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Prog. Theor. Phys. Vol. 73 No. 3 (1985) pp. 657-673

[ Full Text PDF : FREE ACCESS (768K) ]

Dimension of Singularity and Correlation of Density in Expanding Universe

Takashi Nakamura

Department of Physics, Kyoto University, Kyoto 606

(Received August 25, 1984)

Abstract:

Growth of density fluctuations in an expanding universe up to the formation of divergence of density is investigated both analytically and numerically. It is found that when the singularity of density appears the spectrum |δk| (the Fourier transform of density) obeys the power law (kn) where k is a wave number. The value of n depends on the dimension of singularities. n becomes -1/3, -0.75 and -9/7 for disk-like (2D), cylinder-like (1D) and point-like (0D) singularities, respectively. Numerical simulations using a cloud in cell method and a fast Fourier transform have been performed for various initial conditions. Both numerical results and analytic ones give the same conclusions. If the large scale structure of the universe is dominated by randomly distributed cylinder-like singularities and disk-like ones, which may be consistent with obserbations, the observed power index of the correlation functions of galaxies and clusters of galaxies is naturally obtained.


URL : http://ptp.ipap.jp/link?PTP/73/657/
DOI : 10.1143/PTP.73.657

[ Full Text PDF : FREE ACCESS (768K) ] Citation:

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  4. Progress of Theoretical Physics Vol. 81 No. 3 (1989) pp. 648-661 :
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  5. Progress of Theoretical Physics Vol. 90 No. 3 (1993) pp. 569-575 :
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  6. Progress of Theoretical Physics Vol. 95 No. 6 (1996) pp. 1059-1077 :
    Wavelet Analysis of One-Dimensional Cosmological Density Fluctuations
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