Microwave background anisotropies due to non - linear structures in open and Λ universes

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 (Ω0=1, ΩΛ=0), (Ω0=0.3, ΩΛ=0.7), (Ω0=0.3, ΩΛ=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 ΩΛ 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.