A Geometric Reinterpretation of FLRW Cosmology: Gnomonic Holography and an Absorptive Framework Independent of Temporal Dynamics

This work introduces a novel conceptual framework that integrates gnomonic visualization techniques with cosmological geometry. Specifically, we reinterpret the gnomonic holography of three-dimensional crystal structures onto a two-dimensional plane within the three-dimensional spatial sector of the Friedmann–Lemaître–Robertson–Walker (FLRW) metric, formulated following the Landau–Lifshitz approach. Within this framework, the surface of a four-dimensional hypermanifold (a 4D sphere) is heuristically and conjecturally interpreted as exhibiting topological features analogous to the “inside–outside” structure of a Klein bottle. This analogy is not intended as a strict topological identification, but rather as an illustrative conceptual device to motivate geometric intuition about global structure. This geometrical perspective provides a foundation for analyzing the mass–energy budget of the Universe as determined by the Planck mission. We examine the present mass–energy composition—including the relative contributions of visible (baryonic) matter and dark energy, identified here with the zero-point field (ZPF)—within a differential geometric setting. These components are ultimately represented through a gnomonic holography–based formulation of the Planck observational mass–energy budget.