Near Flat Curvature

The observed near-flatness of the universe — Ω_total within ~0.1% of unity — is sometimes presented as two distinct tensions in ΛCDM: the theoretical flatness problem (why is it so close to critical density?) and the observational near-flat curvature problem (why is the measured curvature small but possibly nonzero and not exactly zero?). The former is addressed by SCT's infinite eternal spacetime geometry in Solution 010; this solution addresses the latter. Precision CMB analyses from Planck show a consistent ~2σ preference for a slight closed curvature (Ω_K ≈ −0.002), while BAO data independently prefer slightly open curvature. This tension between CMB-inferred and BAO-inferred curvature within ΛCDM arises because both probes assume a single universal expansion history. In SCT, both measurements are sampling the same multi-frame superposed gravitational environment but at different redshifts and with different geometric weights along the line of sight, so they naturally measure slightly different effective curvatures even when the true global curvature is exactly zero.

The near-flatness itself is understood in SCT as a consequence of the collision geometry. The two parent pockets must have been traveling on nearly antiparallel paths for the collision to produce an overlap volume as large and uniform as our ~46.5 Gly observable universe. A highly oblique or low-velocity collision would have produced a smaller overlap region with more pronounced collision-axis geometry and larger departures from flatness. The observed near-flatness therefore constrains the collision geometry: v_rel and the impact parameter b must together satisfy the condition that the post-collision energy density of the debris closely approximates the critical density for the resulting patch size. This is not a fine-tuning constraint but a selection effect — only collisions that produce large enough overlap volumes with sufficient thermalization produce cosmological patches in which observers can evolve. Near-flatness is thus the natural observational signature of a collision that was violent enough and large-scale enough to create a habitable cosmic patch.