What question did this study set out to answer?

This work aims to explore geometric alternatives to the dark sector by developing signatures of the primordial spin-torsion bounce.

June 12, 2026Open Access

Foundation II: The Chiral Universe and the Three Fossils of the Bounce — Baryogenesis, the Geometric Dark Sector, and Cosmic Alignment within an Einstein-Cartan Framework, Extended Version

Key Points

This work aims to explore geometric alternatives to the dark sector by developing signatures of the primordial spin-torsion bounce.
Built on the Einstein-Cartan Framework and applied the Topological Invariance Principle.
Investigated chiral baryogenesis, geometric dark matter (micro-knots), and cosmic alignment signatures.
Derived parameters and distributions from observational data including the AMPM II survey and DESI.
Identified chiral baryogenesis with η ≃ 6.1×10⁻¹⁰ and a 5:1 dark-to-baryonic matter ratio.
Demonstrated that micro-knots could act as granular dark matter, with a significant fit improvement compared to traditional NFW models.
Explained cosmic alignment through torsion vortex rings, fitting observational structures like the Big Ring and Giant Arc.

Abstract

While ΛCDM provides a robust description of cosmic structure, persistenttensions in H₀, S₈, early galaxy formation (JWST), and dynamical darkenergy (DESI DR1–DR2) motivate exploring geometric alternatives to thedark sector. The H₀ Distance Network (H₀DN) Collaboration has confirmedH₀ = 73. 50 ± 0. 81 km/s/Mpc (arXiv: 2510. 23823), a 7. 1σ tension withflat ΛCDM. Building on the Einstein-Cartan Framework (ECF) non-singular bounce (Foundation I, doi: 10. 5281/zenodo. 19577447) and the TopologicalInvariance Principle (PIT Letter, doi: 10. 5281/zenodo. 19900557), thiswork develops three fossil signatures of the primordial spin-torsionbounce: (1) Chiral Baryogenesis (t ~ 10⁻¹¹ s): η ≃ 6. 1×10⁻¹⁰ from torsioncrystallization; natural 5: 1 dark-to-baryonic partition from 20: 4torsion degrees-of-freedom. (2) Geometric Dark Matter (t ~ 1 s): Micro-Knots (M₀ ~ 6×10²⁴ kg, log-normal KZ distribution σ=1 dex) as granular geometric dark matter;SPARC-175 χ̃²ₘed = 0. 80 vs 1. 31 NFW; Macro-Knots (10⁵ M☉) asprimordial SMBH seeds. The AMPM II survey (Key et al. 2026, arXiv: 2605. 19375) detected Phoebe, a ~1 h microlensing event consistentwith the ECF KZ distribution at 1. 4σ from M₀. (3) Cosmic Alignment (t ~ 365, 000 yr): Torsion Vortex Ring R=322 Mpcexplaining the Big Ring and Giant Arc simultaneously. Dark energy: (w₀, wₐ) = (−0. 904, −0. 153) derived prior to DESI fromPIT calibration (diagonal errors; full covariance: Foundation III). Ghost-freedom established (Sezgin 1980, Karananas 2014). BirefringenceβECF = 0. 35° consistent with Planck PR4 and ACT DR6. Euclid QDR2 (June 2026) provides near-term falsifiability for S₈ = 0. 766. Kill-switches provided for Roman (2028), LISA (2037), LiteBIRD (2032). Code: github. com/pfichant/spin-torsion-cosmology (CC-BY 4. 0)

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