Microwave background anisotropies and non-linear structures - I. Improved theoretical models

A new method is proposed for modelling spherically symmetric inhomogeneitie s in the Universe. The inhomogeneities have finite size and are compensated , so they do not exert any measurable gravitational force beyond their boun dary. The region exterior to the perturbation is represented by a Friedmann -Robertson-Walker (FRW) universe, which we use to study the anisotropy in t he cosmic microwave background (CMB) induced by the cluster. All calculatio ns are performed in a single, global coordinate system, with non-linear gra vitational effects fully incorporated. An advantage of the gauge choices em ployed here is that the resultant equations are essentially Newtonian in fo rm. Examination of the problem of specifying initial data shows that the ne w model presented here has many advantages over 'Swiss cheese' and other mo dels. Numerical implementation of the equations derived here is described i n a subsequent paper.