Section 20: Cosmological Effects of Temporal Flow Physics (TFP)

Section 20: Cosmological Effects of Temporal Flow Physics (TFP)

20.1 Overview

Temporal Flow Physics (TFP) proposes a fundamentally new framework for cosmic evolution, moving away from the standard cosmological narrative of a singular Big Bang, homogeneous expansion, and eventual heat death. Instead, cosmological phenomena emerge as regional, dynamical effects driven by recursive black hole (BH) coherence emissions and spatial-temporal gradients of informational friction \( \delta_{\text{eff}}(r, t) \). The universe is modeled as a complex, eternally cycling information-processing network, where metric expansion, gravitational attraction, and structure formation arise from evolving phase coherence patterns of temporal flows rather than exotic dark matter or finely tuned initial states.

20.2 Black Hole Coherence Emission and Effective Cosmological Term

Define an effective cosmological constant \( \Lambda_{\text{eff}}(r, t) \) as the local ratio between recursive coherence flux and gravitational curvature:

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

Where:

• \( \Phi_{\text{coh}}(r, t) = \sum_i A_i \times \exp\left(-\frac{|r - r_i|^2}{\sigma_i^2}\right) \times \Theta(t - t_i) \)
  Represents localized coherence pulses emitted by individual black holes \( BH_i \) with amplitude \( A_i \) (dimensionless coherence amplitude), spatial decay scale \( \sigma_i \) [L], and onset time \( t_i \) [T].
• \( \Phi_{\text{grav}}(r, t) \) encapsulates local flow-induced curvature, dependent on mass-energy distributions and spatially varying informational friction \( \delta_{\text{eff}}(r, t) \).

This ratio modulates regional metric expansion or contraction, producing inherently non-uniform, dynamic, and cyclical cosmological behavior rather than the global uniform expansion posited by classical models.

20.3 Cyclic Cosmological Phases

20.3.1 Expansion Phase

• Elevated BH coherence emission rates locally reduce \( \delta_{\text{eff}} \).
• Resulting increase in coherence domain scale \( L_c \) [L] corresponds to effective metric expansion.
• This phase aligns with observed accelerated expansion or inflationary epochs.

20.3.2 Contraction Phase

• As BH coherence emissions wane, \( \delta_{\text{eff}} \) increases, allowing gravitational attraction from matter and flows to dominate, causing local contraction.
• Recursive realignment and merging of flow phase domains lead to new BH core formations.
• Matter and flow redistribution trigger successive cosmological cycles.
• Each spatial region experiences independent phase cycling, eliminating the necessity for a single universal cosmological history or fine-tuned initial conditions.

20.4 Emergent Galactic Dynamics

20.4.1 Velocity Profile Equation

Galactic rotation velocities \( v(r) \) [L T\(^{-1}\)] satisfy the modified equilibrium:

\( \displaystyle \frac{v^2(r)}{r} = \frac{G \cdot M_{\text{vis}}}{r^2} - \frac{d \Phi_{\text{coh}}}{d r} \)

Where:

• \( G \) is the gravitational constant [M\(^{-1}\) L\(^3\) T\(^{-2}\)].
• \( M_{\text{vis}} \) is the visible baryonic mass enclosed within radius \( r \) [M].
• \( \frac{d \Phi_{\text{coh}}}{d r} \) is the spatial gradient of the coherence potential, providing additional centripetal acceleration to flatten rotation curves without invoking dark matter halos.

20.4.2 Predictions and Observational Signatures

• Rotation curve profiles correlate with central BH mass and activity level.
• Galaxies lacking central BHs exhibit classical Keplerian velocity decay.
• Coherence gradient effects contribute to gravitational lensing anomalies.
• Time variability in rotation curves arises from fluctuating BH coherence emissions.

20.5 Structure Formation and Density Growth

The growth rate \( \Gamma_{\text{form}} \) [T\(^{-1}\)] of density contrasts \( \delta \rho / \rho \) follows:

\( \displaystyle \Gamma_{\text{form}} \propto \frac{1}{\delta_{\text{eff}}} \times \nabla \Psi \times \text{loop}_{\text{density}} \)

Where:

• \( \nabla \Psi \) is the spatial gradient of flow potential or curvature (dimensionally [L\(^{-1}\)]).
• \( \text{loop}_{\text{density}} \) quantifies local motif saturation (dimensionless).

This mechanism replaces dark matter–seeded gravitational collapse with a topological decoherence ridge breakdown driving matter clustering.

20.6 Implications and Predictions

• Cosmological structure and evolution emerge naturally from recursive flow network dynamics without fine-tuning or anthropic arguments.
• Heat death scenarios are avoided or locally reversed via cyclical coherence resets and black hole emission cycles.
• The cosmological arrow of time arises from spatial gradients in \( \delta_{\text{eff}} \) and recursive phase asymmetries, rather than a global universal timeline.
• Measurable expansion anisotropies and temporal chirality effects are predicted near supermassive BH clusters.
• The Hubble parameter \( H(r, t) \) is non-uniform, reflecting local BH population and coherence distributions.

Summary

Section 20 reframes cosmology within TFP as a dynamic, fractal informational network driven by phase coherence and black hole emissions. This produces novel, testable predictions concerning galactic rotation, cosmic expansion anisotropies, and structure formation—distinguishing Temporal Flow Physics from conventional cosmological paradigms.