A Relativistic Scalar-Tensor Theory with a Fixed Scale a0: Linking Galaxy Dynamics and Cosmology

This work presents a relativistic scalar-tensor theory unifying galaxy dynamics and cosmology via a fixed acceleration scale a0~1.2×10−10m/s2. The model introduces a single complex scalar field Ψ whose spontaneous symmetry breaking gives rise to dark matter (as a 1.1×10−22eV ultralight scalar field) and dark energy (via vacuum energy). Key predictions include: (1) A six-polarization gravitational wave signature (two tensor, two vector, two scalar) detectable by LISA; (2) A 0.0038 tensor-to-scalar ratio for primordial B-modes, testable by LiteBIRD; (3) A 3-year oscillation period for galactic soliton cores, observable via stellar orbit monitoring; (4) A natural resolution of the Hubble tension (H0=70.2±0.8km/s/Mpc). The theory is validated against solar system tests (Mercury perihelion, Shapiro delay) and SPARC galaxy rotation curves (χ2/dof≈1.2). All parameters are derived from first principles, requiring no ad hoc fine-tuning.