Geometric perspective for explaining Hubble tension: theoretical and observational aspects

The Universe expansion rate has two different but very precise values (67.4 +/- 0.5 and 73.30 +/- 1.04 km s(-1) Mpc(-1)) that are not compatible. This problem, known as a Hubble tension, adds to other cosmological questions such as the origin of dark energy and the flatness problem. In turn, alternative models have attempted to explain similar phenomena but without dark energy. The aim of this work was to explain the Hubble tension by using a geometrical interpretation of observational viewpoints in embedded manifolds. Our technique consists of a set of parametric projections of radially inhomogeneous metrics, linking indistinguishable behaviours of accelerated flat and non-accelerated closed universes. A dark-energy-like phenomenon emerges from the distortion of matter-independent hyperconical metrics. To contrast our model, numerical solutions of dark energy/matter densities and Hubble parameter were obtained and compared to the standard model fitted to the Pantheon Supernovae Ia sample and in contrast to the SH0ES LMC Cepheid findings. Finally, Hubble tension is modelled by the different extrinsic/intrinsic viewpoints of the manifold. Compared to the Planck Legacy's 2018 release of H0 = 67.4 +/- 0.5 km s(-1) Mpc(-1), we found.CDM-dependent (intrinsic) ranges between 66.38 and 68.87 km s(-1) Mpc(-1), which were theoretically derived by setting local compatibility of metrics. The.CDMindependent extrinsic viewpoint resulted in a Hubble parameter between 73 and 74 km s(-1) Mpc(-1) (compared to H0 = 73.30 +/- 1.04 km s(-1) Mpc(-1) of SH0ES). Datasets of 1048 Pantheon Type Ia supernovae (0.0101 < z < 2.26) and 34 cosmic chronometers combined with 7 radial baryon acoustic oscillation sizebased samples (0.0708 < z < 1.965) were used to constraint the model. According to this geometrical perspective, dark parameters (energy and matter) could partially or totally be considered 'apparent physical quantities', a consequence of the stereographic projection of the extrinsic curvature.