Avoidance of Singularities in Multiverse Collisions via Bounces: Implications for Eternal Inflation under BMC

In Eternal Inflation models, collisions between bubble universes can lead to singularities or destructive phase transitions, endangering the stability and viability of the resulting universe. The Bergmann Multi-Cycle (BMC) and Bergmann Bounce Relativity (BBR) avoid singularities through stochastic mini-bounces that overlap during collisions and generate local expansions. This paper derives the bounce-damping metric for collision fronts, analyzes stability and energy transfer, compares with classical bubble-collision models, and provides testable predictions (e.g. CMB collision rings, GW signatures with h_c ≈ 10^{-15}–10^{-17}). BMC/BBR transform potentially destructive multiverse collisions into stable fusions or rebounds, making Eternal Inflation cosmologically robust.