Emergent Cyclic Cosmology from a Discrete Tri-Phasic Microstructure: Bounce Dynamics, Phase Transitions, and Multi-Scale Tests

We construct a non-singular cyclic cosmology in which continuous spacetime emerges from a fundamental, discrete weighted graph microstructure governed by tri-phasic order parameters (Out, In, Dual). We explicitly construct the emergent spatial metric from the weighted graph Laplacian and demonstrate that Einstein– Hilbert gravity arises as the universal infrared effective theory under coarse-graining and renormalization group (RG) flow. Utilizing a polymerization scheme analogous to Loop Quantum Cosmology (LQC), we derive a modified Friedmann equation H 2 = 8πG 3 ρ(1 − ρ/ρ c ), ensuring a non-singular quantum bounce at a critical den-sity ρ c ∼ 10 −3 ρ P l . This bounce triggers a density-driven first-order phase transition from a convergent “In-phase” to an expansive “Out-phase.” We demonstrate that this transition naturally generates Standard Model-like “Dual-phase” excitations via non-equilibrium energy transfer and produces a stochastic gravitational wave background detectable by LISA. We analyze linear cosmological perturbations using a regularized Mukhanov–Sasaki formulation valid across the bounce, implemented in a modified CLASS Boltzmann code. The model predicts scale invariance at large scales and controlled oscillatory features near the bounce horizon scale. Furthermore, we identify specific quadratic ultraviolet corrections to dispersion relations induced by the discrete microstructure, proposing novel laboratory-scale tests using resonant cavities, Casimir setups, and quantum interferometers. The framework provides a falsifiable, unified theory connecting the Planck-scale microstructure to both cosmic microwave background anomalies and terrestrial precision experiments.