Higher-Order Volumetric Expansion and a Geometric Contribution to the Hubble Tension

The Hubble tension—the discrepancy between locally measured (H0 ≈ 73 km/s/Mpc) and globally inferred (H0 ≈ 67 km/s/Mpc) expansion rates—suggests potential limitations in the standard linear parametrization of cosmic expansion. This work investigates the geometric consequences of treating expansion as a three-dimensional volumetric process evaluated over finite observational intervals. By explicitly retaining second- and third-order terms in the volumetric expansion binomial, a natural geometric correction factor (Δgeom) emerges. We demonstrate that the omission of these higher-order terms in standard first-order linearizations introduces a systematic bias that numerically aligns with the ∼ 8.9% discrepancy observed between SH0ES and Planck results. This framework identifies a purely geometric truncation effect as a contributing factor to the tension without requiring new physical components or modifications to standard Friedmann dynamics.