his thesis concerns with the study of the large scale motions o f the universe. In particular the peculiar velocities of galaxies are used in a variety o f ways to estimate some of the most important cosmological parameters.

Many galaxies are observed to be moving with a velocity that is not quite consistent with the picture o f a homogeneous and isotropic universe. Such peculiar velocity must thus be caused by the small inhomogeneities that are still present today. By studying this velocity distortion, one should in principle be able to probe the underlying mass which light alone does not reveal.

n chapter 1, a brief introduction o f cosmology is presented. Here I outline some of the most fundamental principles o f cosmology and their evidence, namely the expansion o f the universe and its homogeneity and isotropy. Using the theory o f general relativity, these features lead us to the invention o f the Robertson-Walker metric. I then show how the dynamics o f the universe depend on its dominant constituents and density. The different morphology o f galaxies is also presented where the general features o f spirals and ellipticals are outlined. On the section o f structure formation, the standard Newtonian treatment to the density perturbations is discussed in the linear regime. Here we see how structures such as galaxies can be formed from the growth of some initial density fluctuations. At the end o f the chapter, the importance o f the peculiar velocity to the work o f this thesis is discussed.

Chapter 2 gives an account o f how the correlation o f bulk and shell velocities can be used together with their measurements to constrain (5 = fi°-6/b. The observational evidence of a relatively stationary shell in a large bulk flow environment prompted us
to investigate the likelihood of such an unlikely occurrence. Our analysis shows that the shell velocity measurements can be heavily contaminated with noise. In the absence o f noise, the correlation between these two velocities depends only on the parameter ¡3 and the power spectrum used. We carried out the analysis with different models o f power spectrum and for the theoretical predictions from these models to match up with observations, we conclude that the value of (3 should be in the order o f unity. The two principal models o f power spectrum that we tested are that o f Peacock & Dodds (1994) and the CDM-like model. The content o f this chapter is identical to the paper published by Loke & Heavens (1996

n chapter 3, we applied a statistical likelihood method on the redshift distortion to give a joint probabilistic value o f (3 and cr8. The existence o f peculiar velocity distorts the true spatial galaxy distribution and this hinders us from obtaining the real-space power spectrum. However, if we resolve the density perturbations in the formalism of a continuous spherical transform, it is possible to formulate statistically the likelihood distribution o f the density perturbations under the redshift distortion, given a value of /3 and an appropriate model of the power spectrum. By matching up the likelihood predictions o f the density perturbations in redshift space to that of a real galaxy catalogue, it is then possible to constrain the value o f (3 and the power spectrum, which in this case is assumed to depend on <78 only. The analysis in this chapter is based on the work of Heavens &; Taylor (1995) with the crucial difference that the analysis was carried out by setting the boundary at infinity and as such we do not have to worry about the boundary conditions.

In chapters 4 and 5, a theoretical model o f the velocity field is developed under the linear regime and the assumption of a irrotational flow (V x v = 0). The analysis predicts that the density potential derived from a galaxy catalogue is linearly related to the velocity potential via the parameter /3, if galaxies are linear tracers o f mass. In chapter 4, I compare the predicted velocity potential derived from the IRAS galaxy catalogue with that o f PO TEN T (where potential was constructed from the actual measurement of velocity). In theory the comparison of these two potentials should yield a value of (3. However, the analysis in chapter 4 is flawed by the fact that the redshift distortion was not properly taken into account. Nevertheless, the results do suggest that there might be a correlation between these two potentials. In chapter 5 the redshift distortion was properly treated by expanding the potential into its spherical harmonic components. Much o f the analysis in this chapter is based on the previous work o f Nusser & Davis (1994). Here I attempted constructing the dipole (/ < 1) velocity potential from the IRAS galaxy catalogue using different values of ¡3. This is then compared to the same dipole component of PO TEN T. My results suggest that the predicted dipole potential does not match that of PO TEN T for a reasonable value of (3. This contradicts with the results o f (3 ~ 0.6 found by Nusser & Davis (1994) where the dipole velocity was analysed. For I > 1 multipoles, the construction depends on the boundary conditions at infinity, which the current survey does not probe. Therefore comparison o f the two potentials here does not yield any useful result.

Finally in chapter 6, I give a short conclusion o f my work and an overview o f the current state o f cosmology, in particular the measurements that will be o f immense importance to my work in future. Some o f the most important unresolved issues (such as the values of Hubble constant, density o f the universe, mass/light bias, etc) in cosmology are also discussed.