What does this research mean for the field?

Spatial flatness is an exact topological property of spacetime (ΩK≡0) rather than a dynamical outcome of inflation, and within Einstein-Cartan cosmology, the axial torsion sector yields a static dark-energy term whose relation to the spin fluid remains an open problem to be derived. Novelty: ClaimNovelty.CONTRADICTORY. Consensus alignment: ConsensusAlignment.CHALLENGES_CONSENSUS.

What question did this study set out to answer?

To propose exact spatial flatness as a strict topological property rather than a dynamical result of inflation, and to define the physical link between early-universe spin and dark energy in Einstein-Cartan cosmology.

September 8, 2026Open Access

Exact Spatial Flatness and the Spin-Torsion Link: an Open Problem in Einstein-Cartan Cosmology

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To propose exact spatial flatness as a strict topological property rather than a dynamical result of inflation, and to define the physical link between early-universe spin and dark energy in Einstein-Cartan cosmology.
Formulated an exact spatial flatness postulate (k = 0, ΩK ≡ 0) as a falsifiable topological characteristic of spacetime.
Analyzed the reduction of the axial torsion sector within the Friedmann-Lemaître-Robertson-Walker framework to derive background dark energy behavior.
Evaluated the cosmological closure relation and the coupling between the early-universe Weyssenhoff spin fluid and the late-time torsion condensate.
Demonstrated that the closure identity under exact flatness (k = 0) cannot dynamically constrain dark energy density or its equation of state.
Showed that the axial torsion sector naturally yields a static background condensate acting as dark energy with w = -1, while its fluctuations act as radiation.
Identified propagating torsion modes as the necessary theoretical direction to derive the physical relation connecting early-time spin fluids to dark energy.

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Implication

Theoretical analysis demonstrates exact spatial flatness as a spacetime topological property, highlighting open links between early-universe spin fluids and dark energy.

Cite This Study

Pascal Fichant (2026) studied this question.

synapsesocial.com/papers/6a9fd77658e84d0ff5b4631c https://doi.org/10.5281/zenodo.22545411

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Implication

Theoretical analysis demonstrates exact spatial flatness as a spacetime topological property, highlighting open links between early-universe spin fluids and dark energy.

Exact Spatial Flatness and the Spin-Torsion Link: an Open Problem in Einstein-Cartan Cosmology

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Implication

Cite This Study

Exact Spatial Flatness and the Spin-Torsion Link: an Open Problem in Einstein-Cartan Cosmology

Key Points

Discussion

Implication

Cite This Study

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