Astronomy and Astrophysics – Astrophysics
Scientific paper
May 1968
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1968ap%26ss...1..309f&link_type=abstract
Astrophysics and Space Science, Volume 1, Issue 3, pp.309-335
Astronomy and Astrophysics
Astrophysics
53
Scientific paper
Differential equations are derived, following the methods of Lifshitz (1946) and Lifshitz and Khalatnikov (1963), for density perturbations in isotropic, spatially homogeneous cosmological models of arbitrary space curvature. The unperturbed models contain both matter and radiation. An explicit third-order equation is obtained for the time development of the perturbations, and it is shown that one of the solutions is not covariantly defined. The two remaining solutions are compared with existing solutions for the limiting cases of radiation-filled and dust-filled models. The results of Bonnor's (1957) Newtonian analysis are shown to be a valid limiting case of our equation when the pressurep is finite, but small compared with the densityp timesc 2. A detailed analysis is given of a model containing coupled radiation (p=pc 2/3) and dust (p=0). It is shown that density perturbations with long wavelengths are unstable (with slow growth rate) for all time. The instability exists because for a long-wavelength disturbance, the time scale governing the propagation of pressure effects (which stabilize perturbations) is longer than the time scale for which pressure falls to the point of ineffectiveness. The present value of the critical wavelength is ˜60 Mpc in models based on flat space sections in which the present background radiation temperature is 3 °K.
Field George B.
Shepley L. C.
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