Probing large-scale structure using percolation and genus curves

We study topological properties of large-scale structure in a set of scale-free N-body simulations using the genus and percolation curves as topological characteristics. Our results show that as gravitational clustering advances, the density field shows an increasingly pronounced departure from Gaussian reflected in the changing shape of the percolation curve as well as the changing amplitude and shape of the genus curve. Both genus and percolation curves differentiate between the connectedness of overdense and underdense regions if plotted against the density. When plotted against the filling factor, the percolation curve alone retains this property. The genus curve shows a pronounced decrease in amplitude caused by phase correlations in the nonlinear regime. Both genus and percolation curves provide complementary probes of large-scale structure topology, and can be used to discriminate between models of structure formation and the analysis of observational data, such as galaxy catalogs and microwave background radiation maps.