EDP Sciences
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Volume 431, Number 2, February IV 2005
Page(s) 415 - 421
Section Cosmology (including clusters of galaxies)
DOI http://dx.doi.org/10.1051/0004-6361:20041472

A&A 431, 415-421 (2005)
DOI: 10.1051/0004-6361:20041472

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

Z. Perjés1, M. Vasúth1, V. Czinner1 and D. Eriksson2

1  KFKI Research Institute for Particle and Nuclear Physics, Budapest 114, PO Box 49, 1525, Hungary
    e-mail: [vasuth;czinner]@rmki.kfki.hu
2  Department of Physics, Umeå University, 90187 Umeå, Sweden
    e-mail: daniel.eriksson@physics.umu.se

(Received 15 June 2004 / Accepted 8 October 2004)

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.

Key words: cosmology: cosmic microwave background -- cosmology: large scale structure of Universe

© ESO 2005