Effect of a Collapsing Cluster on the CMB temperature and Power Spectrum

We present a new model for the formation of spherically symmetric clusters in an expanding Universe. Both the Universe and the collapsing cluster are governed by the same pressure less fluid equations for which a uniform initial density profile is assumed. A simple perturbation imposed on the initial velocity field gives rise to an over-density which closely models real clusters. The computation of photon paths allows us to evaluate the gravitational effects imprinted on a Cosmic Microwave Background (CMB) photon passing through such an evolving mass. We also consider the lensing properties of collapsing clusters and investigate the effect of a population of such clusters on the primordial microwave background power spectrum.