## Hierarchial and cellular structures in cosmology

##### Abstract

Though great advances have been made in the field of cosmology by using numerical n-body techniques to investigate large-scale structure formation, these have been hampered by limited dynamic range. Thus there still remains considerable motivation for finding simple methods that link either the final structure or its statistical properties (such as mass and correlation functions) to the initial conditions. This thesis investigates two such approaches — linear theory and the Voronoi foam. (i) Linear Theory: This is based on the principle of smoothing the non-linear density field in order to recover the underlying linear density field. Bound objects are then identified with regions where the density exceeds some critical value. Such a prescription allows the statistical properties of the bound objects to be described as a function of the power spectrum of the initial density field and the smoothing function. This thesis checks the accuracy of such models against the adhesion model, a fully non-linear description of gravitational clustering. In order to provide an accurate test of the linear theory predictions, the simulations are carried out in one dimension, where the adhesion model is exact and there is sufficient dynamic range to allow a thorough test of the linear theory predictions. It is found that despite some of the underlying assumptions of linear theory being incorrect in detail, the linear theory mass functions provide an excellent match to those calculated from the simulations. Linear theory correlation functions are also shown to be a good match to those from the simulations, but only in the case where dynamical evolution of the density field is unimportant (i.e. where large-scale power dominates over small-scale power). (ii) Voronoi foam: This is a simple model where space is divided into cells, each containing a nucleus, with galaxies populating the boundaries between cells, which are equidistant between neighbouring nuclei. The geometric structure of the cells is entirely determined by the
distribution of the nuclei. This forms a continuous network of walls, filaments and nodes, qualitatively similar to that observed. It is shown that, in comparison to a wide range of statistical measures of galaxy clustering, the Voronoi foam lacks sufficient large-scale power to account for the observed galaxy distribution, if the nuclei are distributed at random. However, if the nuclei are identified with the pealcs in a gravitational potential (which are intrinsically clustered), the Voronoi foam can provide an excellent description of the large-scale clustering of galaxies. It is also demonstrated that the Voronoi foam provides, within the context of a cellular model, a. natural explanation for the observed phenomenon of large-scale cluster alignment.