| Summary: | The evolution of large-scale structure in the Universe is well understood in the linear regime, where the density is close to the mean density. Where the density contrast is large, the linearization of the equations of motion is no longer valid, and new techniques are needed. To this end, analytic arguments are combined with n-body simulations in Chapter 2, resulting in an analytic correction for the non-linear evolution of clustering. This method, and models of bias and redshift-space distortion, are then applied to a number of observational power spectra, in order to reconstruct the linear power spectrum of cosmic mass fluctuations. Constraints are put on the values of bias parameters, and a high degree of redshift-space distortion is required, Ω<SUP>0.6</SUP>/<I>b<SUB>IRAS</SUB></I> = 1.0±0.2. A Cold Dark Matter power spectrum can be fit to the data, provided Ω<I>h</I> = 0.255. Chapter 3 is concerned with the formation of galaxy clusters through gravitational collapse. The non-linear techniques developed in Chapter 2 are used to set up the initial conditions for numerical n-body simulations such that the final power spectra are nearly the same for two different cosmological models, Ω = 1 and Ω = 0.2. Galaxy clusters formed in these simulations are identified, and a mean density profile calculated. It is shown that although differences in power spectra have been largely eliminated, significant differences remain in the density profile under different cosmological conditions. In Chapter 4, the angular correlation function, <I>w(θ</I>), of faint blue galaxies is considered. Simple models of the evolution of clustering are unable to reproduce the observed <I>w(θ</I>) of the faint galaxies, over-predicting the amplitude of <I>w(θ</I>) by nearly an order of magnitude. The non-linear evolution model of Chapter 2 is applied to the present epoch correlation function, and it is found that the agreement with the observations is significantly improved, and that the model predictions are consistent with the observations, provided that the faint blue galaxies lie at the highest redshift allowed by the observations. Low Ω models are disfavoured, as they are unable to reproduce the observed shape of <I>w(θ</I>), approximately described by a power-law. A Cold Dark Matter model, with Ω = 1, is well able to reproduce this shape.
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