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 , which extends our previous application ( Lasenby et al .
1999 , Dabrowski et al .
1999 ) .
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 , z = 2 and z = 3 .
Photon geodesics and redshifts are also calculated so that the Cosmic Microwave Background ( CMB ) 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 .
Gravitational lensing effects are also considered and we apply our model to the reported microwave decrement observed towards the quasar pair PC 1643+4631 A & B .