The Zeldovich & Adhesion approximations and applications to the local universe

The Zeldovich approximation (ZA) predicts the formation of a web of singularities. While these singularities may only exist in the most formal interpretation of the ZA, they provide a powerful tool for the analysis of initial conditions. We present a novel method to find the skeleton of the resulting cosmic web based on singularities in the primordial deformation tensor and its higher order derivatives. We show that the A3-lines predict the formation of filaments in a two-dimensional model. We continue with applications of the adhesion model to visualise structures in the local (z < 0.03) universe. 1. The Zeldovich approximation The Zeldovich Approximation (ZA) (Zeldovich 1970, Shandarin & Zeldovich 1989) describes structure formation in the form of a deceptively simple equation x(q, t) = q −D+(t)∇Φ0(q). (1.1) Rather than describing just ballistic motion, this equation hides a formalism of Lagrangian collision-free fluid mechanics. In the context of emerging interest in phase-space folding descriptions of structure formation (Shandarin et al. 2012, Falck et al. 2012, Abel et al. 2012), it becomes all the more relevant to understand this expression at a much deeper level. We can see why there is more to the ZA than inertial motion, if we compute particle densities from the above expression. Density increases or decreases locally as a fluid element contracts or expands. Taking a fluid element from Lagrangian location q, we can quantify its deformation in terms of the deformation tensor dij = −∂i∂jΦ0. This tensor is best studied locally in the eigenvector frame of reference {eλ}, where dij becomes diagonal. The density is then