A Non-Singular Cyclic Cosmology from Tri-Phasic Transitions of a Discrete Out-Force Microstructure: Theory, Implementation, and Observational Constraints

We present a comprehensive framework for a cyclic cosmology where spacetime emerges from a fundamental discrete “Out-force” microstructure. Unlike continuous manifold theories, we postulate that the universe operates on a lattice-regularized network characterized by a minimal lengthscale ℓ O . Utilizing a polymerization scheme analogous to Loop Quantum Cosmology (LQC), we derive a modified Friedmann equation that includes a quadratic density correction ρ 2 /ρ c , naturallyresolving the Big Bang singularity into a non-singular quantum bounce. This bounce triggers a violent first-order phase transition from a convergent “In-phase” (I) to an expansive “Out-phase” (O). We provide a detailed thermodynamic analysis of this transition, calculating the Euclidean action for bubble nucleation and the resulting stochastic gravitational wave background. Furthermore, we demonstrate that a third component, the “Dual-phase” (D), identified as Standard Model matter, is generated via non-equilibrium energy transfer Q ∝ ˙O 2 during the transition. We detail the numerical implementation of this model using a modified CLASS code coupled with Cobaya for MCMC analysis. Our results predict a unique oscillatory feature in the primordial power spectrum and a gravitational wave signal detectable by LISA, offering a falsifiable alternative to the inflationary paradigm.