In this thesis we present the NOAO-XMM Cluster Survey (NXS). NXS has provided optical follow-up of X-ray cluster candidates serendipitously detected by the XMM Cluster Survey (XCS). We report details on the execution, data reduction and analysis of 154 wide-field MOSAIC images containing 630 XCS cluster candidates. We present a redshift algorithm, based on the ‘red-sequence technique', designed to confirm cluster identifications and extract photometric cluster redshifts from NXS data. This algorithm exploits the homogeneity of elliptical cluster galaxies to provide simultaneous redshift and optical richness estimates. In addition, we apply this redshift algorithm to the Sloan Digital Sky Survey public data releases SDSS DR7 and SDSS Stripe 82. The resulting catalogue of ~500 optically confirmed XCS clusters with red-sequence redshifts is presented, spanning the redshift range 0.1<z<1.0. This sample will enable a future XCS measurement of the cosmological parameters Ωm and σ8, as well as a selfconsistent measure of the cluster X-ray luminosity to temperature scaling relation. Furthermore, for clusters with measured X-ray temperatures or luminosities, we measure the optical richness of red-sequence galaxies within the cluster virial radius (R200). Using these measurements, we investigate the optical halo-mass scaling relation. Understanding cluster optical scaling relations, in particular the optical-light to halo-mass relation, is key for surveys hoping to measure cosmological parameters using optically detected clusters alone. By combining the optical NXS and SDSS data sets with X-ray information from XCS, this thesis provides much needed optical to X-ray scaling relations for future optical cluster surveys.

Cosmological inflation is the leading candidate for the origin of structure in the Universe. However, a huge number of inflationary models currently exist. Higher-order statistics, particularly the bispectrum and trispectrum, of the primordial curvature perturbation can potentially be used to discriminate between competing models. This can provide an insight into the precise physical mechanism of inflation. Current constraints on inflationary models using the amplitude fNL of the bispectrum are quoted for specific templates. This results in much of the inflationary parameter space remaining unexplored. By utilizing the symmetries of the underlying quasi-de Sitter spacetime to construct a generic ‘effective field theory' Lagrangian with adjustable parameters, one can encompass many single-field models of inflation in a unifying framework. In the first part of this thesis we perform a partial-wave decomposition of the bispectrum produced at horizon-exit by each operator in the effective Lagrangian, which we use to find the principal components using a Fisher-matrix approach. This allows us to probe much more of the parameter space. Cosmic Microwave Background bispectrum data is used to estimate the amplitude of each component, which can then translated into constraints on particular classes of single-field models. We consider the implications for DBI and ghost inflation as examples. In the second part of this thesis we extend the transport formalism, first introduced by Mulryne, Seery and Wesley, to calculate the trispectrum generated during superhorizon evolution in inflationary models with multiple fields. We provide transport equations that track the evolution of the local trispectrum non-linearity parameters tNL and gNL throughout inflation. We compute these for several models as examples.

The established cosmological theory which describes the history of the Universe since shortly after the “Big Bang” until today is remarkably successful. Thanks to the increasing precision of available observational data, we are now able to considerably constrain the geometry and composition of the Universe - and to glimpse how these will evolve in the near future. However, this success comes at a price: one must assume the Universe “started” in a highly fine-tuned initial condition. Understanding what came before this is therefore one of the main goals of modern cosmology. This thesis attempts to further our understanding of the epoch before this initial condition in three different ways. Firstly, the concept of negative absolute temperatures (NAT) is introduced and its potential relevance for cosmology is investigated. In particular, it is shown that a Universe at a NAT should undergo a period of inflation - although it is unclear whether this would be consistent with current observations. Secondly, work is done on the topic of the evolution of networks of cosmic strings - topological defects which are expected to form in a broad class of phase transitions the Universe may have gone through. A model which takes into account the presence of small-scale structure in strings is used to address questions concerning the existence and stability of scaling regimes for these networks. Finally, it is investigated how future experiments might try to falsify a simple class of canonical single-field slow-roll inflation models by measuring the running and the running of the running of the spectral index of scalar perturbations.

Models of inflation with more than one active field are an important class where it is not fully understood how to compute predictions. This problem can be understood in terms of two characteristics of these models: the sensitivity to initial conditions and the superhorizon evolution of the primordial density perturbation ζ. This thesis seeks to make significant progress in understanding how to overcome these two issues. To track the superhorizon evolution of ζ in general requires numerical techniques. By extending the transport method first proposed by Mulryne, Seery and Wesley, here, a computationally efficient and highly versatile method for computing the statistics of ζ is developed. The increased efficiency and versatility allows models that were previously unaccessible to be studied. Utilising this new capability two models are explored. A new toy model of inflation in the Landscape and a 6-field D-brane model of inflation first proposed by Agarwal, Bean, McAllister, and Xu. The nature of these models allows for a statistical analysis of inflationary realisations to be performed. We conclude that the fundamental ability to constrain models of this kind is determined by the scale of features in the potential. We also show the D-brane model is under considerable pressure from current observations of the spectral index and may be ruled out by future observations. Finally, I show that there exists a class of models for which the probability distribution of observables may be computed analytically. I show the peak of the density function is largely dominated by the geometry of the potential and comparatively insensitive to the distribution of initial conditions. I argue that this characteristic should be expected in a broader range of models and for such models, it is possible to make robust predictions.

The billion years subsequent to the Big Bang pose the next challenging frontier for precision cosmology. The concordant cosmological model, ΔCDM, propounds that during this period, the dark matter gravitationally shepherds the baryonic matter to form the primordial large-scale structures. This era is termed the Dark Ages (DA). The following era, the Epoch of Reionization (EoR), leads to the formation of the first stars and galaxies that reionize the permeating neutral hydrogen. The linear polarization of the cosmic background radiation and the Gunn-Peterson troughs in quasar absorption spectra provide indirect evidence for the EoR. Currently, there is no observational evidence for the DA. While state-of-the-art radio telescope arrays, Low Frequency Array (LOFAR) and Square Kilometre Array (SKA), propose various strategies to observe the early phases of the Universe, the advanced simulations employing high-performance computing (HPC) methodologies continue to play significant role in constraining various models based upon limited observational data. Despite a wide range of research, there is no end-to-end simulation solution available to quantifiably address the observational challenges due to statistical and systematic errors including foregrounds, ionosphere, polarization, RFI, instrument stability, and directional dependent gains. This research consolidates the cutting-edge simulation solutions, Cube-P3M, C2-Ray, and MeqTrees, to build an HPC prototype pipeline entitled, Simulating Interferometry Measurements (SIM). To establish and validate the efficacy of the SIM pipeline, the research builds a theoretical framework of two science drivers, viz., the presence of Lymanlimit absorbers and measuring non-Gaussianity from the 21-cm data. Thereafter, using the LOFAR and SKA telescope configurations, the SIM generates data visibility cubes with direction dependent and independent propagation effects. Finally, SIM extracts the original signal through standard techniques exploring the parametric phase-space. Results are presented herein.

To completely describe the inflationary era in the early universe is an extremely ambitious task. The main reason is that its dynamics are highly sensitive to ultraviolet physics, making the knowledge of inflation dependent on our ignorance of what is happening at these energy scales. This is not necessarily a weakness of inflation as a paradigm; it is ultimately its most interesting characteristic. Accepting this lack of control on the details of inflationary dynamics brings observational cosmology and the search for an ultraviolet complete theory of gravity together. In this thesis, this duality is explored with the aim of making steps towards an efficient way of studying inflation and its predictions and signatures. This challenge is twofold; first, since fundamental theories are far from being able to explicitly determine the early universe physics, the construction of approximate toy models is unavoidable. For this reason, I identify the key issues for the building of a realistic inflation model, in particular the delicate flatness of the inflaton potential, the strong possibility of multifield dynamics and the necessity of a viable reheating, and in the light of these analyze how best to approximate an ultraviolet complete inflation. For this analysis, two different classes of case studies are presented: inflation in the brane picture and in a holography inspired scenario. On the other hand, since any toy model of an ultraviolet complete inflation necessarily presents a high level of complexity, the computation of predictions for observables is not trivial. For this purpose, I develop numerical tools that manage to compute these parameters efficiently and with a high level of accuracy for a broad range of inflation classes with more than one active field. For each case study, I determine the impact of the inclusion of microphysics contributions in the resulting observational signatures and confront them with data.

This thesis presents the Millennium Gas suite of simulations - the largest cosmological hydrodynamical simulations to date - and examines the effects of different prescriptions for energy injection and radiative cooling on populations of galaxy clusters. We conclude that the dfferences between populations of clusters generated by a simulation with an epoch of preheating, and one with a continual injection of energy (feedback), are minimal at the present day (both in good agreement with observations), but that the evolution of the two populations of clusters differs. High redshift observations of cluster gas fractions suggest that continual energy injection is the preferred method. We examine possible causes of scatter in the cluster gas fraction, but are unable to determine a cause, or combination of causes, of this scatter. We combine the previously used feedback prescription with the same radiative cooling prescription as was used in the preheating simulation. Although the bimodality is not as clear as in observations, this model produces a sample containing both cool core and non-cool core clusters.

The anticipated radio telescope SKA is expected to detect the 21-cm signal from the Cosmic Dawn, allowing us to probe the astrophysical processes of this previously unobserved era. The 21-cm differential brightness temperature fluctuations from the Cosmic Dawn are driven by early inhomogeneous heating of the neutral intergalactic medium and variations in Lyman-alpha photon density. Inhomogeneous heating is driven by high energy, X-ray photons which have long mean free paths and thus penetrate deep into the neutral intergalactic medium. Lyman-α fluctuations depend on the soft, UV photons from these sources redshifting into Lyman-α resonance. In this thesis I present a large-volume (349Mpc comoving) suite of fully numerical radiative transfer simulations of this epoch. The simulations include the effects of helium ionisation, secondary ionisations and multi-frequency heating in order to include different types of X-ray sources (high mass X-ray binaries sources and QSO sources) in addition to black body stellar sources and Lyman-alpha fluctuations, which are added as a post-processing step. In our simulations X-ray sources are able to contribute significantly to early heating of the neutral IGM. Different X-ray models produce varying lengths and morphologies of the transition from absorption to emission. When the results are smoothed to the expected resolution of SKA1-Low the mean, rms, skewness, kurtosis and power spectra of the 21-cm differential brightness temperature are notably different for each X-ray model. These rms fluctuations for each heating model are well above the expected noise for deep integrations which suggests direct imaging of X-ray heating during the Cosmic Dawn should be possible. The presence of QSOs greatly affects the non-Gaussianity, suggesting higher order statistics may be a good observational probe of rare X-ray sources. This e_ect is decreased if the Lyman-α background is built up late. We conclude by discussing ongoing and future work on the topic.

Having as a starting point the problem of dark energy described before, this thesis studies modifications of General Relativity (GR), as possible gravitational scenarios for the early and late time Universe, motivated by both classical as well as quantum considerations. In particular, it focuses on modifications of GR of the type f(R) as well as the f(R;G) ones, where R and G is the Ricci scalar and Gauss-Bonnet term respectively. On the same time, a modification of GR based on the Renormalisation Group approach to quantum gravity is considered, as well as its link to f(R) gravity. The main goal of the investigations carried out in this thesis, is to understand the structure, as well as the phenomenological implications of non-linear modifications of GR for cosmology, at both the background as well as the linear perturbation level. In particular, chapter 2 presents a brief introduction to the dynamics of GR in the presence of a "dark component" at the background, as well as at the linear perturbation level, while chapter 3 is an introduction to the fundamental properties of non-linear modifications of GR, reviewing important results of the relevant literature. Chapter 4 elaborates with a fundamental property of non{linear gravity models, namely the study of different representations of vacuum actions proportional to f(R) as well as f(G), in view of Legendre transformations, for the case of spacetime manifolds with a boundary. As it is explicitly shown there, although the dynamical equivalence is always true in the bulk, it is not guaranteed on the boundary of the spacetime manifold. On the other hand, chapter 5 focuses on understanding the role of the effective anisotropic stress present in f(R;G) gravity models, attempting to construct particular models of the latter type, with a vanishingly small anisotropic stress, so as to agree with current observations. As it turns out, suppression of the effective anisotropic stress in this class of models is very difficult, highlighting the role of the effective anisotropic stress as a smoking gun for testing modified gravity models with current and future observations. Chapter 6 serves as an introduction to the idea of the Renormalisation Group (RG) and its applications in cosmology, while chapter 7 starts from an RG improved Einstein{Hilbert action and studies its connection with f(R) gravity, as well as its implications for the primordial and the late time acceleration of the Universe. It is shown that the effective f(R) model has some remarkable properties and interesting implications for both early and late time cosmology.

This work concentrates on theoretical cosmology in the aspect of modelling the inflationary cosmology, and the central work investigates Non-Canonical inflation (NCI) through the Kinflation paradigm. In this work the objective NCI models can be classified to three classes which are summation-separable models, product-separable models and an ansatz for NCI models, respectively. For simplicity of discussion, the application of the methods, and also the generality of the resulting predictions, I studied NCI models which are associated with the single-term polynomial potential V (�) = A�m. By means of several methods, which include scalar field redefinition and the asymptotic method, as well as the efficient approximations such as slow-roll approximation, for the first time I formulated and revealed the degeneracy and the correlations for the model parameters, in for instance both the scalar potential and the kinetic energy for different investigated NCI models in the work. The work also introduces one developed code, namely Kinetic Model (KMC) for the considered NCI models which implements and extends the scope of ModeCode based on the CosmoMC packages from the conventional canonical inflation to the generic NCI models. The results from numerical exploration helps in illustrating the constraints on the model parameters without the limits of slow-roll assumptions, and the generated results present the consistency as well as similar correlations to those derived from theoretical calculations. Specifically, all investigated NCI models which are driven by a quartic potential ��4 present a novel explanation as a viable candidate theory in modelling our universe given the current high precise observational data, such as from Wilkinson Microwave Anisotropy Probe (WMAP) satellite and Planck satellite.