Inhomogeneities in cosmology

The standard ΛCDM cosmological model has been successful in accommodating most of the cosmological observations to date. However, there are still many theoretical and observational issues that this model needs to address before it can constitute a reliable framework in this era of 'precision cosmology'. In this thesis, we focus on some of these issues and shortcomings of the ΛCDM model that stem from inhomogeneities in the universe. We begin by focusing on the generation of inhomogeneities by suggesting a generic approach to building suitable models for the origin of structure within the inflationary paradigm. This is in contrast with the study of specific models that has been commonly practised so far. Within the inflationary paradigm the universe in the earliest stages undergoes exponential expansion that stretches quantum fluctuations to astronomical scales, thus providing seeds of future structure. However, this inflationary phase can be generated by many different theoretical 'toy' models of inflation. To alleviate this arbitrariness, we argue that certain potentials for a scalar field are preferred from the viewpoint of the renormalisation group. We arrive at these potentials by decomposing generic UV complete theories for a scalar field in a way that isolates the part that dominates at energies lower than the initial UV scale of the theory. In our calculations, we adopt approximations usually made within the inflationary paradigm. We obtain predictions for the main inflationary observables consistent with the current measurements. We continue by studying the way how the inhomogeneous distribution of matter can be characterised. The structure in the universe at late times exhibits complicated fractal-like behaviour. We propose new methods built on the ideas of anomalous diffusion and random walks to characterise this behaviour. Our methods complement the wellestablished 'count-in-spheres' approach. Moreover, we draw attention to and explicitly demonstrate biases that have existed in the previous applications of these methods, thus improving on them. Finally, we determine the distance scale above which the fractal behaviour disappears and the distribution of matter can be considered homogeneous. The inhomogeneities can also be analysed in terms of the velocity field. We study the most extreme example of it observed to date, namely the ‘Bullet Cluster’, a system of two massive clusters of galaxies which have collided at a high relative speed. This collision poses a potential issue for the standard cosmological model since such mergers are expected to be extremely rare. We calculate the observationally relevant quantity – the expected number of such mergers on the sky in a survey complete up to some redshift. We find that, up to the redshift of the Bullet Cluster, we only expect about 0.1 such collisions. Many more similar merging clusters have been found recently, thereby increasing the tension with the ΛCDM model. We provide a formula for the expected number of mergers within the ΛCDM model given their collisional parameters and their redshift, which can be used to aid the future analyses and directly confront the model. Finally, we focus on the role of the inhomogeneous velocity field in determining the background rate of expansion of space. The Hubble parameter, when measured in the frame of the Local Group of galaxies, has less variation about the background value than when it is measured in the Cosmic Microwave Background frame. This appears to be at odds with the standard cosmological model in which the CMB frame is the one where quantities are expected to be most uniform. We quantify this apparent discrepancy and show that the boost to the frame that makes the Hubble flow most uniform for our position is in fact consistent with the standard model. We show that such boosts to the frame of most uniform flow are typical if observers are located in underdensities and participate in local bulk flows, which is indeed the case for our position.