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Prog. Theor. Phys. Vol. 45 No. 6 (1971) pp. 1747-1762

[ Full Text PDF : FREE ACCESS (885K) ]

Non-Linear Theory of Gravitational Instability in the Expanding Universe. II

Kenji Tomita

Research Institute for Theoretical Physics, Hiroshima University, Takehara, Hiroshima-ken

(Received December 18, 1970)

Abstract:

The general relativistic non-linear theory of gravitational instability is reformulated in order to get a hydrodynamical system of equations which are applicable at any early stage of cosmic expansion. Non-linearity is taken into account to the second-order smallness. On this basis, the second-order density perturbations associated with the first-order rotational and gravitational waves are derived, and the amplitudes of the density perturbations are shown to become comparable with the square of the amplitudes of the first-order waves. Moreover the second-order density perturbations corresponding to the first-order ones are derived and examined.


URL : http://ptp.ipap.jp/link?PTP/45/1747/
DOI : 10.1143/PTP.45.1747

[ Full Text PDF : FREE ACCESS (885K) ] Citation:

References:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 47 No. 2 (1972) pp. 416-443 :
    Non-Linear Theory of Gravitational Instability in the Expanding Universe. III
    Kenji Tomita
  2. Progress of Theoretical Physics Vol. 48 No. 5 (1972) pp. 1503-1516 :
    Primordial Irregularities in the Early Universe
    Kenji Tomita
  3. Progress of Theoretical Physics Vol. 49 No. 5 (1973) pp. 1770-1772 :
    The Sound Generated by Cosmic Turbulence and the Origin of Galaxies
    Takuya Matsuda, Hidenori Takeda and Humitaka Sato
  4. Progress of Theoretical Physics Vol. 50 No. 2 (1973) pp. 472-487 :
    On the Generatin of Sound from the Primordial Turbulence in an Expanding Universe
    Hidekazu Nariai
  5. Progress of Theoretical Physics Vol. 50 No. 4 (1973) pp. 1285-1301 :
    Element Formation in a Chaotic Early Universe
    Kenji Tomita
  6. Progress of Theoretical Physics Vol. 54 No. 3 (1975) pp. 719-729 :
    On the Acoustic Decay of Primordial Cosmic Turbulence
    Kenji Tanabe, Hidekazu Nariai, Takuya Matsuda and Hidenori Takeda
  7. Progress of Theoretical Physics Vol. 59 No. 4 (1978) pp. 1150-1169 :
    On Inhomogeneous Cosmological Models Containing Space-Like and Time-Like Singularities Alternately
    Kenji Tomita
  8. Progress of Theoretical Physics Vol. 117 No. 1 (2007) pp. 17-74 :
    Second-Order Gauge Invariant Cosmological Perturbation Theory
    Kouji Nakamura

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