Proceedings of the

We now consider photon energy and concentrate on the CMB anisotropy produced when the photon passes through the cluster described in section 3. One must remember however that our model assumes a pressure-less fluid and so the cluster, in pure-infall, might evolves too rapidly. Therefore the temperature perturbations given in this section should be considered as upper limits.

Figure 5 shows the CMB anisotropy due to the gravitational perturbation of the cluster described in table 1. The maximum temperature distortion occurs at the centre of the cluster and has the value and for and respectively. One notices that the distortion extends to rather large projected angles (e.g. for an observed angle of in the case). We may also point out the fact that the anisotropy becomes slightly positive at large angles.

**Figure 5:** Temperature perturbation imprinted
on the CMB as a function of the observed angle from the centre of the cluster.

We can compare the central decrements calculated above with those of previous authors. For Panek (1992) type I and type II clusters, the calculated central decrements are and respectively, whereas Quilis et al. (1995) quote the decrement . For two cluster models with similar physical properties Chodorowski (1991) finds . Finally Nottale (1984) used the SC model to predict a considerably larger central decrement of . However, this last value corresponds to a very dense, unrealistic cluster. We can notice that, for , our predicted value is in rough agreement with Panek (1992) type II, Chodorowski (1991) and Quilis et al. (1995). However our result for is about five times larger since previous works predict the same value whatever is . We then suggest that, in such a Universe, the effect on CMB photons may be more significant that previously stated.

Mon Jul 7 10:52:41 BST 1997