Inhomogeneous cosmology in an anisotropic Universe

With the era of precision cosmology upon us, and upcoming surveys expected to further improve the precision of our observations below the percent level, ensuring the accuracy of our theoretical cosmological model is of the utmost importance. Current tensions between our observations and predictions from the standard cosmological model have sparked curiosity in extending the model to include new physics. Although, some suggestions include simply accounting for aspects of our Universe that are ignored in the standard model. One example acknowledges the fact that our Universe contains significant density contrasts on small scales; in the form of galaxies, galaxy clusters, filaments, and voids. This small-scale structure is smoothed out in the standard model, by assuming large-scale homogeneity of the matter distribution, which could have a measurable effect due to the nonlinearity of Einstein's equations. This backreaction of small-scale structures on the large-scale dynamics has been suggested to explain the measured accelerating expansion rate of the Universe. Current standard cosmological simulations ignore the effects of General Relativity by assuming purely Newtonian dynamics. In this thesis, we take the first steps towards quantifying the backreaction of small-scale structures by performing cosmological simulations that solve Einstein's equations directly. Simulations like these will allow us to quantify potentially important effects on our observations that could become measurable as the precision of these observations increases into the future.