A relativistic scalar-tensor theory with a fixed scale a₀: linking galaxy dynamics and cosmology

Abstract / Description About the Paper This is the first part (P1) of the Unary Field Theory (UFT) research series. This paper introduces the Unary Field Theory, a unified framework built on three fundamental parameters. It successfully unifies inflation, dark matter, dark energy, and gravity as a phenomenon emerging from the kt flow substrate. This specific document focuses on the observational predictions of the theory, specifically the "two-year delay" phenomenon in LISA scalar gravitational waves. We present the exact calculations for the time delay between scalar and tensor gravitational wave modes, demonstrating the robust 1/f² spectral scaling law. The document also outlines the observational strategy for LISA SMBH mergers and the discriminatory power of this prediction against standard astrophysics and ΛCDM. Key Highlights Unified Framework: Successfully unifies inflation, dark matter, dark energy, and gravity based on the unary field Ψ. Core Prediction: Predicts a robust "two-year delay" phenomenon in LISA scalar gravitational waves. Exact Calculations: Demonstrates the strict Δt ∝ 1/f² scaling law for the time delay between scalar and tensor modes. Observational Strategy: Outlines a clear strategy for detecting supermassive black hole (SMBH) mergers with LISA. Unified Framework: Successfully unifies inflation, dark matter, dark energy, and gravity based on the unary field Ψ. Core Prediction: Predicts a robust "two-year delay" phenomenon in LISA scalar gravitational waves. Exact Calculations: Demonstrates the strict Δt ∝ 1/f² scaling law for the time delay between scalar and tensor modes. Observational Strategy: Outlines a clear strategy for detecting supermassive black hole (SMBH) mergers with LISA. Unsolved Observational Hints: Resolves multiple lingering anomalies in existing datasets with zero free parameters: (1) The ~2σ excess in cosmic shear power at ℓ~3608 seen in KiDS-1000/DES Year6 (Prediction Paper V, DOI: 10.5281/zenodo.21188916); (2) The tentative 21-cm absorption trough detected by EDGES, explained as a Jeans-scale oscillation at k_J=1.34 Mpc⁻¹ (Prediction Paper III, DOI: 10.5281/zenodo.21197950); (3) The ~5σ Hubble tension, resolved via dual early/late-Universe modifications (Prediction Paper VII, DOI: 10.5281/zenodo.21198098).