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.

During the Qing Dynasty (1644-1912) in Nanbu County, land was not only measured in quantitative dimensions, but also assessed through cosmological principles. These understandings of land often framed property claims while shaping rural geographies in the county under study. Drawing on 700 cases from the Nanbu Archive, this dissertation makes two related claims. First, in the mountainous periphery of Northern Sichuan, situated knowledge of land pervaded contracts, genealogies, stone inscriptions, and official handbooks. This information, composed of vernacular place-names, localized land boundaries, expressions of patrimonial merit and status, and cosmological dimensions of property, was often immediately understandable only to the members of a lineage or community, but could be interpreted by the state if needed. One type of situated information was geomantic information, which regularly entered the magistrate’s court. Local officials engaged this information in legal practice and took geomantic claims or documentation into consideration during litigation. Sites holding great geomantic significance, such as ancient trees, graves, and temples, were often identified by locals as the landmarks or borders of private estates, market towns, or the county itself; these understandings were regularly woven into the administrative documents of the state. During the Qing, such interpretations were even extended to a local shrine of a Muslim (Qadiri) saint. Through routine engagement with these interpretations of the earth throughout the increasing landed commercialization of the nineteenth and early twentieth centuries — in processing lawsuits, the Nanbu yamen (state administrative office) ordered landscapes concerning geomancy to be officially illustrated more than any other genre of claim — the Qing state legitimated highly situated knowledge of the land within the local property regime while upholding geomantic information as a binding mechanism for the regulation of common lands and resource access. The dissertation’s second point is that, while it is well-known that the early decades of the twentieth century saw increased state penetration into local society across China, Nanbu maintained a remarkable degree of continuity with its imperial heritage. Land surveyors working in the early twentieth century struggled to extract structured knowledge of land from the layered territorialities of the county’s terrains that had persisted from the Qing. This process was highly negotiated and often interpretive, rather than based on precise statistical surveying or the clear directives of a hegemonic state. Through exploring the legal, environmental, and religious dimensions of a single county’s terrains in the late imperial period, this study identifies situated geomantic information as one of the key arenas for the projection of — and limitations on — state power in the county in relation to the property system. The dissertation also provides the first English-language history of Nanbu, a county with a remarkably complete administrative and legal archive from 1656 to 1951.

Orientador: José Geraldo Pereira / Banca: Bruto Max Pimentel Escobar / Banca: Roldão da Rocha Junior / Banca: Davi Cabral Rodrigues / Banca: José abdalla Helayel-Neto / Resumo: A assimetria temporal observada na física macroscópica se deve à configuração de entropia extremamente baixa do universo primordial. Apesar de a matéria estar muito quente e com uma temperatura uniforme naquele estágio, os graus de liberdade gravitacionais estavam em grande medida suprimidos, fato este que contribui para o baixo valor da entropia e está codificado no alto grau de simetria espacial (caráter aproximadamente Friedman-Lemaître-Robertson-Walker) da superfície de último espalhamento. Analisamos diferentes tentativas de explicar a origem de tal configuração especial. O paradigma inflacionário é testado com respeito a esse problema, e é concluído que a baixa entropia inicial não pode ser explicada dentro dele. Conclusões similares são obtidas com respeito a formulações estatísticas (i.e. antrópicas). Por outro lado, o paradigma conhecido como cosmologia cíclica conforme (CCC) se apresenta como uma nova alternativa que ultrapassa muitas das dificuldades enfrentadas pelos seus rivais, apesar de levantar suas próprias questões em aberto. Introduzimos o modelo juntamente com a estrutura matemática das geometrias de Cartan como um meio possível de atingir um melhor entendimento das condições de contorno cosmológicas. Um elemento que é crucial nessa análise é a modelagem de uma estrutura geométrica de Cartan sobre o espaço de de Sitter SOe(4,1)/SOe(3,1) com um parâmetro de comprimento variável. A introdução de um parâmetro de comprimento na cinemática é favorecida pela observação de uma constante cosmológica positiva e também desejável por motivos oriundos da gravitação quântica, devido à escala natural determinada pelo comprimento de Planck / Abstract:The observed T-asymmetry of macroscopic physics is traced back to the extremely low entropy configuration of the early universe. Although matter was very hot and with a uniform temperature at that stage, the gravitational degrees of freedom were largely suppressed, which fact contributes to the lowness of the entropy and is encoded in the high level of spatial symmetry (nearly Friedman-Lemître-Robertson-Walker character) of the last scattering surface. I analyze different attempts to explain the origin of such special configuration. The inflation paradigm is probed with respect to this problem, and it is concluded that the initial low entropy cannot be accounted for within it. Similar conclusions are reached with respect to statistical (i.e. anthropic) reasonings. On the other hand, the paradigm known as conformal cyclic cosmology (CCC) presents itself as a new alternative which surpasses many of the difficulties faced by its rivals, although raising its own open questions. I introduce the model together with the mathematical structure of Cartan geometries as a possible means of achieving a better understanding of cosmological boundary conditions. One element which is crucial in this analysis is the modeling of the Cartan geometric structure over a de Sitter space SOe(4,1)/SOe(3,1) with varying length parameter. The introduction of a length parameter in the kinematics is favored by the observation of a positive cosmological constant and also desirable for quantum gravity reasons, due to the natural scale set by Planck's constant / Doutor

Chan, Kwan Chuen = 宇宙微波背景幅射數據對非標準物理的規範 / 陳坤全. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 95-101). / Text in English, abstracts in English and Chinese. / Chan, Kwan Chuen = Yu zhou wei bo bei jing fu she shu ju dui fei biao zhun wu li de gui fan / Chen Kunquan. / Chapter 1 --- Overview of Cosmology --- p.1 / Chapter 1.1 --- Friedmann-Robertson-Walker Universe --- p.1 / Chapter 1.2 --- The Hubble Diagram and Type Ia Supernovae --- p.3 / Chapter 1.3 --- Big Bang Nucleosynthesis --- p.5 / Chapter 1.4 --- Cosmic Microwave Background --- p.8 / Chapter 1.5 --- Matter Power Spectrum and Galaxy Surveys --- p.10 / Chapter 1.6 --- The Energy Density Budget of the Universe and Outlook --- p.13 / Chapter 2 --- Review of CMB Physics --- p.17 / Chapter 2.1 --- Main Physics of the CMB Power Spectra --- p.17 / Chapter 2.1.1 --- Photon-Baryon Fluid --- p.17 / Chapter 2.1.2 --- Initial Conditions --- p.20 / Chapter 2.1.3 --- Acoustic Peaks --- p.22 / Chapter 2.1.4 --- Baryons in Action --- p.23 / Chapter 2.1.5 --- Damping --- p.24 / Chapter 2.1.6 --- Polarization --- p.25 / Chapter 2.2 --- Computation of CMB Power Spectrum --- p.26 / Chapter 3 --- Constraints on Variation of the Gravitational Constant by CMB --- p.30 / Chapter 3.1 --- Current Constraints on G and Theoretical Motivations --- p.31 / Chapter 3.2 --- Parametrization of G --- p.32 / Chapter 3.3 --- Effect of Variation of G on the CMB Temperature and Polarization Power Spectra --- p.34 / Chapter 3.4 --- Constraining G by MCMC and Discussions --- p.40 / Chapter 3.5 --- Conclusion --- p.45 / Chapter 4 --- Constraints on f(R) Cosmology in the Palatini Formalism --- p.47 / Chapter 4.1 --- Introduction --- p.48 / Chapter 4.2 --- Field Equations in Theories of Palatini - f(R) Gravity --- p.50 / Chapter 4.2.1 --- General Theory of f(R) Gravity in the Palatini Approach --- p.50 / Chapter 4.2.2 --- The Perturbation Equations --- p.52 / Chapter 4.3 --- Numerical Results and Cosmological Constraints --- p.56 / Chapter 4.4 --- Discussion and Conclusion --- p.62 / Chapter 5 --- CMB Constraint on Radion Evolution in the Brane World Scenario --- p.65 / Chapter 5.1 --- Introduction --- p.66 / Chapter 5.2 --- Dimensional Reduction and Low Energy Effective Actions --- p.68 / Chapter 5.3 --- Numerical Constraints on the Evolution of the Radion --- p.72 / Chapter 5.3.1 --- Effects of Variation of Higgs VEV on CMB Power Spectra --- p.72 / Chapter 5.3.2 --- Numerical Constraints on the Higgs VEV and Radion by CMB --- p.75 / Chapter 5.4 --- Conclusion --- p.80 / Chapter 6 --- Summary of the Thesis --- p.81 / Chapter A --- Markov Chain Monte Carlo Method --- p.84 / Chapter A.1 --- Basic Theory of MCMC --- p.84 / Chapter A.2 --- The Metropolis-Hastings Algorithm --- p.86 / Chapter A.3 --- Convergence Diagnostics --- p.87 / Chapter B --- Forecast by Fisher Matrix --- p.89 / Chapter C --- Modified Equations in RECFAST with Variation me --- p.92 / Bibliography --- p.95