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

This work introduces a novel conceptual framework that integrates crystallographic visualization techniques with cosmological geometry. Specifically, we reinterpret the crystallo-graphic 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 conceptually interpreted as exhibiting topological features analogous to the “inside–outside” structure of a Klein bottle. This geometrical perspective provides a foundation for analyzing the mass–energy budget of the Universe as determined by the Planck's mission. We examine the present mass–energy composition—including the relative contributions of visible matter (baryonic), and dark energy identified with the zero-point field (ZPF)—within a differential geometric setting. These components are ultimately represented through a crystallographic holography–based formulation of the Planck observational mass–energy budget.