Unifying Isotropy and Anisotropy in the Breathing Universe Model Using Legendre Polynomials

The Breathing Universe Model (BUM) introduces a novel framework for understanding the dynamics of the universe, incorporating three boundary fields: the Light-field, Shadow-field, and Color-field. These fields govern energy-mass transitions, gravitational interactions, and mass generation, respectively. While the mathematical tools to describe isotropic and anisotropic phenomena—such as Legendre polynomials—are well established in physics, the BUM uniquely integrates these tools to model new phenomena, including monopole-snapping events, dark matter interactions, and positive-negative acceleration effects. This article demonstrates how the BUM reinterprets classical mathematical methods to unify large-scale cosmological behavior with local field interactions, presenting a compelling addition to current theories.