On Beltrami Model of de Sitter Spacetime

Abstract

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

arXiv comment4 pages

References in corpus (2)

• Adventures in de Sitter space
• The Wilkinson Microwave Anisotropy Probe

Cited by in corpus (47)

• On Special Relativity with Cosmological Constant
• Special Relativity in the 21${}^{\mathrm{st}}$ century
• Yang's Model as Triply Special Relativity and the Snyder's Model--de Sitter Special Relativity Duality
• Mechanics and Newton-Cartan-Like Gravity on the Newton-Hooke Space-time
• On Principle of Inertia in Closed Universe
• Temperature at Horizon in de Sitter Spacetime
• Three Kinds of Special Relativity via Inverse Wick Rotation
• Snyder's Quantized Space-time and De Sitter Special Relativity
• Conservation laws and scattering for de Sitter classical particles
• Hamiltonian Formalism of the de-Sitter Invariant Special Relativity
• The Principle of Relativity, Kinematics and Algebraic Relations
• The Principle of Relativity and Special Relativity Triple
• Newton-Hooke Limit of Beltrami-de Sitter Spacetime, Principles of Galilei-Hooke's Relativity and Postulate on Newton-Hooke Universal Time
• The Triality of Conformal Extensions of Three Kinds of Special Relativity
• Cosmological Solutions with Torsion in a Model of de Sitter Gauge Theory of Gravity
• Thermodynamics of Schwarzschild-Beltrami-de Sitter Black Hole
• Scale-invariant cosmology in de Sitter gauge theory
• De Sitter spacetimes with torsion in the model of dS gauge theory of gravity
• de Sitter Gauge Theory of Gravity: An Alternative Torsion Cosmology
• Schwarzschild-de Sitter Metric and Inertial Beltrami Coordinates
• Superluminal Neutrinos from Special Relativity with de Sitter Space-time Symmetry
• A Kaluza--Klein-like model of the gauge theory of gravity and its cosmological meaning
• Possible Supersymmetric Kinematics
• Geometries for Possible Kinematics
• On Torsion-free Vacuum Solutions of the Model of de Sitter Gauge Theory of Gravity (II)
• Implication of Spatial and Temporal Variations of the Fine-Structure Constant
• On determination of the geometric cosmological constant from the OPERA experiment of superluminal neutrinos
• Atlas of Coordinate Charts on de Sitter Spacetime
• Cosmological meaning of the gravitational gauge group
• Ether and Relativity
• On Torsion-free Vacuum Solutions of the Model of de Sitter Gauge Theory of Gravity
• Loop Variables and Gauge Invariant Exact Renormalization Group Equations for (Open) String Theory
• Loop Variables and Gauge Invariant Exact Renormalization Group Equations for Closed String Theory
• Quantized space-time and its influences on some physical problems
• Geometries with the second Poincaré symmetry
• The equivalence between Finsler and non-commutative geometries by massive gravity black hole
• Variation of the Fine-Structure Constant from the de Sitter Invariant Special Relativity
• From the Complete Yang Model to Snyder's Model, de Sitter Special Relativity and Their Duality
• A new single-dynamical-scalar-field model of dark energy
• An Inflationary Scenario Taking into Account of Possible Dark Energy Effects in the Early Universe
• Energy, momentum and angular momentum conservations in de Sitter gravity
• Cosmological Dynamics of de Sitter Gravity
• Energy, momentum and angular momentum conservations in de Sitter special relativity
• Two-Parameter Dynamics and Geometry
• Noether Charge, Thermodynamics and Phase Transition of a Black Hole in the Schwarzschild-Anti-de Sitter-Beltrami spacetime
• Killing Vectors in Spacetime of the De Sitter Invariant Special Relativity
• Smooth Solutions and Discrete Imaginary Mass of the Klein-Gordon Equation in the de Sitter Background