse of its contents even under the influence of extremely energetic magnification), and the addition of it is said to have left relativity more complicated mathematically, but still able to meet all of its experimental proofs, as well as allowing a cosmology--described in numerous papers posted by Nikodem J. Poplawski on the Arxiv website between 2010 and 2020--which would not originate from a singularity.
Because fermions have spin, which might cause interactions through actual contact between them to be less direct and immediate than whatever interactions between them are possible through the fiber bundle alternative employed in General Relativity, I'd like to find out whether either Einstein-Cartan Theory, or the "ECSK" version of it which has prevailed since modifications to it that were made by Sciama and Kibble around 1970, might allow past and future eternality to prevail in a single cosmology (rather than the doubled one implied by Aguirre and Gratton's 2007 paper "Steady-state eternal inflation"), without a continuously exact balancing between expansion and contraction that appears (by a footnote in the last--2003's--reformulation of the BGV Theorem by all three of its authors) to be the only way around the tendency of shear to obviate any cosmological role of torsion, as described by Trautmann in his short 2006 paper "Einstein-Cartan Theory".
A "coherent fiber bundle" is defined, per a google search for definition of that phrase, as a collection of single fiber strands assembled together so that the relative orientation of the individual fibers is maintained throughout the length of the bundle, and, consequently, does appear to represent shear, rather than torsion. (The "fiber bundle" analogy appears, per a Youtube lecture given by Vilenkin on the occasion of Stephen Hawking's 70th birthday, to have been a factor in his conclusion that all geodesics, "possibly excluding a few test particles" essential to the presentation of the BGV Theorem, would reach "the boundary" of any plausible spacetime rather than continuing through it toward spatial infinity and temporal eternity, and his 2014 paper, cited at the start of this question, is described by him as reaching the "perplexing" conclusion that any contracting phase of a bouncing cosmology would not be eternal to the future, so that use of that analogy in preference to acceptance of a spatial extent for fermions seems to be a little inimical to the plausibility of some of the various cosmologies involved.)