From Collapse to Cosmos: A Sophia-Regulated Cosmogenesis Model within the ToE-2PS Framework

This work investigates a cosmogenesis scenario emerging from the interior dynamics of black holes within the ToE-2PS framework. The model introduces a structural coherence field governed by a scalar-tensor action and regulated by the dimensionless Sophia factor, which amplifies the response of the field to spacetime curvature and matter density. We derive the full dynamical system for an anisotropic Kantowski-Sachs interior spacetime with dust matter and perform numerical integration using an adaptive RK45 solver. The results demonstrate the emergence of a non-singular cosmological bounce, where gravitational collapse transitions smoothly into expansion at finite curvature and density. For representative parameters: Keff = 0.9 xi = 1 m^2 = 10 lambda_4 = 0.5 The simulations produce a bounce at t* approx 0.119 with minimum angular radius b_min approx 0.187 and a peak Sophia amplification lambda_S approx 6 x 10^3. Anisotropies decay rapidly after the bounce, leading to an isotropic expanding phase. The results suggest that a curvature-regulated coherence field may provide a mechanism for cosmological expansion emerging from gravitational collapse while avoiding classical singularities. Possible observational implications include primordial gravitational-wave signatures, residual large-scale anisotropies, and modified early-universe dynamics. This work extends previous studies within the ToE-2PS research program, connecting black-hole interior physics, scalar-tensor gravitational dynamics, and cosmological evolution into a unified framework.