##### Abstract

Galaxy surveys contain a wealth of information on the distribution of galaxies and dark matter in the Universe. Modern surveys yield large numbers of redshifts giving an unprecedented insight into the clustering of galaxies. The peculiar velocities of galaxies - motions caused by the local gravitational potential - allow the dark matter distribution to be inferred. This thesis deals with the statistical analysis of galaxy redshift and peculiar velocity surveys, concentrating on their exploitation for cosmological parameter estimation. The work is divided into two themes. Firstly predictions are made of the information content of galaxy surveys and the problem of optimising surveys’ designs to maximize this information is discussed. The second part is the development of a maximum likelihood method of constraining key parameters which deals most accurately with the spherical nature of modern wide-field surveys. Throughout the thesis, the 6 degree Field Galaxy Survey (6dFGS) is used to demonstrate the methods. Through application of the information theory to the 6dFGS, key predictions are made as to the strengths of the survey. The likelihood method is also developed with the intention that it be used in a future analysis of the 6dFGS.

In the information analysis section, the Fisher information matrix is introduced. It is used to obtain new analytical expressions for the cosmic variance of key cosmological parameters constrained from the galaxy power spectrum of any survey given its volume. A technique for survey optimisation is introduced, which defines a set of parameters to describe the geometry and selection criteria of a galaxy survey. Using reasonable assumptions about the dependency of a survey’s Limescale on these parameters, it is shown that the survey design may be optimized in the sense of maximizing its information content with respect to a cosmological parameter. The optimal design is calculated for the 6dFGS and predictions are made from the Fisher matrix, of the attainable uncertainties on future cosmological parameter predictions from the survey. Similar analysis is performed for the peculiar velocity survey.

To fully exploit the information content of redshifts and velocities it is necessary to perform a joint analysis of the two. This is particularly suitable for the 6dFGS since it incorporates a redshift and velocity survey which use similar selection critetia. The Fisher matrix for the two data sets of redshifts and velocities is derived. It is then used to predict the information content of the combined surveys, as well as the correlations between the parameters. It is found that the great advantage of combining redshifts and peculiar velocities is that the combination breaks the degeneracy between the redshift distortion parameter and the mass-galaxy correlation coefficient - allowing the simultaneous constraint of both.

The second part of the work develops a method of constraining these two parameters. Redshift space distortions are best dealt with by expanding the galaxy distribution of a survey in spherical Bessel functions and spherical harmonics. This separation of angular and radial distributions is also convenient analytically as a way of separating out the window function from the radial selection function. Models are constructed of the combined covariance matrix of the redshift—velocity data set. The models accurately describe the effects of redshift space distortions and stochastic galaxy biassing. to linear order. Software developed to perform this analysis is then tested on a suite of simulations of the 6dFGS.

Finally attention is paid to the problem of optimal data compression. In a real survey with a complicated survey mask, the final covariance matrix can be unfeasibly large to invert at different points in parameter space. The best way of performing this compression is shown to be Generalised Optimal Mode Analysis (GOMA) which optimally compresses the data set in a way that retains the most information on a specific parameter. The results of the maximum likelihood method applied to a compressed data set from the 6dFGS simulations are shown. The results are a good reflection of what will be possible when the survey reaches completion in mid-2005.