Tau-Phase Cosmology V4.1: Dynamic Spacetime Rheology and Consistency Across Cosmic Scales

Tau-Phase Cosmology V4. 1: Dynamic Spacetime Rheology and Consistency Across Cosmic Scales Tau-Phase Cosmology V4. 1 presents a generalized phenomenological 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. Experimental Verification Crucially, V4. 1 moves beyond theoretical phenomenology by proposing a concrete laboratory test: the Iso-Potential Density Test, detailed in Supplementary Material A. This protocol outlines how high-precision optical lattice clocks may be used to disentangle conventional collisional frequency shifts from a predicted, density-coupled rheological time dilation. The experiment is designed as a decisive null-test capable of falsifying or supporting the proposed framework. Version Notes V4. 1 (Current): V4. 1 adds a structured interpretation of existing underground clock-comparison experiments (Grotti et al. , 2018) as sign-consistent but confounded evidence. It further clarifies the Iso-Potential Density Test as a necessary controlled null-test designed to reduce dimensionality, rather than merely a precision upgrade. 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 (Al vs. Os). V3. 1: Defined the “Cosmic Main Sequence” and the “Group A” anchors (Sgr A*, M31). Established the linear scaling Δt ∝ κ・ρ, now identified as the static limit of V4. 0. Addressed galactic downsizing via the Solid-First model. V3. 0: Introduced spacetime viscosity η as a unifying physical quantity. Derived the Refining Equation. Defined the Habitable Viscosity Zone (HVZ).