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, η_eff, 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 ≫ γ̇_c) — 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 (Δρ=0). Parameter Estimation: Estimated the phenomenological parameter ε ≈ 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 Δ t ∝ κ · ρ. V3.0: Introduced spacetime viscosity η as a unifying physical quantity. Derived the Refining Equation.