In this poster we are concerned with the formation of spherical galaxy clusters (i.e. pure infall) in an expanding background universe. As in the Tolman--Bondi model applied by Panek (1992), the evolution of both the collapsing cluster and the expanding Universe are governed by the same pressure-less fluid equations. Initially, the density of our fluid is uniform. Only the velocity field is perturbed in order to form a realistic cluster. In a given cosmology, this perturbation is controlled by two parameters ( and ) as illustrated in figure 1. is related to the size of the perturbation and to its rate of growth. Those parameters are free and we choose them so that the resulting observed cluster is realistic (see section 3).
Figure 1: Fluid initial conditions for our model. Two parameters control the perturbation: and .
We find that our model has many advantages and treats the problem much more rigorously than older attempts, particularly in the case of works based on the ``Swiss Cheese'' (SC) models. Indeed, as shown in figure 2, the SC models deals with discontinuous density and velocity distributions since an unrealistic vacuum region is needed to separate the perturbation from the Universe. Another improvement made with regard to the SC models is that our perturbation is defined by only two free parameters rather than three in the SC case.
Figure 2: Fluid initial conditions for Swiss-Cheese models. Three parameters control the perturbation: , and .
More recent studies of the problem use the Tolman--Bondi solution (Panek (1992), Sáez et al. (1993)), which gives a similar approach to our own. In particular, both the forming cluster and the external Universe are treated as a whole and the fluid distributions are continuous. We believe our model is a refinement of the work based on the Tolman Bondi solution. Our mathematical formulation is clearer and does not need any approximation. The underling gauge theory of gravity (Lasenby, Doran & Gull (1997)) that we use deals straightforwardly with observable quantities such as the photon energy (Lasenby et al. (1997)). Therefore, we do not need to remove a posteriori dipole nor quadrupole-like anisotropy form the obtained CMB fluctuation (e.g. Panek (1992)).