Gravity as the Non-Markovian Memory of Spacetime: A Unified K-Kernel Paradigm for Cosmological Bounce & Baryogenesis

We propose a radical paradigm shift in cosmology: Gravity is not a fundamental force acting instantaneously, but the accumulated mathematical trace of the non-Markovian memory of spacetime. By introducing a density-dependent memory kernel K(ρ) = (1 - ρ/ρ_c), we modify the standard Friedmann equations. This modification eliminates the Big Bang singularity, replacing it with a smooth Cosmological Bounce at the Planck density. Furthermore, we demonstrate that the temporal gradient of this memory field naturally drives the asymmetry between matter and antimatter (Baryogenesis), producing a matter surplus consistent with current observations (M/M̄ > 10^9). The framework establishes a macroscopic, continuous bridge to microscopic Loop Quantum Gravity (LQG), resolving cosmological singularities and laying the foundation for quantum-classical unification.