Chaotic dynamics in the Friedmann equation

Yosuke Tanaka, Yuzi Mizuno and Tatsuhiko Kado

Chaos, Solitons & Fractals, 2005, vol. 24, issue 2, 407-422

Abstract: We have studied relativistic equations and chaotic behaviors of the gravitational field on the basis of general relativity and chaotic dynamics. The Friedmann equation [the space component] shows chaotic behaviors in case of the inflation (G˙/G>0) and open (ζ=−1) universe. There occurs non-chaotic behaviors in other cases (G˙/G≦0,ζ=0,ζ=+1). We have shown the following properties of the Friedmann chaos; (1) the sensitive dependence of solutions on parameters, (2) the self-similarity of solutions in the x–x˙ plane and the x–ρ plane. Numerical calculations were carried out with the use of the microsoft EXCEL. We have also discussed the self-similarity and the hierarchy structure of the universe on the basis of E infinity theory.

Date: 2005
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Citations: View citations in EconPapers (23)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:24:y:2005:i:2:p:407-422

DOI: 10.1016/j.chaos.2004.09.034

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