Spacetime Quantization Through Time Waves: Unifying Micro– and Macro–Bang Dynamics in a Quantum–Gravitational Inflationary Framework

This paper introduces the Time Field Model (TFM) as a spacetime quantization approach, wherein time is promoted to a fundamental scalar field with wave-like excitations. When the energy density of these time waves surpasses a Planck-scale threshold (ρcritical ∼ c5 ℏG2), discrete space quanta nucleate—initiating a phase-transition-like process closely resembling cosmic infla tion. We incorporate a Lagrangian derivation to explain how the time field couples to emergent space quanta, and show how a lattice-based formulation avoids contradictions between discrete and continuum pictures: on small scales, space is inherently discrete, but on large scales, the metric recovers smooth geometry consistent with general relativity. Building on TFM Papers #1–3, which established time as a two-component field driving micro– and macro–Bang expansions, this work unifies those concepts under a single threshold-driven mechanism, providing a testable blueprint for a quantum–gravitational basis of cosmic expansion and emergent spacetime, with signatures detectable by next-generation cosmological surveys.