Cosmological Bounce in Noncommutative Geometric Unification

This work establishes a singularity-free cosmological bounce within the noncommutative geometric unification framework. The mechanism emerges from Perelman-inspired topological surgery applied to Einstein’s equations, generating a repulsive term Θsurg µν that prevents collapse below the Planck scale. Combined with entropic stabilization of spatial geometry, this yields a nonsingular bounce at critical density ρcrit = c^5/(G^2ℏ).Key predictions include: imprinted spatial curvature K = +1 in CMB low-ℓ modes, characteristic gravitational wave spectrum ΩGW(f) ∝ (1 + f /fΛ) −1, and finite maximum temperature Tmax ∼ 1032 K. The modelresolves the initial singularity problem while remaining testable through next-generation cosmological surveys.