Cosmological Phase Projection Principle: A Geometric Interpretation of Visible and Dark Matter

I propose a geometric principle in which visible matter and dark matter arise as orthogonal projections of a single complex cosmological field. The total energy density of the system is determined by the amplitude of the field, while the phase controls the distribution between visible and dark components. Writing the fundamental field as Ψ(x)=R(x)e^{iφ(x)}, the two observable sectors arise from the real and imaginary projections of the field. This leads to energy densities ρ_visible = R² cos²φ and ρ_dark = R² sin²φ, ensuring total density conservation ρ_visible + ρ_dark = R². The ratio between dark and visible matter becomes tan²φ. The framework suggests that dark matter may correspond to a phase component of a deeper field structure rather than a separate particle species. Possible cosmological implications and dynamical evolution of the phase field are discussed.