A fundamental prediction of modern cosmological models is that matter density fluctuations in the early Universe possess a remarkable property: fluctuations decrease with scale in the fastest possible way compatible with a statistically homogeneous distribution. Understanding the nature and consequences of this prediction has been one of the central themes of my research.
To investigate these systems, we developed a statistical-physics framework that led to the introduction of the concept of super-homogeneous distributions. Independently, the same class of systems was identified by Salvatore Torquato and Frank Stillinger, who coined the term hyper-uniformity. These ideas have since found important applications in several fields of physics, including the study of quasicrystals, disordered materials, and complex systems.
In cosmology, super-homogeneity provides a precise characterization of the initial matter distribution from which galaxies and large-scale structures formed. Our work explored both the theoretical foundations of this concept and its observational implications, identifying statistical signatures that can be tested in galaxy surveys and in measurements of the cosmic microwave background. In addition we have explored, in collaboration with Joel Lebowitz and Bernard Jancovici, the problem of generating a particle distribution with the super-homogeneous properties predicted by standard cosmological models.
More broadly, this research illustrates how concepts developed in statistical physics can provide new insights into fundamental questions about the origin, evolution, and large-scale organization of the Universe.
Francesco sylos labini 