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 {\it 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.