Matter is distributed across the present-day Universe in a very non-uniform manner: galaxies are self-gravitating systems containing perhaps hundreds of billions of stars; galaxies themselves are clustered together gravitationally in a variety of structures, from small groups to massive clusters, and on the very largest scales the galaxy distribution is thought to be interconnected via vast filamentary structures of dark matter, colloquially known as the cosmic web. One of the main goals of observational cosmology is to measure the statistical properties of this large-scale structure and to understand how it has grown through cosmic time from the initially smooth conditions of the early Universe. Those statistical properties are governed both by the large-scale geometry and expansion history of the Universe and by the matter and energy content of the Universe: how much ordinary matter, dark matter and dark energy is there, and what is the nature of the dark matter?
Large-scale structure studies have two strands: observationally we want to try to measure the statistical properties of the actual distribution, as a function of cosmic epoch, and to try to infer the distributions of both ordinary baryonic matter and dark matter. Tools to do this include galaxy clustering studies, measurements of the velocities of galaxies as they fall towards overdense regions and measurements of the fluctuations in mass with position afforded by gravitational lensing studies. Experiments such as the upcoming Euclid mission aim to carry out new, accurate measurements of some of these observables. A key component of our work is to link these measurements of the relatively recent Universe to the much lower amplitude structures we can observe in the earlier Universe via the cosmic microwave background.
The second strand is to be able to make predictions from theoretical cosmological models of what large-scale structure we should expect to see. In our 13.8 billion year old Universe, structure on the scales of galaxies, galaxy groups and galaxy clusters has grown into the "non-linear" regime, where the fluctuations in matter density are large compared with the mean density of the Universe. Under these conditions, we are not able to predict accurately the statistical properties expected for the large-scale structure using only analytical mathematical theory, and so we have to supplement analytical theory with numerical simulations that incorporate all the physics that we currently understand about the processes of galaxy and structure formation. The figure above shows a visualisation of one of these recent numerical simulations.