Benjamin Hertzsch, Job Feldbrugge, Maé Rodriguez, Rien van de Weygaert
Abstract The caustic skeleton model is a mathematically rigorous framework for studying the formation history of the emerging cosmic web from the caustics in the underlying dark matter flow. In a series of two papers, we use constrained N -body simulations to investigate the different cosmic web environments. For the current study, we focus on the cosmic walls. We derive the conditions of the centres of proto-walls and analyse their evolution with N -body simulations. Next, we investigate the statistical properties of Zel'dovich pancakes by studying the number density of the cosmic wall centres in scale space and, for the first time, we calculate the Lagrangian-space volume of cosmic walls. Finally, we infer the mean density and velocity fields and the distribution of haloes around cosmic walls with a suite of physically realistic dark-matter-only simulations. We compare the cosmic walls obtained with the caustic skeleton framework with previously proposed saddle point conditions on the primordial potential and density perturbation.