Cambridge CB3 0HE, England

A new method arising from a gauge-theoretic approach to general relativity is applied to the formation of clusters in an expanding universe. The three cosmological models ($\Omega_0$=1, $\Omega_{\Lambda}$=0), ($\Omega_0$=0.3, $\Omega_{\Lambda}$=0.7), ($\Omega_0$=0.3, $\Omega_{\Lambda}$=0) are considered. A simple initial velocity and density perturbation of finite extent is imposed at the epoch $z=1000$ and we investigate the subsequent evolution of the density and velocity fields for clusters observed at redshifts $z=1$, $2$ \& $3$. Photon geodesics and redshifts are also calculated so that the Cosmic Microwave Background anisotropies due to collapsing clusters can be estimated. We find that the central CMB temperature decrement is slightly stronger and extends to larger angular scales in the non-zero $\Omega_{\Lambda}$ case. This effect is strongly enhanced in the open case.

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