Poincaré-De Sitter Flow and Cosmological Meaning

Abstract

We introduce the Poincaré-de Sitter flow with real numbers $\{r,s\}$ to parameterize the relativistic quadruple ${\mathfrak{Q}}_{PoR}=[\mathcal{P},{\mathcal{P}}_2,{\mathcal{D}}_{+},{\mathcal{D}}_{-}{]}_{M/M_{\pm }/D_{\pm }}$ for the triple of Poincaré/\dS/\AdS\ group $\mathcal{P}/{\mathcal{D}}_{+}/{\mathcal{D}}_{-}$ invariant special relativity. The dual Poincaré group ${\mathcal{P}}_2$-invariant degenerated Einstein manifold $M_{\pm }$ of ${\Lambda }_{\pm }=\pm 3l^{-2}$ is for the space/time-like domain ${\dot{R}}_{\pm }$ of the compact lightcone ${\bar{C}}_O$ associated to the common space/time-like region $R_{\pm }$ of the lightcone $C_O$ at common origin on Minkowski/\dS/\AdS\ spacetime $M/D_{+}/D_{-}$. Based on the principle of relativity with two universal constants $(c,l)$, there are the law of inertia, coordinate time simultaneity and so on for the flow on a Poincaré-\dS\ symmetric Einstein manifold of ${\Lambda }_s=3s{l}^{-2}$. Further, there is Robertson-Walker-like cosmos of the flow for the propertime simultaneity. The \dS\ special relativity with double $[{\mathcal{D}}_{+},{\mathcal{P}}_2{]}_{D_{+}/M_{+}}$ can provide a consistent kinematics for the cosmic scale physics with an upper entropy bound $S_R=k_B\pi g^{-2},g^2:=({\ell }_P/R{)}^2\simeq 10^{-122}$, for $R\simeq (3/\Lambda {)}^{1/2}\sim 13.7Gly$.

25 pages

References in corpus (5)

• Snyder's Model -- de Sitter Special Relativity Duality and de Sitter Gravity
• On Principle of Inertia in Closed Universe
• Hamiltonian Formalism of the de-Sitter Invariant Special Relativity
• The Principle of Relativity, Kinematics and Algebraic Relations
• On Torsion-free Vacuum Solutions of the Model of de Sitter Gauge Theory of Gravity (II)