A Phenomenological Model Where Vacuum Energy Tracks Local Proper Time Rate: Implications for Evolving Dark Energy and a Null Test with Casimir Cavities

Abstract

A Phenomenological Model Where Vacuum Energy Tracks Local Proper Time Rate: Implications for Evolving Dark Energy and a Null Test with Casimir Cavities — v0.2 We propose rho_vac = rho_0 [1 + k Phi/c^2] where Phi is the local gravitational potential. This is equivalent to vacuum energy tracking local proper time rate. Motivation: Voids have fast clocks, clusters have slow clocks. If vacuum density tracks clock rate, voids have slightly more vacuum energy. From inside a cluster this looks like evolving dark energy, as hinted by DESI. Constraint: BBN requires |epsilon| < 4% integrated shift. Laboratory test (NEW in v0.2 - explicit phasing): A Casimir cavity should show an annual modulation as Earth moves in the Sun's potential. Fractional amplitude ~3e-10. Explicit prediction: Pressure is LARGER at perihelion in early January (~Jan 3-4) when we are deeper in the Sun's potential and proper time runs slower, and SMALLER at aphelion in early July (~July 4). ΔP/P ≈ k * 3.3e-10. Jan max, July min is the smoking-gun phase. Testable with CANNEX. A null result <1e-10 rules out k~1. v0.1 DOI: 10.5281/zenodo.21951772 - priority timestamp 2026-08-15Concept DOI (all versions): 10.5281/zenodo.21951771Draft with AI language assistance disclosed. License CC-BY 4.0.