$C^\infty$ perturbations of FRW models with a cosmological constant
  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. 
Zolt\'an Perj\'es, M\'aty\'as Vas\'uth, Viktor Czinner and Daniel   Eriksson