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We investigate the effects of density inhomogeneities on the cosmic microwave background (CMB) radiation as they grow throughout the history of the Universe. To do this, we have developed two numerical codes, one code that evolves the matter content of the Universe, and a second code that propagates CMB photons in the gravitational field of the evolving matter. We present preliminary simulations, along with code tests, describing the growth of non-linear density inhomogeneities with length-scales comparable to the dynamical time-scale and the horizon-scale of the Universe. We solve for the gravitational field using finite difference techniques to discretize the 3+1 form of the Einstein equations and for the matter content using particle-mesh methods.
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