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Non-Linear Theory of Gravitational Instability in the Expanding Universe

May 1, 1967
16 pages
Published in:
  • Prog.Theor.Phys. 37 (1967) 5, 831-846
  • Published: May 1, 1967
DOI:
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Abstract: (Oxford University Press)
The gravitational instability in the expanding universe is studied in the second-order approximation. This work is an extension of Lifshitz's linearized theory on the basis of general relativity. Basic equations are formulated generally, but their analysis is confined to a special case where pressure effects are negligible and the spatial curvature of the unperturbed model universe is zero. The results show that the second-order density contrast tends to accentuate the increase of the first-order density contrast with time, unless the linear dimension of the perturbation is too great. Moreover it is shown that gravitational wave is induced by deformed density perturbations even if the first-order metric perturbation includes no part of gravitational wave. If time is reversed, our results will be applicable to the problem of the gravitational instability in the contracting universe or in the collapsing star.