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The subject of this dissertation lies in the region where modern particle physics and cosmology intersect. Broadly speaking, its context is provided by the shortcomings of the 'standard cosmology', and the more recent inflationary scenario. The particular aspects which are tackled - the origin of density fluctuations and the boundary conditions of the universe - are outlined below. A. <i>The Cosmic String Scenario:</i> Phase transitions in the early universe may have produced topological 'knots' or defects, such as monopoles cosmic strings and domain walls. Cosmic strings, in particular, have attracted much interest recently because of the alluring model of galaxy formation they have the potential to produce. The viability of this new scenario, however, rests on untested assumptions about string interaction properties - whether or not they intercommute. A detailed study of global U(1)-strings has demonstrated that under most circumstances they will intercommute, a result expected for other varieties of strings (Part A). Given this firmer foundation for the cosmic string scenario, some of their astrophysical implications are explored. In particular, the large scale peculiar velocities predicted in this model are examined. B. <i>The domain wall problem of the Axion:</i> The axion has attracted considerable interest as a cold dark matter candidate. In part B, we concentrate on what potentially is a cosmological flaw of the axion: The non-trivial vacuum topology of axion models gives rise to cosmic vortex strings and domain walls. The latter are catastrophic unless removed by some mechanism soon after formation. In the dissertation we demonstrate the efficacy of their removal through string/domain wall intercommuting and annihilation. Causality constraints purporting to restrict the rate of this mechanism are found to be circumvented. C. <i>Quantum Cosmology and Recollapse:</i> Regardless of whether all the physical laws of system are known, its boundary conditions must still be given. In a quantum cosmological context, Hartle and Hawking have proposed that these be specified by a path-integral over compact four geometries. In Part C detailed studies of the implications of this proposal are made for two restricted models, the Freidmann-Robertson-Walker universe with a massive scalar field and the anisotropic Kantowski-Sachs cosmology. We evaluate the respective wavefunctions and the trajectories to which they correspond in the classical limit. Attention is focussed on the fact that most classical trajectories will recollapse to a singularity - the difficulty that this presents for the H-H proposal is discussed. The Kantowski-Sachs universes generically evolve from isotropy during expansion to increasing anisotropy during recollapse, ending as a black hole interior. Some comment is made on the arrow of time thereby induced by the Hartle-Hawking proposal.

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This thesis describes the creation of a X-ray selected galaxy cluster catalogue — the Southern Serendipitous High-redshift Archival ROSAT Cluster (SHARC) catalogue — and the use of the high-redshift subsample in constraining models of structure formation. X-ray selection provides the only way of creating an unbiased catalogue of distant galaxy clusters free from the projection effects that plague optical selection. The ROSAT All Sky Survey has a relatively high flux limit (~ 10(^-12)erg cm(^-2)s(^-1)); and has been used to create large, local cluster samples. The public availability of data from the pointed phase of PSPC observations means that deep, small-area, X-ray selected cluster surveys can be created. At the flux limits reachable by the PSPC pointings (~10(^-14) erg cm(^-2)s(^-1)), the dominant source population consists of QSOs and AGNs, with clusters forming < 10% of the X-ray population: cluster samples are therefore prone to a high level of contamination. Since clusters are the only class of object which are extended at cosmologically significant distances, this contamination can be greatly reduced by selecting sources which are extended. A reduction method is described which uses a maximum-likelihood fitting procedure, based on the Cash statistic, to detect extended sources. The survey consists of 66 RQSAT PSPC fields, covering an area of 17.7 deg(^2). Optical imaging and spectroscopy has been used to provide spectroscopic confirmation of the presence of distant galaxy clusters. The Southern SHARC catalogue is 90% complete, and consists of 36 clusters with redshifts 0.05 < z < 0.7 and X-ray luminosities between 7 x 10(^42) ergs(^-1) and 4 x lO(^44) ergs(^-1) The high-redshift subsample contains 16 clusters with z ≥ 0.3 and luminosities greater than 2 x 10(^43) ergs(^-1). The 11 unidentified sources include systems which could be low-redshift groups, and ones which could be high-redshift clusters. The high-redshift sample has been used to examine the evolution of the cluster population. Both the redshift distribution of the z ≥ 0.2 clusters and the XLF of the 0.3 ≤ z < 0.7 redshift shell are consistent with the properties of local cluster samples. The Southern SHARC catalogue is therefore consistent with little, or no, evolution of the z l0(^44) erg s(^-1) cluster population at z = 0.44 - the median redshift of the z ≥ 0.3 sample. This is in direct contrast with the negative evolution seen in the RIXOS cluster sample. It is presently not clear what the difference is due to, although preliminary results from other ROSAT-selected cluster surveys are also consistent with no evolution. Comparison of the high-redshift XLF of this survey, with that of the EMSS, shows that any evolution of the cluster population can only occur at luminosities > 3 x 10(^44) ergs(^-1) The z ≥ 0.2 redshift distributions of both the Southern. SHARC catalogue, and the EMSS, have been fitted by models for the evolution of the XLF. The best fit model has a spectral index of n = -1.8(^+0.8)(_0.3), and moderate heating of the gas, ϵ = -1.7(^+2.5)(_-2.2) Recent constraints on the evolution of the cluster LT relation restrict the model to the range -1.7 < n < -1.0 and -1.2 < ϵ < 0.7. Although the models used assume an Einstein-de Sitter universe, the lack of evolution is also similar to that expected in a low-density universe.

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