Quantum Geometric Emergence and the Origin of the Cosmos: A Non-Singular Percolation Scenario

Abstract: Within the framework of "Quantum Geometric Emergence, " this paper provides a complete and rigorous formal description for the genesis of the universe. This background-independent theory of quantum gravity posits that spacetime, matter, and their dynamics emerge from a fundamental network of quantum relations. The "Big Bang" is not a singular event in a pre-existing spacetime, but rather an entanglement percolation phase transition of a pre-geometric quantum network from a subcritical disconnected phase to a supercritical giant connected component. This phase transition enables the coarse-graining procedure to generate a continuous Lorentzian spacetime geometry. Based on the axiomatic foundation of our previous works 1, 2, 3, we construct an origin scenario that addresses four progressive questions: the production of network seeds, growth towards the percolation threshold, the mechanism of the percolation phase transition, and the self-regulation of the network after the transition into the standard hot Big Bang cosmology. We rigorously characterize each stage using scale-dependent dynamic quantum spectral triples (consisting of the algebra AL, the Hilbert space HL, and the Dirac operator DL), Connes spectral distance, and renormalization group methods. The percolation phase transition naturally generates exponential inflation through the divergence of correlation length, without the need for an inflaton field, and the curvature backreaction is self-limiting due to algebraic crystallization constraints and spectral action. This scenario produces unique, testable observational signatures: scale-dependent primordial non-Gaussianity anchored at a characteristic wavenumber kₛtar (which is approximately equal to the inverse of the core length Lcore), residual statistical anisotropy from nucleation seeds, and specific Lorentz symmetry breaking patterns. We also discuss how global consistency constraints (where the operator Cₕat acting on the network state Psiₙet equals zero) transform the "probability of seeds" from a fine-tuning problem into a structural selection problem, thereby eliminating the need for anthropic explanations in a multiverse.