Open AccessPhase Space of Compact Bianchi Models with Fluid
Author(s) -
Hideo Kodama
Publication year - 2002
Publication title -
progress of theoretical physics
Language(s) - English
Resource type - Journals
eISSN - 1347-4081
pISSN - 0033-068X
DOI - 10.1143/ptp.107.305
Subject(s) - physics , degrees of freedom (physics and chemistry) , phase space , topology (electrical circuits) , type (biology) , space (punctuation) , dynamical systems theory , homogeneous , perfect fluid , dynamical system (definition) , symmetry (geometry) , universe , moduli space , phase (matter) , pure mathematics , mathematical physics , classical mechanics , geometry , mathematics , statistical physics , quantum mechanics , combinatorics , computer science , ecology , biology , operating system
The structure of phase space is determined for spatially compact and locallyhomogeneous universe models with fluid. Analysis covers models with allpossible space topologies except for those covered by S^3, H^3 or S^2xR whichhave no moduli freedom. We show that space topology significantly affects thenumber of dynamical degrees of freedom of the system. In particular, we give adetailed proof of the result that for the systems modeled on the Thurston typesH^2xR and SL_2, which have locally the Bianchi type III or VIII symmetry, thenumber of dynamical degrees of freedom increases without bound when the spacetopology becomes more and more complicated, which was first pointed out byKoike, Tanimoto and Hosoya in an incomplete form.Comment: 58 pages in LaTeX with the PTP style. No figur
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