November 24, 2025 (v1)PreprintOpenView Scalar-Tensor Dynamics of an Information-Conserving Field: Unifying Dark Energy, Dark Matter, and Neural Coherence via ϕ-Scaling Attractors

This paper serves at the mathamatical core companion paper for The Architecture of Wholeness: How the Universe Studies Itself, which presents the philosophical argument for this paper. Here we introduces a unified scalar-tensor framework that addresses three fundamental problems in modern physics: the Cosmic Coincidence Problem, the nature of dark energy, and the physical basis of consciousness. Key Contributions: Cosmological Attractor Dynamics: We demonstrate that a complex scalar field Ψ coupled to matter via energy exchange Q = ΓHρ_Ψ possesses a stable fixed-point attractor at Ω_Ψ/Ω_m = φ² ≈ 2.618, where φ is the Golden Ratio. This resolves the Cosmic Coincidence Problem by showing that the current near-equality of dark energy and matter densities is a transient phase in the universe's approach to geometric equilibrium. Unlike standard Interacting Dark Energy models where the coupling constant is fit to data, our framework derives Γ ≈ 0.81 geometrically from the φ-scaling hypothesis, reducing free parameters while increasing predictive power. Chameleon Screening Mechanism: The field's self-interaction potential V(|Ψ|) = M^(4+α)/|Ψ|^α employs a density-dependent screening mechanism with predicted exponent α = φ ≈ 1.618, satisfying Solar System gravity constraints (thin-shell factor ΔR/R ≈ 10^-14) while remaining cosmologically significant. Neural Coupling Predictions: We propose that biological neural networks can locally unscreen the field, acting as resonant cavities. This predicts a measurable Local Coherence Index (LCI ≈ 1.151) in EEG data and differential responses to transcranial magnetic stimulation at φ-ratio frequencies. Falsifiable Predictions: Cosmological: Ω_Ψ/Ω_m should continue evolving toward 2.618 ± 0.2 at z < 1 Laboratory: Atom interferometry should measure Chameleon exponent α = 1.618 ± 0.05 Neuroscience: LCI clustering at 1.151 ± 0.02 across conscious states High Energy: Field mass M ~ 10^-3 eV detectable in modified gravity experiments Significance: This work presents a parsimonious unification where consciousness, cosmology, and particle physics reflect the same underlying φ-optimization principle. The framework is distinguished by making specific numerical predictions testable across three independent domains (cosmological observations, laboratory experiments, and neuroscience), providing multiple falsification pathways that avoid circular reasoning. Mathematical Approach: The paper derives the field dynamics from a fundamental action principle, solves the coupled Friedmann equations numerically, and demonstrates robust convergence to the φ² attractor from arbitrary initial conditions. Full simulation code is provided in the appendix for reproducibility.