Title:

Dark energy and the inhomogeneous universe

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 nonzero '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 smallscale 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 statisticallyhomogeneous 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 sphericallysymmetric LemaitreTolmanBondi spacetimes, are unable to simultaneously fit a selection of observational data, thus effectively rulingout this possibility. These data include the Kinematic SunyaevZel'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 SunyaevZel'dovich signal of clusters from CMB sky maps.
