Non-Linear Growth of One-Dimensional Cosmological Density Fluctuation and Catastrophe Theory

Details Non-Linear Growth of One-Dimensional Cosmological Density Fluctuation and Catastrophe Theory Non-Linear Growth of One-Dimensional Cosmological Density Fluctuation and Catastrophe Theory

Mar 1989

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989pthph..81..633g&link_type=abstract

Progress of Theoretical Physics, Vol. 81, No. 3, pp. 633-647

Physics

14

Scientific paper

We have examined the non-linear growth of density fluctuations in a one-dimensional self-gravitating system in the expanding universe. We found that the Fourier spectrum of the density fluctuation obeyed a power law for small-scales when the singularities of the density appeared. The power index of the Fourier spectrum is almost independent of initial conditions and is determined by the type of the singularity of the density. There appear A2 and A3 types in a one-dimensional system. The type of singularity in density is categorized in accord with the classification in the catastrophe theory. According to this classification, there is only one type (A2) in one-dimensional system. In fact, the A3 type appears only in an instant, which corresponds to structural instability in the catastrophe theory.

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