Characterizing the nonlinear growth of large-scale structure in the Universe

The local Universe displays a rich hierarchical pattern of galaxy clusters and superclusters1,2. The early Universe, however, was almost smooth, with only slight ‘ripples’, as seen in the cosmic microwave background radiation3. Models of the evolution of cosmic structure link these observations through the effect of gravity, because the small initially overdense fluctuations are predicted to attract additional mass as the Universe expands4. During the early stages of this expansion, the ripples evolve independently, like linear waves on the surface of deep water. As the structures grow in mass, they interact with each other in nonlinear ways, more like waves breaking in shallow water. We have recently shown5 how cosmic structure can be characterized by phase correlations associated with these nonlinear interactions, but it was not clear how to use that information to obtain quantitative insights into the growth of structures. Here we report a method of revealing phase information, and show quantitatively how this relates to the formation of filaments, sheets and clusters of galaxies by nonlinear collapse. We develop a statistical method based on information entropy to separate linear from nonlinear effects, and thereby are able to disentangle those aspects of galaxy clustering that arise from initial conditions (the ripples) from the subsequent dynamical evolution.