$C^{\infty }$ perturbations of FRW models with a cosmological constant

Abstract

Spatially homogeneous and isotropic cosmological models, with a perfect fluid matter source and non-vanishing cosmological constant, are studied. The equations governing linear perturbations of the space-time and the variation of energy density are given. The complete solution of the problem is obtained for $C^{\infty }$ perturbations, using a comoving time. The Sachs-Wolfe fluctuations of the temperature of the cosmic background radiation are obtained for the relatively growing density perturbations. It is found that the observable celestial microwave fluctuation pattern underwent a reversal approximately two billion years ago. What is observed today is a negative image of the last scattering surface with an attenuation of the fluctuations, due to the presence of the cosmological constant.

arXiv comment15 pages, 5 figures

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• Astrophysics in 2005
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• Revisiting Rotational Perturbations and the Microwave Background
• Covariant Linear Perturbations in a Concordance Model