Rethinking Cosmic Structure: Geometric Projection Errors in a Finite 3-Sphere Universe

This work examines the observational consequences of modeling the Universe as a finite 3-sphere surface of a 4D hypersphere, emphasizing geometric projection errors inherent in flat-sky cosmology. Standard cosmological analyses that assume flat space systematically overestimate distances and velocities for high-redshift objects. By accounting for the curved geodesics of the 3-sphere, this paper identifies specific corrections to BAO angular scales, galaxy surveys, and supernova measurements. These corrections have direct implications for the interpretation of cosmic acceleration and the consistency of H₀ determinations.