### Abstract

Over the last few decades enormous progress has been made in the study of the Universe and we are now entering the age of precision cosmology, with numerous upcoming high precision surveys expected to provide us with an incredible wealth of information. Observational data is usually interpreted once assumptions about the underlying cosmology are made. One of those commonly made assumptions is that the Universe is homogeneous and istropic, which observations seem to indicate is the case on very large scales.We develop a class of exact inhomogeneous solutions to general relativity for dust and a cosmological constant with which we can model a line of sight with arbitrary matter distribution; far away from this line of sight the solutions tend towards a standard homogeneous model of the Universe. This class of solutions is very well suited to model the effects of inhomogeneities along the line of sight on cosmological observations. We find that the effects of the inhomogeneities on the relation between distance and redshift are small if one imposes that the inhomogeneities along the line of sight average to the background density. Using compensated structures of several shapes and sizes, we find the deviations from the distance redshift relation to be below 1%. However, as soon as the lines of sight are not completely compensated larger deviations are found. We investigate this effect further and compare several exact solution to general relativity and perturbative approaches. The results from the three exact solution are very similar and indicate that uncompensated lines of sight can result in distance – redshift relations very different to the homogeneous ones. For small fluctuations we find that the complete linear analysis agrees with the results from exact solution but weak lensing predictions do not. The expansion rates along lines of sight which are not compensated are different than in the background which causes the large deviations in the distance – redshift relation. We find that void regions expand faster than in the background, but can they expand fast enough to explain the observed cosmic acceleration? However, on smaller scales such as galaxies and groups of galaxies this is clearly not the case. With the precision of observations increasing to unprecedented levels, is it still justifiable to make the assumption that the Universe is homogeneous on all scales even though we know that this is not the case on most scales? Much of this thesis is dedicated to this question.

To answer this question from the exact solutions point of view we develop an inhomogeneous solution to general relativity for a single fluid with a constant equation of state parameter in the background. Within this solution we investigate the expansion properties of compensated regions and void regions. We find that compensated regions expand as the background and find that void regions do expand faster than the background but cannot cause cosmic acceleration.

The physical mechanisms at work during the early Universe are not very well understood yet, but the hope is that through the data provided by future high precision surveys we might be able to constrain some of the theories. In particular constraints on the levels of primordial non-Gaussianity will be a powerful discriminator between theories. Therefore we investigate the growth of matter inhomogeneities to second perturbative order in a concordance cosmology and find the dependence of the density fluctuations on primordial non-Gaussianities. We also show how Newtonian and purely general relativistic non-linear effects enter into the second order density fluctuations. This understanding is essential in extracting information about primordial non-Gaussianties from the distribution of large scale structure today.

Lastly, we analysed a proposed way of probing cosmic expansion by using the well studied Alcock-Paczynski effect in the dynamics of galaxy pairs. We studied the dynamics of galaxy pairs in an N-body simulation and found that once several cuts are made on the selection of the galaxy pairs, including isolation criteria, mass cuts and separation cuts, there might be a possibility of using pairs with such properties as cosmic tracers. Modelling of the velocities of the galaxies due their mutual attraction and local densities needs to be done first though to remove systematic errors in the observations.

Date of Award | Sep 2012 |
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Original language | English |

Supervisor | Marco Bruni (Supervisor), David Wands (Supervisor) & Roy Maartens (Supervisor) |