Monotonic functions in Bianchi models: Why they exist and how to find them

Details Monotonic functions in Bianchi models: Why they exist and how to find them Monotonic functions in Bianchi models: Why they exist and how to find them

2009-07-03

arxiv.org/abs/0907.0653v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

26 pages, replaced to match published version

Scientific paper

All rigorous and detailed dynamical results in Bianchi cosmology rest upon the existence of a hierarchical structure of conserved quantities and monotonic functions. In this paper we uncover the underlying general mechanism and derive this hierarchical structure from the scale-automorphism group for an illustrative example, vacuum and diagonal class A perfect fluid models. First, kinematically, the scale-automorphism group leads to a reduced dynamical system that consists of a hierarchy of scale-automorphism invariant sets. Second, we show that, dynamically, the scale-automorphism group results in scale-automorphism invariant monotone functions and conserved quantities that restrict the flow of the reduced dynamical system.

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