Oscillations toward the singularity of LRS Bianchi type IX cosmological models with Vlasov matter

Abstract

We analyze the dynamics of a class of cosmological solutions of the Einstein-Vlasov equations. These equations describe an ensemble of collisionless particles (which represent galaxies or clusters of galaxies) that interact gravitatively through Einstein's equations of general relativity. The cosmological models we consider are spatially homogeneous, of Bianchi type IX, and locally rotationally symmetric (LRS). We prove that generic solutions exhibit an oscillatory approach toward the singularities (the "big bang" in the past and the "big crunch" in the future); this is in contrast to the behavior of Einstein-vacuum or Einstein-Euler solutions. To establish this result we make use of dynamical systems theory; we introduce dimensionless dynamical variables that are defined on a compact state space; in this formulation the oscillatory behavior of generic solutions is represented by an approach to heteroclinic cycles.

arXiv comment18 pages, 5 figures

References in corpus (4)

• Sharp bounds on $2m/r$ of general spherically symmetric static objects
• Cosmic Censorship for Some Spatially Homogeneous Cosmological Models
• Bianchi Cosmologies with Anisotropic Matter: Locally Rotationally Symmetric Models
• On closed cosmological models that satisfy the strong energy condition but do not recollapse

Cited by in corpus (6)

• Bianchi Cosmologies with Anisotropic Matter: Locally Rotationally Symmetric Models
• Proof of the cosmic no-hair conjecture in the T^3-Gowdy symmetric Einstein-Vlasov setting
• Isotropization of non-diagonal Bianchi I spacetimes with collisionless matter at late times assuming small data
• Future non-linear stability for reflection symmetric solutions of the Einstein-Vlasov system of Bianchi types II and VI${}_0$
• Dynamics of locally rotationally symmetric Bianchi type VIII cosmologies with anisotropic matter
• Late-time behaviour of the Einstein-Vlasov system with Bianchi I symmetry