Tau-Phase Cosmology V4.2: Dynamic Spacetime Rheology and Consistency Across Cosmic Scales

Tau-Phase Cosmology V4. 2: Dynamic Spacetime Rheology and Consistency Across Cosmic Scales This work is presented as a phenomenological framework intended to motivate targeted experimental tests, rather than as a replacement for established gravitational theory. Tau-Phase Cosmology V4. 2 presents a generalized framework addressing the growing tension between early-universe observations and the apparent stability of local cosmic structures. In this model, spacetime is reinterpreted as a non-Newtonian, shear-thinning viscous medium whose effective properties depend on both matter density and kinematic shear. Building upon the “Solid-First” hypothesis introduced in V3. 1, this version extends the static, density-dependent formulation by incorporating the shear rate γ̇ as a fundamental dynamical variable governing the fluidity of the vacuum. Key Theoretical Advances In this framework, the effective viscosity of spacetime, ηₑff, is dynamically determined by the interplay between local energy density ρ and shear rate γ̇. This Dynamic Spacetime Rheology resolves the apparent dichotomy between the local universe and the primordial cosmos: Static Limit (Regime 1): In relaxed systems characterized by low shear (γ̇ → 0), the model strictly recovers the linear mass–time scaling of V3. 1 (Δt ∝ κ・ρ). This confirms the validity of “Group A” galaxies (e. g. , Sgr A*, M31) as the Rheologically Relaxed State, providing a stable anchor for cosmic evolution. Dynamic Enhancement (Regime 2): In high-energy environments with large shear (γ̇ ≫ γ̇c) — such as the early universe or active accretion flows — a shear-thinning mechanism strongly suppresses spacetime viscosity. This leads to Effective Process-Time Compression, offering a physical explanation for the unexpectedly mature galaxies observed by JWST (e. g. , GN-z11, JADES-GS-z14-0) without invoking changes to fundamental constants. Quantitative Validation V4. 2 introduces a quantitative meta-analysis of existing high-precision clock comparisons to test the framework's predictions: Null Test Passed (BACON 2021): The model correctly predicts zero deviation for clocks co-located in homogeneous environments (Δρ ≈ 0), consistent with the < 10^-17 agreement observed in the Boulder Atomic Clock Optical Network. LSM Anomaly Explained (Grotti et al. 2018): For high-contrast underground experiments (Δρ ≈ 700 kg/m³), the model predicts a specific viscous redshift (slower clock rate). Re-evaluation of LSM residuals suggests a negative offset consistent with the theoretical prediction using a spacetime susceptibility of ε ≈ 1. 4 × 10⁻¹⁹ m³/kg. Experimental Verification To definitively distinguish this rheological effect from geodetic noise, V4. 2 proposes the Iso-Potential Density Test (Supplementary Material A). This protocol outlines a controlled laboratory experiment designed to disentangle conventional collisional frequency shifts from density-coupled spacetime viscosity. Version Notes V4. 2 (Current): Quantitative Analysis: Added a rigorous consistency check against existing experimental data. Null Test Validation: Explicitly demonstrated that the framework passes the BACON null test (=0). Parameter Estimation: Estimated the phenomenological parameter 1. 4 10^-19 m³/kg based on LSM residuals. Figure 5: Added a trend analysis plot comparing density contrast vs. frequency residuals across multiple campaigns. V4. 1: Added a structured interpretation of existing underground clock-comparison experiments as sign-consistent but confounded evidence. Clarified the Iso-Potential Density Test as a necessary controlled null-test designed to reduce dimensionality. V4. 0: Introduced Dynamic Spacetime Rheology: a shear-dependent generalization of spacetime viscosity (Eq. 2. 2). Unified the static local universe and the accelerated early universe within a single rheological framework. Provided a physical mechanism for rapid high-redshift galaxy formation via viscosity suppression. Reinterpreted observational scatter in mass–time relations as a signal of non-zero shear history. Added Supplementary Material A, detailing a specific laboratory test using density-contrasting spherical shells. V3. 1: Defined the “Cosmic Main Sequence” and the “Group A” anchors. Established the linear scaling t. V3. 0: Introduced spacetime viscosity as a unifying physical quantity. Derived the Refining Equation.