Last Monday, at another of our popular seminars, Niko Meures (ICG, Portsmouth) gave us an intriguing talk on the topic of non-linear inhomogeneities in LCDM cosmology. His work involves looking at exact solutions to the Einstein Field Equations which allow for non-linear structures. They developed models for an arbitrary matter distribution along a particular line of sight and also performed ray-tracing to see how light would be affected.
Niko showed us 3-d graphs indicating a pseudo-sinusoidal variation of overdense and underdense regions as you look farther along the line of sight (here δ is the fractional deviation from the average density). If the overdensities and underdensities average out, the angular distance (as a function of z) in this model is essentially identical to that in the ΛCDM model if the wavelength of the variations is Mpc scale. However, if the inhomogeneities do not average out, they do create observable effects on distances that could potentially be relevant to supernovae observations (see the Riess and Perlmutter papers).