Gravity from Ternary Vacuum Geometry: Scalar Torsion as the Source of Cosmic

This work develops a cosmological framework in which scalar torsion plays the role of an emergent dark-energy component arising from an internal ternary symmetry of the vacuum. Within the Einstein–Cartan geometry, the model links late-time cosmic acceleration to a dynamical vacuum structure that requires no new particles, no additional fields beyond torsion and curvature, and no modification of local gravitational physics. The resulting cosmology produces measurable signatures while remaining fully compatible with standard observational constraints.

A key feature of the model is a conformal interaction between dark matter and torsion that naturally suppresses the growth of large-scale structure. This mechanism provides an explanation for the observed reduction in the sigma_8 parameter without fine-tuning and predicts a mild shift in the distance to the surface of last scattering. Both signatures are directly testable with future surveys, offering clear observational falsifiability.

The framework derives these cosmological effects from a simple internal geometric relation encoded by the cubic condition J^3 = -I. In this picture, the vacuum possesses three internal phases connected by a ternary structure. One of these phases projects at cosmological scales as a scalar torsion mode. Remarkably, the same internal structure governs the emergence of photonic, scalar, and neutrino sectors at particle scale, and produces a rigid geometric scaling in nuclear binding energies. The cosmological model presented here is therefore not an isolated construction, but the large-scale limit of a unified geometric picture.

Several conceptual consequences follow from this approach:

• Scalar torsion behaves as a dynamical vacuum degree of freedom whose evolution mimics dark energy without requiring a fixed equation of state.

• Dark matter experiences an effective conformal coupling that moderates structure formation, offering a natural link between cosmic acceleration and sigma_8 suppression.

• The evolution of the torsion sector predicts mild deviations in early-universe distances, potentially distinguishable in next-generation CMB and BAO measurements.

• The model preserves local General Relativity while embedding it in a broader geometric structure consistent across particle, nuclear, and cosmological domains.

The work therefore contributes a coherent and testable alternative to dark-energy models based solely on scalar fields or modified gravity. Instead, it proposes that dark energy and large-scale structure anomalies may arise from the internal geometry of the vacuum itself.

Interactive numerical exploration is available on the J3 ATOMIC platform: https://www.j3atomic.com

In Free Low-Res mode, the calculation reproduces exactly the function (Eq. 11) from the preprint:
Evidence for Internal Ternary Geometry in Nuclear Binding Energies — https://doi.org/10.5281/zenodo.17847017

In High-Res mode (contractual), the platform extends this formalism for deterministic calculations, with a global precision on the order of:
RMS ≈ 0.002625 eV/n (per nucleon)

Direct precision verification is available at:
https://www.j3atomic.com → LABORATORY → VERIFY PRECISION

The probability that a formula depending exclusively on Z and N would reproduce exactly the first 8 significant digits for all 3558 nuclei in AME2020 is ≈ 10⁻²⁸⁴⁶⁴;
this result strongly refutes the hypothesis of a global overfit.

The platform provides a demonstrative and exploratory implementation of the formalism and parameter set described in this preprint, 
intended to illustrate the structure of the model and its qualitative behaviour across the nuclear chart.

Observation: This work is part of a broader series exploring a possible ternary structure of the vacuum and the ways in which it may manifest across physical domains. Readers wishing to follow the ideas in their natural progression may consult the related studies:

• Evidence for Internal Ternary Geometry in Nuclear Binding Energies

• Unified Vacuum Dynamics from a Ternary Internal Symmetry

• Photon Emergence from a Discrete Ternary Vacuum Symmetry

• Photon, Neutrinos and the Higgs Boson as Emergent Structures of a Ternary Symmetry of the Vacuum

• Ternary Unified Physics: Internal Torsion, Phase Geometry, and Emergent Correspondence Limits

This work is also archived on Figshare
Gravity from Ternary Vacuum Geometry: Scalar Torsion as the Source of Cosmic.
DOI: 10.6084/m9.figshare.30867671