Emergent Spacetime from Chaotic Synchronization: Resolving the Big Bang and Vacuum Energy Paradoxes

The physical unification of quantum field theory and general relativity remains the ultimate fron- tier of theoretical physics, yet modern cosmology is deadlocked by two conceptual crises: the 120- order-of-magnitude cosmological constant problem and the initial Big Bang singularity. Both paradoxes stem from the foundational axiom that sub-Planckian quantum fluctuations are driven by uncorrelated, stochastic Gaussian noise. Here, we introduce Deterministic Chaotic Quantization, demonstrating that a microscopic coupled map lattice governed by generalized Boole transformations autonomously gen- erates a heavy-tailed Cauchy vacuum profile. Utilizing chaotic reduction theory, we prove that our three-dimensional spatial reality is uniquely selected as the critical saturation threshold that optimizes geometric complexity while preventing the emergent metric from dissolving into an infinite-dimensional mean-field vacuum. Crucially, as the spatial coupling reaches the thermodynamic limit, an entropic implosion triggers complete phase synchronization, structurally neutralizing the catastrophic zero-point energy accumulation of quantum field theory without requiring any fine-tuning, while simultaneously driving a natural, automated Big Bang singularity expansion. This framework bridges non-linear dy- namics, quantum mechanics, and cosmology, offering precise, testable non-Gaussian spectral signatures for next-generation satellite missions.