The Hubble Tension Interpretation in Terms of Gnomonic Holography

Abstract

The Hubble tension—the discrepancy between early- and late-Universe measurements of the Hubble constant—remains an open problem in cosmology. This paper proposes a geometric interpretation of the Universe based on gnomonic holography, in which a Hubble-like parameter emerges naturally from the projection geometry of the 4D‑globe manifold´s 3D‑curved Riemannian hypersphere into Euclidean locally 3E‑flat space, rather than being introduced as an independent cosmological constant. Using the Planck matter-energy dencity fractions, the model predicts two characteristic gnomonic radii associated with the baryonic and dark sectors. Although these differ by only about 0.2%, the nonlinear reconstruction yields Hubble-like values of 71.63 and 67.04, closely matching the observed Hubble tension. The model also predicts an emergent timescale ratio of approximately 80.3 between the visible and dark sectors. Furthermore, it interprets the Big Bang as a phase transition of a primordial background energy field, conceptually similar to Hoyle’s phase-transition cosmology but derived from an entirely different geometric framework. Although exploratory, the proposed approach suggests that the Hubble tension may reflect an intrinsic property of cosmic geometry rather than new fundamental physics.