The Shape of the SV0 Universe: Reconciling Spherical Topology with Observational Flatness

Abstract:The SV0 framework predicts that the entire universe is a finite, closed 3-sphere (positive curvature) with a maximum radius R_max ~ 1.5 × 10²⁷ m. However, standard cosmology considers the universe to be spatially flat, consistent with Planck CMB observations. In this paper (Paper LI of the SV0 series), we resolve this apparent contradiction. We show that the SV0 universe is globally spherical (positive curvature) but locally flat, because the observable universe (R_obs ~ 4.4 × 10²⁶ m) is a small fraction of the total volume. The curvature parameter Ω_k is dynamically suppressed by the SV0 attractor, which drives the equation of state to w → -1 and flattens the universe. We demonstrate that the SV0 model is fully consistent with CMB flatness observations, while providing a finite, closed topology that resolves the singularity and horizon problems.