Theoretical modeling

Irregular distributions like fractals can be statistically stationary and isotropic distributions in space: their statistical properties are invariant under translation and rotation in space and they satisfy a relaxed version of the Cosmological Principle. We described (with Phil Anderson) a model  in which a fractal matter distribution, even extending to arbitrarily large scales, showing that it can actually be treated above a finite scale as a perturbation to a FRW cosmology. As an alternative approach, we have given an exact solution of a Lemaitre-Tolman-Bondi universe based on the assumption that such a smooth metric is able to describe, on average, a fractal distribution of matter. Finally we considered a model where the fractal structure is treated as a perturbation to a uniform background.