What question did this study set out to answer?

To formulate spatial flatness as an exact topological invariant rather than an inflationary coincidence, and define the theoretical relationship between primordial spin fluids and dark energy in Einstein-Cartan cosmology.

August 16, 2026Open Access

The Topological Invariance Principle: Exact Spatial Flatness and the Spin–Torsion Link: an Open Problem in Einstein–Cartan Cosmology

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To formulate spatial flatness as an exact topological invariant rather than an inflationary coincidence, and define the theoretical relationship between primordial spin fluids and dark energy in Einstein-Cartan cosmology.
Postulated exact spatial flatness (Omega_K = 0) as a fundamental geometric property of spacetime.
Derived background dark energy contributions using the Friedmann-Lemaître-Robertson-Walker reduction of the axial torsion sector in the Einstein-Cartan action.
Analyzed the dynamical relation between the pre-recombination Weyssenhoff spin fluid and the frozen torsion condensate.
Demonstrated that the cosmic closure condition represents a mathematical identity under exact flatness and cannot dynamically constrain dark energy components.
Showed that the axial torsion sector naturally yields a static background dark energy condensate with an equation of state parameter w = -1 and radiation-like fluctuations.
Framed the connection between the primordial spin parameter (peak Omega_spin = 0.093) and dark energy as an open problem requiring propagating torsion mode derivations.

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Implication

Theoretical analysis reveals exact spatial flatness as a topological property in Einstein-Cartan cosmology, suggesting a fundamental action-based link between spin fluids and dark energy.

Cite This Study

Pascal Fichant (2026) studied this question.

synapsesocial.com/papers/6a819d36f2fb91fc834aecf0 https://doi.org/10.5281/zenodo.21945791

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Implication

Theoretical analysis reveals exact spatial flatness as a topological property in Einstein-Cartan cosmology, suggesting a fundamental action-based link between spin fluids and dark energy.

The Topological Invariance Principle: Exact Spatial Flatness and the Spin–Torsion Link: an Open Problem in Einstein–Cartan Cosmology

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Discussion

Implication

Cite This Study

The Topological Invariance Principle: 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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