Geometric interpretation of the dark energy from projected hyperconical universes

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 ${\mathrm{\Omega }}_{\mathrm{\Lambda }}=0.6937181(2)$. 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.