On Beltrami Model of de Sitter Spacetime

Abstract

Based on some important properties of $dS$ space, we present a Beltrami model ${\cal B}_Λ$ that may shed light on the observable puzzle of $dS$ space and the paradox between the special relativity principle and cosmological principle. In ${\cal B}_Λ$, there are inertial-type coordinates and inertial-type observers. Thus, the classical observables can be defined for test particles and light signals. In addition, by choosing the definition of simultaneity the Beltrami metric is transformed to the Robertson-Walker-like metric. It is of positive spatial curvature of order $Λ$. This is more or less indicated already by the CMB power spectrum from WMAP and should be further confirmed by its data in large scale.