A MINIMAL-BASIS PEDAGOGICAL FRAMEWORK FOR ΛCDM COSMOLOGICAL PARAMETERS

This paper presents a pedagogical framework for organizing the standard ΛCDM cosmological parameters into three conceptually independent physical constraints: Ω_b (baryonic matter density from Big Bang nucleosynthesis and cosmic microwave background observations), Ω_m (total matter density from structure formation probes such as gravitational clustering and weak lensing), and Ω_total (effective spatial curvature from cosmic microwave background geometry). These constraints algebraically determine the derived quantities Ω_c (cold dark matter density) as Ω_m - Ω_b and Ω_DE (dark energy density) as Ω_total - Ω_m. The framework emphasizes the distinct physical processes underlying each constraint, nuclear physics and photon-baryon dynamics for Ω_b, gravitational dynamics of matter perturbations for Ω_m, and spacetime geometry from photon propagation for Ω_total, while noting their model-conditional nature within flat ΛCDM assumptions. It relates to standard parameterizations using physical densities (Ω_b h², Ω_c h²) but focuses on present-day energy fractions for educational clarity, without proposing new physics or methodological improvements over multi-parameter likelihood analyses. Numerical values are drawn from Planck 2018 and DESI 2024 data, with extensions discussed for time-dependent cosmology and modified gravity scenarios.