Froth across the Universe Dynamics and Stochastic Geometry of the Cosmic Foam

The interior of the Universe is permeated by a tenuous space-filling frothy network. Welded into a distinctive foamy pattern, galaxies accumulate in walls, filaments and dense compact clusters surrounding large near-empty void regions. As borne out by a large sequence of computer experiments, such weblike patterns in the overall cosmic matter distribution do represent a universal but possibly transient phase in the gravitationally propelled emergence and evolution of cosmic structure. We discuss the properties of this striking and intriguing pattern, describing its observational appearance, seeking to elucidate its dynamical origin and nature and attempting to frame a geometrical framework for a systematic evaluation of its fossil content of information on the cosmic structure formation process. An extensive discussion on the gravitational formation and dynamical evolution of weblike patterns attempts to put particular emphasis on the formative role of the generic anisotropy of the cosmic gravitational force fields. These tidal fields play an essential role in shaping the pattern of the large scale cosmic matter distribution. A profound investigation of their role will be a key element in understanding the implications of the observed cosmic foam for the very process of cosmic structure formation. The apogee of this contribution is reached in the specific attention for the geometric and stochastic aspects of the cosmic fabric. Its distinct geometric character – linking various distinct anisotropic morphological elements into a global all-encompassing framework – and the stochastic nature of this assembly provides the cosmic web with some unique and at first unexpected properties. The implications for galaxy clustering and its potential as discriminating of the galaxy distribution are discussed on the basis of its relevant branch of mathematics, stochastic geometry. Central within this context are Voronoi tessellations, which have been found to represent a surprisingly versatile model for spatial cellular distributions, whose flexibility and efficient exploitation warrant a central role in systematic assesments of the cosmic foam.