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In this thesis, I study the relativistic effects of matter inhomogeneities on the accelerating expansion of the Universe. The acceleration is often taken to be caused by the presence of an exotic fluid called Dark Energy, or else a non-zero 'cosmological constant' term in the field equations of General Relativity. I consider whether this result could instead be an artefact caused by using an incorrect model to interpret observations. The standard 'concordance' cosmological model assumes the Cosmological Principle, which states that the matter distribution on large scales is homogeneous. One possibility is that correction terms appear in the field equations when small-scale inhomogeneities are smoothed over to produce this homogeneous model. These 'backreaction' effects could affect the dynamics of the spacetime, causing an apparent acceleration. I clarify the relationship between acceleration of the averaged spacetime and acceleration inferred from observable quantities, and show that they are closely related in statistically-homogeneous spacetimes. Another possibility is that the Universe could be inhomogeneous on large scales. If there was a large ‘void’, with us at the centre, the lensing of light by the void could reproduce the observations that imply cosmic acceleration. I show that a popular class of void models, based on spherically-symmetric Lemaitre-Tolman-Bondi spacetimes, are unable to simultaneously fit a selection of observational data, thus effectively ruling-out this possibility. These data include the Kinematic Sunyaev-Zel'dovich (KSZ) effect, which is a distortion/shift of the Cosmic Microwave Background (CMB) frequency spectrum caused by the Compton scattering of photons by hot gas in galaxy clusters. This, and other distortions of the CMB frequency spectrum, are sensitive to the degree of anisotropy in the CMB about a scattering cluster. I suggest tests involving these observables that exploit the strong link between isotropy and homogeneity to (a) distinguish between different causes of a deviation from spatial flatness on the horizon scale, and (b) potentially confirm the Cosmological Principle using observations. Finally, I describe a novel Bayesian CMB component separation method for extracting the Sunyaev-Zel'dovich signal of clusters from CMB sky maps.

This thesis describes the analysis of pointed thermal Sunyaev-Zel'dovich (SZ) effect data from observations using the Cosmic Background Imager 2 (CBI2). CBI2 is an upgrade to the original Cosmic Background Imager, with antennas that have twice the effective collecting area, and hence provide greater sensitivity on longer baselines. Observations of the thermal SZ effect constrain the line-of-sight integrated gas pressure within clusters of galaxies and, when combined with X-ray data, provide an excellent tool for deriving the physical properties of these large structures. The CBI2 SZ data combine relatively low-resolution with a large field-of-view, and can therefore be used to constrain the gas properties of medium-redshift clusters out to the virial radius. By jointly fitting a suitable analytical model to SZ data and X-ray surface brightness data, it is possible to obtain constraints on the temperature and total mass of the cluster. For the analysis work presented in this thesis I choose to parametrise the gas based upon the known behaviour of the entropy, and the total mass by the Navarro, Frenk and White (NFW) prescription. This model is tested against Hydrodynamic/N-body simulations and is found to reproduce the radial behaviour of key cluster properties. The CBI2 observations presented in this work focus on the REFLEX-DXL clusters, an X-ray luminous sub-sample of the REFLEX survey at z ~ 0.3, which have previously published X-ray surface brightness data. The Bullet Cluster, a significant merger system, is a member of this sample and is presented here as a case study for use of the entropy-based model. The derived total mass and gas mass fraction of this cluster are found to be consistent with results from previous X-ray observations. The derived properties from the REFLEX-DXL sample are used to construct a preliminary set of SZ scaling relations out to the virial radius, and are found to be consistent with the self-similar model for massive clusters.

A hierarquia de equações de Boltzmann que descreve a temperatura e polarização da radiação cósmica de fundo ´e tratada no espaço das posições. Mostramos neste formalismo que temperatura e polarização podem ser descritas como medias dos termos de fonte ponderados por probabilidades associadas a um problema de voos aleatórios. Decorre da estrutura geral da hierarquia que se pode fazer uma expansão da temperatura e polarização em termos do numero de espalhamentos ocorridos durante a recombinação. Incorporamos o efeito de lentes gravitacionais sobre a radiação cósmica de fundo tirando proveito da estrutura das equações no espaço das posições. Mostraremos que o efeito ´e incorporado através de correções aos coeficientes da decomposição angular dos campos de temperatura e polarização. Para descrever o efeito de lentes gravitacionais fazemos uma revisão sobre resultados formais da teoria e apresentamos uma derivação de equações centrais em espaços-tempo arbitrários. / The Boltzmann hierarchy describing the temperature and polarization of the cosmic microwave background is presented in a position space formalism. We show that temperature and polarization can be described in terms of averages over source terms weighted by probabilities densities that appear in problems of random flights. The temperature and polarization signals can be expanded in terms of the number of scatterings photons suffered during the recombination. The gravitational lensing effects are incorporated over the free-propagation phase of the CMB photons. This effect can be included in the position space formalism as a correction to the expansion coefficients of the temperature and polarization fields. The bases of the theory of gravitational lensing are also presented and a rederivation of the central equations of the theory in arbitrary spacetimes is here developed.

N.c. / N.c.