Cosmological models

A common misconception is that irregular matter distributions, such as fractals, are necessarily incompatible with the Cosmological Principle. In fact, fractal structures can be statistically homogeneous and isotropic in the sense that their statistical properties remain invariant under translations and rotations, satisfying a generalized or weaker form of the Cosmological Principle.

Part of my research has focused on exploring the cosmological implications of such distributions. In collaboration with Philip W. Anderson, we investigated a model in which matter is distributed according to a fractal pattern extending over very large scales. We showed that, above a sufficiently large scale, such a distribution can still be treated as a perturbation of a standard Friedmann–Robertson–Walker (FRW) cosmology.

We also developed an alternative approach based on an exact Lemaître–Tolman–Bondi solution universe, assuming that a smooth spacetime metric can describe, in an average sense, an underlying fractal distribution of matter. In addition, we studied models in which fractal structures are treated as fluctuations superimposed on a homogeneous cosmological background.

These investigations were motivated by a broader question: how much large-scale inhomogeneity can the Universe contain while remaining consistent with cosmological observations and the fundamental principles of modern cosmology? More generally, they explore the relationship between the observed complexity of cosmic structures and the theoretical assumptions used to describe the Universe on its largest scales.