The structural elements of the cosmic web

In 1970 Zel’dovich published a far-reaching paper presenting a simple equation describing the nonlinear growth of primordial density inhomogeneities. The equation was remarkably successful in explaining the large scale structure in the Universe that we observe: a Universe in which the structure appears to be delineated by filaments and clusters of galaxies surrounding huge void regions. In order to concretise this impression it is necessary to define these structural elements through formal techniques with which we can compare the Zel’dovich model and N-body simulations with the observational data. We present an overview of recent efforts to identify voids, filaments and clusters in both the observed galaxy distribution and in numerical simulations of structure formation. We focus, in particular, on methods that involve no fine-tuning of parameters and that handle scale dependence automatically. It is important that these techniques should result in finding structures that relate directly to the dynamical mechanism of structure formation. 1. A Short Historical Introduction In the early 1960’s there was an ongoing debate between the proponents of two different cosmological models. There was also a debate as to whether or not galaxy clusters were stable agglomerations of galaxies. The first of these was to be resolved in 1965 with the discovery of the cosmic background radiation (CBR) by Penzias & Wilson (1965) and its interpretation by Dicke et al. (1965) in terms of the relict radiation from a hot big bang origin of the Universe. The second debate would take several decades to resolve in terms of the existence of non-luminous “dark matter” in the Universe. Nonetheless, progress on describing the origin of cosmic structure started very soon after the CBR discovery with seminal papers by Peebles (1965), Sachs & Wolfe (1967), Silk (1967), Zel’dovich (1970), Sunyaev& Zeldovich (1970), Peebles & Yu (1970), among others. 1.1. The Zel’dovich Legacy Zel’dovich (1970) presented a simple model describing the non-linear evolution of structure in a co-expanding frame of reference described by a coordinate system {x} : x = r/a(t). a(t) is the usual cosmic expansion factor and r is the position of the particle in the expanding space. The Zel’dovich ansatz is that a particle starting from initial position x(t0) = q would move ballistically according to x = q−D(t)v(q), with v = ∂Φ