Cosmic Respiration: Mathematical Foundations of Spiral Growth in Fractional Field Evolution (QFE)

This paper presents a novel evolutionary cyclic cosmology based on Fractional Field Evolution (QFE), utilizing the Caputo fractional derivative (α ≈ 0.85). We demonstrate that the gravitational singularity is replaced by a non-local ”Bounce” due to the UVfiniteness of the fractional potential. The core of our theory lies in the introduction of a ”Memory Kernel” that functions as a physical storage for cosmic information. Unlike traditional cyclic models that suffer from entropy stagnation, our model incorporates an ”Amplification Factor A,” derived from the information exchange with a high-dimensional Meta-potential. We mathematically prove that this mechanism leads to ”Spiral Growth,” where the universe increases in energy density and structural complexity with each successive cycle. This framework provides a unified resolution to the singularity problem, the nature of the dark sector, and the thermodynamic arrow of time.