The Single Breath Euler Universe: The dark sector as a glassy substance, and the rotation as its ring
Abstract
This capstone of the Euler Cosmos series recasts the model so that a single uniform rotation in the plane is its generator rather than a lens laid over it. The dark-energy sector is carried by one first-order law: a complex density Z rotating at constant rate Ω_N, whose real part is the observed density — a cosine in e-folds — and whose conserved modulus is the amplitude a spatially flat, zero-energy universe holds fixed. Projected onto the equation of state, the rotation is a Riccati equation with the single parameter Ω_N, and the harmonic oscillator of the earlier papers is recovered as its linearization. The three conjugacy classes of the Möbius group sort into the breath, the cosmological constant (ΛCDM as the degenerate Ω_N → 0 limit), and an excluded region, so the exclusion boundary is a transition of the group. The one zero-energy (Hamiltonian) constraint is read twice: as an amount, its residual — one part in 10^122 — appears as dark energy, entropy, and gravity; as a motion, it is a single traversal from a low-entropy dawn to a crunch that cannot close. A dedicated section derives the rotation from fundamentals — it is the unique modulus-conserving, scale-free, linear dark sector — and evaluates, as a graded conjecture, whether the breath frequency Ω_N and the dark-matter acceleration scale a₀ are two faces of one complex de Sitter modulus (the weld pins a₀ = cH/2π at KSS saturation but leaves Ω_N free). Throughout, the parameters are the DESI DR2 calibration (H₀ = 62.75 km s⁻¹ Mpc⁻¹, Ω_m0 = 0.3605, Ω_N = 1.4908, φ = 0.8624), and every claim is graded — forced, fits, or conjecture. The model is falsifiable now and under test, with pre-registered blades for DESI DR3, Euclid, Rubin, Roman, and Gaia.
Related
- The alternative scalar field dark sector of the Universe: Cosmological inflation, quintessence and ekpyrotic model in the framework of scalar-tensor cosmology
- Complex-Time Cosmology: A Three-Sector Model of the Universe and the Probabilistic Interpretation of Cosmic Composition
- Surface Nitrogen enrichment from the LMC to the Early Universe: the roles of rotation, overshooting and mass loss
- The Nature of Time, Entropy, and the Cyclic Structure of the Universe: A Unified Framework Based on Relational Time, the Second Law of Thermodynamics, and Complex Time Rotation at Black Hole Singularities
- Post-merger rotational evolution of magnetised single hot subdwarfs results in slow rotation due to magnetic braking
BibTeX
@misc{sanders2026single,
title = {{The Single Breath Euler Universe: The dark sector as a glassy substance, and the rotation as its ring}},
author = {Nicholas Archer Sanders},
howpublished = {Zenodo (CERN European Organization for Nuclear Research)},
year = {2026},
month = sep,
doi = {10.5281/zenodo.22836822},
url = {https://doi.org/10.5281/zenodo.22836822},
note = {CC BY},
}
RIS
TY - UNPB
TI - The Single Breath Euler Universe: The dark sector as a glassy substance, and the rotation as its ring
AU - Nicholas Archer Sanders
PY - 2026
DA - 2026/09/18
PB - Zenodo (CERN European Organization for Nuclear Research)
DO - 10.5281/zenodo.22836822
UR - https://doi.org/10.5281/zenodo.22836822
AB - This capstone of the Euler Cosmos series recasts the model so that a single uniform rotation in the plane is its generator rather than a lens laid over it. The dark-energy sector is carried by one first-order law: a complex density Z rotating at constant rate Ω_N, whose real part is the observed density — a cosine in e-folds — and whose conserved modulus is the amplitude a spatially flat, zero-energy universe holds fixed. Projected onto the equation of state, the rotation is a Riccati equation with the single parameter Ω_N, and the harmonic oscillator of the earlier papers is recovered as its linearization. The three conjugacy classes of the Möbius group sort into the breath, the cosmological constant (ΛCDM as the degenerate Ω_N → 0 limit), and an excluded region, so the exclusion boundary is a transition of the group. The one zero-energy (Hamiltonian) constraint is read twice: as an amount, its residual — one part in 10^122 — appears as dark energy, entropy, and gravity; as a motion, it is a single traversal from a low-entropy dawn to a crunch that cannot close. A dedicated section derives the rotation from fundamentals — it is the unique modulus-conserving, scale-free, linear dark sector — and evaluates, as a graded conjecture, whether the breath frequency Ω_N and the dark-matter acceleration scale a₀ are two faces of one complex de Sitter modulus (the weld pins a₀ = cH/2π at KSS saturation but leaves Ω_N free). Throughout, the parameters are the DESI DR2 calibration (H₀ = 62.75 km s⁻¹ Mpc⁻¹, Ω_m0 = 0.3605, Ω_N = 1.4908, φ = 0.8624), and every claim is graded — forced, fits, or conjecture. The model is falsifiable now and under test, with pre-registered blades for DESI DR3, Euclid, Rubin, Roman, and Gaia.
ER -