| The gravitational formation of large-scale structure in an expanding universe is studied within the framework of the standard hot big bang model. We work in the scenario whereby small fluctuations in the initial density field are amplified via gravitational instability generating frothy, sheet-like structures which span scales from a few million to a few hundred million light-years. Perturbation theory is utilized, based on the equations of a collisionless gravitating fluid. Using an efficient approximation which reproduces essential aspects of the complete model, we perform computer simulations of large-scale matter and galaxy distributions. Random realizations of the initial conditions are produced with varying initial statistical properties, and the final, evolved matter distribution is investigated. The power spectrum and bispectrum (the two-point and three-point correlation functions in Fourier space) are measured to statistically characterize the spatial fluctuations. Perturbation theory is tested, and the transition from the linear to nonlinear evolutionary regimes is investigated. It is found that a perturbative approach can be selectively used beyond its expected range of applicability. In some instances, highly structured, yet dilute, galaxy distributions can be usefully distinguished utilizing results from perturbation theory. |
