Emergence of filamentary structure in cosmological gravitational clustering

The morphological nature of structures that form under gravitational instability has been of central interest to cosmology for over two decades. A remarkable feature of large-scale structures in the universe is that they occupy a relatively small fraction of the volume and yet show coherence on scales comparable to the survey size. With the aid of a useful synthesis of percolation analysis and shape statistics we explore the evolution of morphology of isolated density clumps in real space, and that of the cluster distribution as a whole, in scale-invariant cosmological models of gravitational instability. Our results, based on an exhaustive statistical analysis, indicate that at finite density thresholds one-dimensional filaments are more abundant than two-dimensional sheets (pancakes) at most epochs and for all spectra, although the first singularities could be pancake-like. Both filamentarity and pancakeness of structures grow with time (in scale-free models this is equivalent to an increase in resolution), leading to the development of a long coherence length scale in simulations.