| Summary: | Includes bibliographical references. === The main work of this thesis can be summarised as: ■ An implementation of canonical quantisation to the covariant and gauge-invariant approach to cosmological perturbations. Standard results are reproduced. We discuss the advantages of this formalism over non-covariant and non gauge-invariant formalisms. ■ A characterisation of linear gravitational waves in a covariant way is achieved. The evolution equations for the electric and magnetic parts of the Weyl tensor are shown to be of different order. In particular, the electric part appears to have a third order evolution equation, while the magnetic part has a second order evolution equation. It is shown that the "silent" nature of the evolution equations for irrotational dust can be extended to the case of vortical dust. This may be relevant for the endpoints of gravitational collapse since the vorticity begins to grow as soon as density contrast becomes non-linear, as is the case in galaxies, showing that the irrotational silent universes are unstable. The main problem in accepting such vortical silent universes lies in proving integrability of the equations which has not been achieved so far, even in the irrotational case. ■ A review of issues in the Cosmic Microwave Background (CMB) is given, focussing particularly on points such as ergodicity, decaying modes, foreground contamination, recombination, spectral distortions and polarisation of the CMB. ■ A review of methods in gravitational lensing is presented, together with a hierarchy of distance measures in cosmology, forming an introduction to the following two chapters. ■ A common belief that photon conservation implies that the all-sky averaged area distance in inhomogeneous universes must be that of the background, matter-averaged Robertson-Walker area distance is dis proven. This means that there will in general be gravitational lensing effects even on large angular scales. ■ The realistic situation in which gravitational lensing leads to caustic formation is discussed. It is claimed that this invalidates many accepted beliefs concerning high-redshift observations in inhomogeneous universes. One application of importance is the CMB. Possible implications are discussed. ■ Random Gaussian fields are ubiquitous in modern statistical physics, and particularly important in CMB studies. Here we give accurate analytical functions approximating ∫e⁻ˣ²dx, the simplest of which is just the kink soliton.
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