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

The local Universe displays a rich hierarchical pattern of galaxy clusters and superclusters(1,2). The early Universe, however, was almost smooth, wit h only slight 'ripples', as seen in the cosmic microwave background radiati on(3). Models of the evolution of cosmic structure link these observations through the effect of gravity, because the small initially overdense fluctu ations are predicted to attract additional mass as the Universe expands(4). During the early stages of this expansion, the ripples evolve independentl y, like linear waves on the surface of deep water. As the structures grow i n mass, they interact with each other in nonlinear ways, more like waves br eaking in shallow water. We have recently shown(5) how cosmic structure can be characterized by phase correlations associated with these nonlinear int eractions, but it was not clear how to use that information to obtain quant itative insights into the growth of structures. Here we report a method of revealing phase information, and show quantitatively how this relates to th e formation of filaments, sheets and clusters of galaxies by nonlinear coll apse. We develop a statistical method based on information entropy to separ ate linear from nonlinear effects, and thereby are able to disentangle thos e aspects of galaxy clustering that arise from initial conditions (the ripp les) from the subsequent dynamical evolution.