Geometric interpretation of the dark energy from projected hyperconical universes

TL;DR

This paper presents a geometric approach to explaining dark energy by projecting hyperconical universes, deriving a specific dark energy density, and fitting a distortion parameter using supernova data.

Contribution

It introduces a novel geometric interpretation of dark energy via hyperconical universe projections and predicts key cosmological parameters.

Findings

Predicted dark energy density Ω_Λ ≈ 0.694

Derived a distortion parameter α ≈ 0.325–0.36

Fitted model to 580 supernova observations with χ² = 562

Abstract

This letter explores the derivation of dark energy from a locally conformal projection of hyperconical universes. It focuses on the analysis of theoretical compatibility between the intrinsic view of the standard cosmology and an adequate transformation of hyperconical manifolds. Choosing some parametric family of locally conformal transformations and taking regional (second order) equality between the Hubble parameter of both theories, it is predicted that the dark energy density is $\Omega_{\Lambda} = 0.6937181(2)$. In particular, we used a radially distorted stereographic projection, the distortion parameter of which is theoretically predicted about $\alpha = 0.325 \pm 0.005$ and empirically fitted as $\alpha = 0.36 \pm 0.02$ ($\chi_0^2 = 562$) according to 580 SNe Ia observations.