The evolution of a spatially homogeneous and isotropic universe filled with a collisionless gas

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...

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Bibliographic Details
Published in:Journal of physics. Conference series 2014-01, Vol.545 (1), p.12001-15
Main Authors: Astorga, Francisco, Sarbach, Olivier, Zannias, Thomas
Format: Article
Language:English
Subjects:
Cosmological constant
Current density
Distribution functions
Energy density
Evolution
Flux density
Homogeneity
Liouville equations
Mathematical analysis
Physics
Singularity (mathematics)
Spacetime
Tensors
Universe
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Summary: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.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/545/1/012001