How did our Universe evolve from a nearly uniform initial state into today’s cosmos with structures on a wide range of scales? And what does that structure tell us about our Universe and its constituents? Large-scale structure formation investigates the emergence of the Cosmic Web – the skeleton of matter in the present universe – from small density fluctuations observed in the Cosmic Microwave Background (CMB) – the relic radiation left over from the early universe.

Tiny deviations from a uniform density distribution of order ten parts in a million acted as seeds for structures to grow through gravitational attraction. Dark matter formed the first structures, since it experiences virtually no forces that counteract gravity. These growing dark matter lumps acted as catalysts for the clustering of ordinary matter, which eventually became today’s galaxies. Hence, observations of the large-scale structure enable us to learn about the initial conditions and processes that affect the growth of structure – and thereby to pin down cosmological parameters. To gain these insights, we need a thorough understanding of the statistics and dynamics of clustering. I will introduce the statistics of densities averaged in spheres as an interesting theoretical tool to study large-scale structure in the nonlinear regime of gravitational clustering beyond what is commonly achievable via other statistics such as correlation functions. I will present fully analytical predictions for counts-in-cells statistics that are in excellent agreement with numerical simulations and discuss their promise for future applications to galaxy surveys.