Observations of the Universe show that, on megaparsec scales galaxies are not distributed homogeneously but rather arranged in a filamentary network, the most luminous of them residing at the nodes of this "cosmic web". In current cosmological models, the large-scale structure of the Universe is the result of tiny fluctuations generated during an inflationary phase and subsequently amplified by gravity. As these fluctuations grew nonlinearly, the baryons fell into the potential wells created by some unknown "cold" (non-relativistic) dark matter component to form stars and galaxies. Because the physics describing the nonlinear stage of galaxy formation is highly complex, numerical simulations have become an absolute must to study the large-scale distribution of galaxies. These simulations can follow the nonlinear collapse of baryons and dark matter over a large dynamical range.
The large-scale structure of the Universe can strongly constrain viable cosmological scenarios. Weak lensing (distortions in the image of background galaxies induced by the matter distributed along the line-of-sight), galaxy clustering (number of galaxy pairs, triplets etc. in excess of random) and cluster counts (abundance of massive cluster of galaxies) are among the most powerful probes of the large-scale structure. When combined, they can shed light on the mystery of dark energy, the nature of dark matter and the origin of the Universe and its initial conditions.