The evolution of a spatially homogeneous and isotropic universe filled with a collisionless gas
| Autor: | Francisco Astorga, Thomas Zannias, Olivier Sarbach |
|---|---|
| Rok vydání: | 2014 |
| Předmět: |
Physics
History Statistical Mechanics (cond-mat.stat-mech) Spacetime media_common.quotation_subject Isotropy FOS: Physical sciences General Relativity and Quantum Cosmology (gr-qc) Cosmological constant Curvature General Relativity and Quantum Cosmology Universe Computer Science Applications Education Classical mechanics Distribution function Singularity Homogeneity (physics) Condensed Matter - Statistical Mechanics media_common |
| Zdroj: | Journal of Physics: Conference Series. 545:012001 |
| ISSN: | 1742-6596 1742-6588 |
| Popis: | We review the evolution of a spatially homogeneous and isotropic universe described by a Friedmann-Robertson-Walker spacetime filled with a collisionless, neutral, simple, massive gas. The gas is described by a one-particle distribution function which satisfies the Liouville equation and is assumed to be homogeneous and isotropic. Making use of the isometries of the spacetime, we define precisely the homogeneity and isotropicity property of the distribution function, and based on this definition we give a concise derivation of the most general family of such distribution functions. For this family, we construct the particle current density and the stress-energy tensor and consider the coupled Einstein-Liouville system of equations. We find that as long as the distribution function is collisionless, homogenous and isotropic, the evolution of a Friedmann-Robertson-Walker universe exhibits a singular origin. Its future development depends upon the curvature of the spatial sections: spatially flat or hyperboloid universes expand forever and this expansion dilutes the energy density and pressure of the gas, while a universe with compact spherical sections reaches a maximal expansion, after which it reverses its motion and recollapses to a final crunch singularity where the energy density and isotropic pressure diverge. Finally, we analyze the evolution of the universe filled with the collisionless gas once a cosmological constant is included. Comment: Typos corrected, references added, 13 pages, 1 figure, prepared for the proceedings of the X Workshop on Gravitation and Mathematical Physics, Pachuca, Mexico, December 2013 |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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