On Beltrami Model of de Sitter Spacetime

TL;DR

This paper introduces a Beltrami model for de Sitter space that provides a framework with inertial observers and classical observables, potentially resolving key puzzles in cosmology and linking to observational data.

Contribution

The paper presents a novel Beltrami model of de Sitter space that incorporates inertial coordinates and observers, offering new insights into observable properties and cosmological principles.

Findings

Beltrami model defines inertial-type coordinates in de Sitter space

Transforming the Beltrami metric yields a Robertson-Walker-like metric with positive curvature

Model aligns with CMB observations suggesting positive spatial curvature

Abstract

Based on some important properties of $dS$ space, we present a Beltrami model ${\cal B}_\Lambda$ that may shed light on the observable puzzle of $dS$ space and the paradox between the special relativity principle and cosmological principle. In ${\cal B}_\Lambda$, 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 $\Lambda$. 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.