The ‘Farthest Equals Nearest’ Paradox in Cosmology: Antipodal Points, Cosmic Horizons, and Universe Topology

This study examines how the concepts of "farthest" and "nearest" points change depending on the geometric structure of the universe. The research comparatively analyzes three fundamental cosmological models: (1) the static closed universe model (Ω > 1), (2) the flat or semi-open universe model (Ω ≤ 1), and (3) the dynamic expanding universe model (ΛCDM). The philosophical proposition expressed as "The point infinitely approached is the farthest point, and at the same time the nearest point" has been evaluated within each model framework. Analysis results reveal that this paradoxical statement is mathematically valid only in the closed universe model, remains conceptually meaningless in the flat universe model, and becomes physically impossible in the dynamic expanding universe due to the cosmological event horizon. The study utilizes Planck Collaboration (2020) observational data, Einstein (1915, 1917) field equations, and Friedmann (1922) cosmology equations as the theoretical framework.