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Our universe is inherently inhomogeneous yet it is common in the study of cosmology to model our universe after the homogeneous and isotropic Friedmann-Lemaıtre-Roberson-Walker (FLRW) model. In this thesis spacetime matchings are applied to investigate more general inhomogeneous cosmologies. The Cheese Slice universe, constructed from matching together FLRW and Kasner regions satisfying the Darmois matching conditions, is used as a prime example of an inhomogeneous cosmology. Some observational consequences of this model are presented. The lookback time verses redshift relation is calculated using a numerical algorithm and it is shown that the relative thickness of the Kasner regions have the greatest impact on anisotropies an observer would see. The number of layers and distribution of layers play a smaller role in this regard. The relative thickness of the Kasner slice should be on the order of one ten thousandth the thickness of the FLRW regions to have the anisotropies fall within the observed CMB limit. The approach to the singularity of a spacetime matching is examined. A criterion is presented for a matched spacetime to be considered Asymptotically Velocity Term Dominated (AVTD). Both sides of the matching must be AVTD and each leaf of the respective foliations mush match as well. It is demonstrated that the open and flat Cheese Slice universe are both AVTD and the singularity is also of AVTD type. The Cheese Slice model is then examined as a braneworld construction. The possibility of a Cheese Slice brane satisfying all the energy conditions is shown. However, the embedding of such a brane into a symmetric bulk is non-trivial. The general embedding of a matched spacetime into a bulk is investigated using a Taylor series approximation of the bulk. It is found that the energy-momentum tensor of such a brane cannot have discrete jumps if the embedding does not have a corner. A 3+1+1 decomposition of the bulk spacetime is then carried out. With the spacetime being deconstructed along two preferred timelike hypersurfaces, this becomes a natural environment to discuss the matching of branes. We find that there are conditions on the matter content of the branes to be matched if an observer on the brane is to see the matching surface as a boundary surface with no additional stress energy. Matching more than two bulks is also examined and shown to allow for more general brane configurations.

Several projects are currently underway to obtain large galaxy redshift surveys over the course of the next decade. The aim of this thesis is to study how well the resultant three-dimensional maps of the galaxy distribution will be able to constrain the various parameters of the standard Big Bang cosmology. The work is driven by the need to deal with data of far better quality than has previously been available. Systematic biases in the treatment of existing datasets have been dwarfed by random errors due to the small size of the sample, but this will not be the case with the wealth of data that will shortly become available. We employ a set of high-resolution /V-body simulations spanning a range of cosmologies and galaxy biasing schemes. We use the power spectrum of the galaxy density field, measured using the fast Fourier transform process, to develop models and statistics for extracting cosmological information. In particular, we examine the distortion of the power spectrum by galaxy peculiar velocities when measurements are made in redshift space. Mock galaxy catalogues are drawn from these simulations, mimicking the geometries and selection functions of the large surveys we wish to model. Applying the same models to the mock catalogues is not a trivial task, as geometrical effects distort the power spectrum, and measurement errors are determined by the survey volume. We develop methods for assessing these effects and present an in-depth analysis of the likely confidence intervals we will obtain from the surveys on the parameters that determine the power spectrum. Real galaxy catalogues are prone to additional biases that must be assessed and removed. One of these is the effect of extinction by dust in the Milky Way, which imprints its own angular clustering signal on the measured power spectrum. We investigate the strength of this effect for the SDSS survey.

In this thesis, we present a new photometric catalogue of the local Coma galaxy cluster in the Johnson U- and V- bands. We cover an area of 3360arcmin(^2) of sky, to a depth of V = 20mag in a 13 arcsec diameter aperture, and produce magnitudes for ~ 1400 extended objects in metric apertures from 8.8 to 26arcsec diameters. The mean internal RMS scatter in the photometry is 0.014mag in V, and 0.026mag in U, for Via(_13) < 17mag. We use this photometric catalogue to place limits on the levels of scatter in the colour- magnitude relation (CMR) in the Coma cluster. We subdivide the galaxy population by morphology, luminosity and position on the sky, and analyse the CMR in each of them. The lowest levels of scatter are found in the elliptical galaxies, and the late type galaxies have the highest numbers of galaxies blue-wards of the CMR. We finds signs of decreased scatter and systematically bluer galaxy colours with increasing projected radius from the center of the cluster, and attribute it to a mean galactic age gradient. We find that the typical mass of galaxies within clusters can increase by a factor of two through dissipationless merging without destroying the CMR. We compare the spectral line indices of galaxies in the Coma cluster with their deviation from the mean colour-magnitude relation (CMR). We find that the CMR in Coma is driven primarily by a luminosity-metallicity correlation, however we cannot rule out a contribution from age effects. Colour deviations blue-ward of the mean relation are strongly correlated with the Hydrogen Baimer line series absorption, indicating the presence of a young stellar population in these blue galaxies. We use a wavelet code to suggest an association between X-ray cluster substructure and 'E+A' galaxy activity in high redshift clusters.

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In this thesis we present the NOAO-XMM Cluster Survey (NXS). NXS has provided optical follow-up of X-ray cluster candidates serendipitously detected by the XMM Cluster Survey (XCS). We report details on the execution, data reduction and analysis of 154 wide-field MOSAIC images containing 630 XCS cluster candidates. We present a redshift algorithm, based on the ‘red-sequence technique', designed to confirm cluster identifications and extract photometric cluster redshifts from NXS data. This algorithm exploits the homogeneity of elliptical cluster galaxies to provide simultaneous redshift and optical richness estimates. In addition, we apply this redshift algorithm to the Sloan Digital Sky Survey public data releases SDSS DR7 and SDSS Stripe 82. The resulting catalogue of ~500 optically confirmed XCS clusters with red-sequence redshifts is presented, spanning the redshift range 0.1<z<1.0. This sample will enable a future XCS measurement of the cosmological parameters Ωm and σ8, as well as a selfconsistent measure of the cluster X-ray luminosity to temperature scaling relation. Furthermore, for clusters with measured X-ray temperatures or luminosities, we measure the optical richness of red-sequence galaxies within the cluster virial radius (R200). Using these measurements, we investigate the optical halo-mass scaling relation. Understanding cluster optical scaling relations, in particular the optical-light to halo-mass relation, is key for surveys hoping to measure cosmological parameters using optically detected clusters alone. By combining the optical NXS and SDSS data sets with X-ray information from XCS, this thesis provides much needed optical to X-ray scaling relations for future optical cluster surveys.

Cosmological inflation is the leading candidate for the origin of structure in the Universe. However, a huge number of inflationary models currently exist. Higher-order statistics, particularly the bispectrum and trispectrum, of the primordial curvature perturbation can potentially be used to discriminate between competing models. This can provide an insight into the precise physical mechanism of inflation. Current constraints on inflationary models using the amplitude fNL of the bispectrum are quoted for specific templates. This results in much of the inflationary parameter space remaining unexplored. By utilizing the symmetries of the underlying quasi-de Sitter spacetime to construct a generic ‘effective field theory' Lagrangian with adjustable parameters, one can encompass many single-field models of inflation in a unifying framework. In the first part of this thesis we perform a partial-wave decomposition of the bispectrum produced at horizon-exit by each operator in the effective Lagrangian, which we use to find the principal components using a Fisher-matrix approach. This allows us to probe much more of the parameter space. Cosmic Microwave Background bispectrum data is used to estimate the amplitude of each component, which can then translated into constraints on particular classes of single-field models. We consider the implications for DBI and ghost inflation as examples. In the second part of this thesis we extend the transport formalism, first introduced by Mulryne, Seery and Wesley, to calculate the trispectrum generated during superhorizon evolution in inflationary models with multiple fields. We provide transport equations that track the evolution of the local trispectrum non-linearity parameters tNL and gNL throughout inflation. We compute these for several models as examples.

The established cosmological theory which describes the history of the Universe since shortly after the “Big Bang” until today is remarkably successful. Thanks to the increasing precision of available observational data, we are now able to considerably constrain the geometry and composition of the Universe - and to glimpse how these will evolve in the near future. However, this success comes at a price: one must assume the Universe “started” in a highly fine-tuned initial condition. Understanding what came before this is therefore one of the main goals of modern cosmology. This thesis attempts to further our understanding of the epoch before this initial condition in three different ways. Firstly, the concept of negative absolute temperatures (NAT) is introduced and its potential relevance for cosmology is investigated. In particular, it is shown that a Universe at a NAT should undergo a period of inflation - although it is unclear whether this would be consistent with current observations. Secondly, work is done on the topic of the evolution of networks of cosmic strings - topological defects which are expected to form in a broad class of phase transitions the Universe may have gone through. A model which takes into account the presence of small-scale structure in strings is used to address questions concerning the existence and stability of scaling regimes for these networks. Finally, it is investigated how future experiments might try to falsify a simple class of canonical single-field slow-roll inflation models by measuring the running and the running of the running of the spectral index of scalar perturbations.