Gravity Echo: Topological Metric Solitons and Dynamic Time Dilation under Higgs‑Type Vacuum Phase Transitions

Abstract

This is a completely revised and extended version (v2.0). The numerical calibration suite (v3.3.4) has been added, confirming hierarchy resolution, Lyapunov stability, critical exponent β = 0.500, unified dark sector EoS, quantum amplification χ_Q = 826.11, and a BAO‑scale cosmological peak.We formulate a novel quantum‑gravitational framework demonstrating how localised phase curvature in a non‑linear scalar field actively warps space‑time geometry in the absolute absence of physical baryonic mass. Moving away from standard stress‑energy tensors generated by macroscopic material bodies, we model the vacuum potential via a self‑interacting Landau–Higgs symmetry‑breaking mechanism (V(θ) = (λ/4)(θ² − ν²)²). By deriving a 4D‑reduced spherical Schwarzschild‑like effective reduction of the coupled Einstein‑scalar field equations via Killing vector fields and conformal invariance, we track the dynamic co‑evolution of the scalar phase θ(r,t) and the dual components of the metric tensor: the time dilation factor g₀₀(r,t) and the spatial curvature component g₁₁(r,t). Numerical simulations executed through an implicit, fifth‑order Radau IIA ODE scheme reveal a macroscopic phase transition: as the scalar phase undergoes a gradient catastrophe and condenses into a stable double‑kink soliton profile, it dynamically deforms the local metric. This multi‑variable phase scan eliminates numerical fit paradoxes, showing that the metric parameters scale continuously with the coupling constant, verifying a localised coordinate time dilation channel where g₀₀ drops systematically down to 0.50 while g₁₁ mirrors its contraction by expanding to 2.00. We further discuss the cosmological implications of this framework, proposing that large‑scale antigravitational anomalies—arising from distributed resonant states of the vacuum—may offer an alternative to the standard dark energy paradigm. This positions Topological Resonance as a candidate mechanism for the accelerated expansion of the Universe.