SECTION 20 — COSMOLOGICAL DYNAMICS: FROM SUBSTRATE FRICTION TO GLOBAL EXPANSION (v11.1)

SECTION 20 — COSMOLOGICAL DYNAMICS: FROM SUBSTRATE FRICTION TO GLOBAL EXPANSION (v11.1)

By John Gavel

20.0 The Unified Cosmological Principle (Anchor-Referenced)

In TFP, the universe does not expand into pre-existing space. Instead, the Global Metric Drift (\(H_0\)) emerges as the substrate clock drift required to accommodate informational friction \(\delta_{\text{eff}}\) generated by local ΔF updates.

All cosmological phenomena—Hubble expansion, Dark Energy, Dark Matter—emerge from the scale gap:

\(\Sigma_{\text{gap}} = a_p / L_p \approx 10^{20}\) (electroweak grain → Planck floor)

Cluster scales are anchored via \(f_{\text{substrate}}\) (Anchor A) and \(\alpha_{\text{EM}}\) (Anchor B)

Lorentz invariance at cosmological scale emerges from K=12 handshake allocation (Section 18.10)

Logical principle: No additional spacetime or energy assumptions are imposed; all dynamics follow directly from ΔF network coherence and calibrated scales (\(\lambda_X\)).

20.1 Hubble Constant as Substrate Clock Drift

Origin: Each ΔF node incurs microscopic processing lag \(\tau_p\); cumulative lag creates metric drift.

\(H_0 = \frac{1}{\tau_p} \cdot \frac{\Omega_S}{\Sigma_{\text{gap}}^4}\)

Where:

• \(\tau_p = T_c \cdot \lambda_T\) (Anchor A physical time)
• \(\Omega_S \approx 285.51\) (4D Entropy Factor, Section 16.8)
• \(\Sigma_{\text{gap}} = a_p / L_p\)

Prediction:

• \(H_0 \approx 72.41\ \text{km/s/Mpc}\) (96.5% accuracy)
• H₀ emerges directly from substrate coherence and minimal anchors
• Resolution of H₀ tension: Local variations in \(\Phi_{\text{coh}}\) correspond to regional clock speed differences, consistent with Lorentz-adjusted local frames (Section 18.10)

20.2 Emergent Dark Energy: Informational Pressure (Λ)

Physical origin: Volume-averaged Geometric Dilution of Strong Force → emergent Dark Energy

Equation of state \(w = -1\) arises because informational friction \(\delta_{\text{eff}}\) is topologically fixed

Local effective cosmological term:

\(\Lambda_{\text{eff}}(r, t) = \frac{\Phi_{\text{coh}}}{\Phi_{\text{grav}}}\)

Where:

• \(\Phi_{\text{coh}} =\) cluster coherence contribution (Sections 16.2, 18.10 handshake)
• \(\Phi_{\text{grav}} =\) emergent gravitational potential calibrated via \(G_{\text{phys}}\) (Anchor A & Section 18.5)

Prediction: High coherence regions (e.g., near BHs) accelerate local expansion

No free parameters: scaling follows from \(\lambda_L, \lambda_T, \lambda_E, \lambda_h\)

20.3 Galactic Dynamics: Dark Matter as Coherence Stiffness

Mechanism: Flattened rotation curves arise from substrate stiffness, not WIMPs

High-coherence phase near baryonic clusters increases local vacuum modulus

1.96× Gravity Boost:

Substrate coherence gradient: \(\nabla \Phi_{\text{coh}} \rightarrow\) centripetal acceleration ≈ 1.96 × Newtonian expectation

Velocity profile:

\(v(r)^2 / r = G_{\text{phys}} \cdot M_{\text{vis}} / r^2 + \text{Tension Flux}\) (from Section 18.6, \(\lambda_X\))

Notes:

• \(G_{\text{phys}} = G_{\text{dim}}(l_\star) \cdot \lambda_G\) (Anchor A)
• Lorentz corrections included for moving stars/galaxies: time dilation and length contraction from handshake allocation (Section 18.10)

20.4 Cyclical Substrate: Black Hole–Mediated Flow

Universe dynamics: Eternally cycling network: expansion ↔ contraction

BH-mediated ΔF emissions reduce local \(\delta_{\text{eff}} \rightarrow\) increase \(L_c \rightarrow\) push metric outward

Contraction: waning BH coherence → substrate pulled back by \(G_{\text{pixel}}\)

No singular Big Bang: Phase transition in ΔF network, not creation of space

All time intervals reference \(T_c \cdot \lambda_T\) (Anchor A)

Relativistic timing arises naturally from handshake vector allocation (Section 18.10)

20.5 Structure Formation and the Decoherence Ridge

Mechanism: Galaxies form at intersections of High-Coherence Filaments (Cosmic Web)

Filaments correspond to minima of informational friction \(\delta_{\text{eff}}\)

Baryonic motifs (d=5 clusters) slide into coherence wells

Predictions: Coherence-driven assembly reproduces observed large-scale structure

Galaxy clustering depends on ΔF coherence gradients and Lorentz-consistent time allocation

20.6 Arrow of Time

Arrow of time = directional gradient of \(\gamma_{\text{asym}} \cdot \delta_{\text{eff}}\)

Irreversibility arises from node-level additive informational friction

Time intervals reference \(T_c \cdot \lambda_T\) (Anchor A) and Lorentz allocation ensures frame consistency across observers

20.7 Observational Predictions and TFP Validation (Anchor & Lorentz Referenced)

Phenomenon	TFP Variable	Physical Result	Anchor / Lorentz Reference
Expansion	\(\Omega_S / \tau_p\)	\(H_0 \approx 72.4\ \text{km/s/Mpc}\)	\(\lambda_T\) (Anchor A), handshake \(\gamma\) from 18.10
Dark Matter	\(\nabla \Phi_{\text{coh}}\)	Flat rotation curves (1.96× boost)	\(\lambda_G\) (Anchor A), Lorentz \(m(v) = \gamma M_{\text{phys}}\)
Cosmic Web	\(\delta_{\text{eff}}\) gradients	Coherence-driven clustering	\(\lambda_L / \lambda_T\), Lorentz \(t(v), L(v)\)
BH Horizons	\(\beta_{\text{edge}}(l)\)	Dimensional reduction, holography	\(\lambda_X\) scaling, handshake allocation

Key Point: All predictions are fully derived from:

• Anchor A: \(f_{\text{substrate}} \rightarrow\) physical scales \(\lambda_X\)
• Anchor B: \(\alpha_{\text{EM}} \rightarrow\) interaction normalization
• K=12 handshake allocation → Lorentz transformations

No free parameters remain. All cosmology emerges directly from ΔF substrate dynamics.

20.8 Summary

• TFP cosmology is completely anchored to minimal physical inputs (\(f_{\text{substrate}}, \alpha_{\text{EM}}\))
• Global expansion, Dark Energy, Dark Matter, and cosmic structure emerge from calibrated ΔF coherence
• Relativistic effects arise naturally from handshake budget allocation
• Predictions are parameter-free, falsifiable, and fully consistent with Sections 18 (calibration) and 19 (particle & cosmological predictions)