A Scalar-Tensor Gravity Model with Mass-Time Duality Symmetry: Chronal Inversion Operator, Holographic Dual and Dual Cosmological Phase Transitions

We establish the Mass-Time Duality Symmetry (MTDS) as a new fundamental symmetry in gravitational physics. Realized via a time-density scalar field ρ_t and the chronal inversion operator Ĉ, this symmetry enforces the exact equivalence m = λ t, leading to m = t = F/a = w/g = E/c² = F·s/c². The Jordan-frame action yields a minimal scalar-tensor theory that recovers general relativity exactly in the low-density limit while admitting dual mass-phase and time-phase descriptions of any spacetime. In FLRW cosmology, MTDS triggers a spontaneous duality phase transition that drives late-time acceleration without a cosmological constant. A holographic interpretation maps the chronal inversion to a bulk-boundary correspondence in AdS/CFT, providing a novel emergent spacetime mechanism. High-precision numerical simulations (error < 10^{-12}) confirm duality invariance. The model predicts unique, falsifiable signatures — dual gravitational-wave polarization modes and chronal echoes — detectable in LIGO-Virgo-KAGRA O5 and LISA. Unlike prior time-density proposals, MTDS introduces an exact symmetry group and dual-phase cosmology, offering a consistent, second-order extension of general relativity with profound implications for quantum gravity and precision cosmology.