Abstract

We construct a single-metric complex-scalar model in which cosmic acceleration, radial dark-matter-like excitations, and a local phase clock arise from one covariant action. The structural relation m_sigma^2 v = M^3 links the radial potential curvature to the phase kinetic scale, while a conserved phase charge determines the evolution of the radial minimum and the phase contribution to the energy budget.

We prove that the fixed-charge radial energy has a unique global minimum and establish the exact bound epsilon_core >= M^4/2 + sqrt(2) M^2 |Q_*|/(v a^3) for v >= 4M. The same threshold governs stationary energy convexity and the low-momentum acoustic response. For expanding flat cosmologies satisfying the specified initial-energy and regularity conditions, we prove future convergence to an accelerating de Sitter state.

In the controlled rapid-oscillation regime, radial excitation energy approaches matter-like dilution proportional to a^-3. The same dynamics yield a quantitative relation between radial excitation energy and the variance of the internal phase-clock rate. We derive additional consistency conditions connecting the background expansion, scalar perturbations, and gravitational-wave propagation.

A numerical benchmark resolving 293 radial cycles verifies charge conservation, the controlled matter-like regime, and the clock-variance approximation. Together, these results establish linked, testable consequences for dark-energy, radial-matter, and phase-clock dynamics without introducing independent phenomenological functions for each sector.