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Prog. Theor. Phys. Vol. 81 No. 3 (1989) pp. 633-647

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

Naoteru Gouda and Takashi Nakamura^*

Department of Physics, Kyoto University, Kyoto 606
^*National Laboratory for High Energy Physics, Tsukuba 305

(Received July 21, 1988)

Abstract:

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.

URL : http://ptp.ipap.jp/link?PTP/81/633/
DOI : 10.1143/PTP.81.633

[ Full Text PDF : FREE ACCESS (715K) ] Citation: Plain Text BiBTeX EndNote(RIS) RSS

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References:

1. P. J. E. Peebles, The Large-Scale Structure of the Universe (Princeton University Press, 1980).
2. K. Miyoshi and T. Kihara, Publ. Astron Soc. Jpn. 27 (1975), 333.
   C. S. Frenk, S. D. M. White and M. Davis, Astrophys. J. 271 (1983), 417[CrossRef].
   M. Davis et al., Astrophys. J. 292 (1985), 371[CrossRef].
   G. Efstathiou et al., Astrophys. J. Suppl. 57 (1985), 241.
3. E. J. Groth and P. J. E. Peebles, Astrophys. J. 217 (1977), 385[CrossRef].
   M. Davis and P. J. E. Peebles, Astrophys. J. 267 (1983), 465[CrossRef].
4. F. R. Bouchet, J. C. Adam and R. Pellat, Astron. Astrophys. 144 (1985), 413.
5. M. Davis and P. J. E. Peebles, Astrophys. J. Suppl. 34 (1977), 425.
   W. C. Saslaw, Astrophys. 235 (1980), 299.
6. T. Nakamura, Prog. Theor. Phys. 73 (1985), 657[PTP].
7. N. Gouda and T. Nakamura, Prog. Theor. Phys. 79 (1988), 765[PTP].
8. A. G. Dorshkevich et al., Mon. Not. R. Astron. Soc. 192 (1980), 321.
9. R. A. Sunyaev and Ya. B. Zeldovich, Astron. Astrophys. 20 (1972), 189.
10. F. Hohl and M. R. Feix, Astrophys. J. 147 (1967), 1164[CrossRef].
11. N. Gouda and T. Nakamura, in the Proceedings of the 20th Yamada Conference “ Big Bang, Active Galactic Nuclei and Supernovae” (1988), ed. S. Hayakawa and K. Sato (Universal Academy Press, Inc., Tokyo, Japan).
12. V. I. Arnold, Functional Anal. Appl. 6 (1972), 254; Mathematical Methods of Classical Mechanics (Springer-Verlag, New York, Heidelberg, Berlin, 1980).
    V. I. Arnold, S. F. Shandarin and Ya. B. Zeldovich, Geophys. Astrophys. Fluid Dynamics 20 (1982), 111.
13. T. Poston and I. Stewart, Catastrophe Theory and Its Applications (Pitman Publishing Limited, 1978).

Citing Article(s) :

1. Progress of Theoretical Physics Vol. 81 No. 3 (1989) pp. 648-661 :

   Non-Linear Growth of Density Fluctuations in the Spherically Symmetric Expanding Universe and Catastrophe Theory

   Naoteru Gouda

2. Progress of Theoretical Physics Vol. 99 No. 1 (1998) pp. 55-68 :

   Morphology in Cosmological Gravitational Clustering and Catastrophe Theory

   Naoteru Gouda

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