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.

Thesis (Th. M.)--Westminster Theological Seminary, Philadelphia, 1989. / Includes bibliographical references (leaves 129-133).

Thesis (Th. M.)--Westminster Theological Seminary, Philadelphia, 1989. / Includes bibliographical references (leaves 129-133).

Thesis (Th. M.)--Westminster Theological Seminary, Philadelphia, 1989. / Includes bibliographical references (leaves 129-133).

Issued also as thesis, Fribourg. / "Literaturverzeichnis": p. [9]-16.

Inaug.-dis.--Rostock.

My aim in this thesis is to show how Plato differentiates the everlastingness of eternity from the everlastingness of time in the cosmogony of his Timaeus, where time is classified as the everlasting ‘moving image’ of ‘eternity-remaining-in-unity’ (Tim. 37c 6-d 7). Of course, as many scholars know, this distinction between eternity and time follows from his distinction between unchanging Being and ever-changing Becoming, so much so that our understanding of what it is that makes time the ‘image’ of eternity—and yet also something other than eternity—proves fundamental to our understanding of Platonic ontology. However, our understanding of Being and Becoming and the relation between them is complicated by the view that what exists in time was and is and will be, whereas what exists in eternity ‘is’ alone (Tim. 37e 4-38a 8). Does this mean that eternity is temporal, given that it ‘is’ in some sense? Or is eternity atemporal, given that it is itself distinguishable from time? Also, if eternity is atemporal, how should one conceive of atemporality in this particular respect? Does this entail existing altogether apart from time? Or can one speak of eternity as just another type of time, a timeless time, as it were? Not surprisingly, it has long been a matter of controversy among scholars whether the eternal ‘is’ is actually tensed or tenseless, temporal or timeless. So too, the very fact that eternity is said to be ‘remaining in unity’ has led some scholars to conceive of eternity as durational, and thus temporal in some sense, on the assumption that duration entails temporality. But then again, still other scholars speak of eternity as an ‘eternal present’ which is non-durational, precisely because it has its being ‘in unity’. By contrast, I argue that the Platonic distinction between Being and Becoming entails a twofold notion of everlastingness, the one temporal, the other extra-temporal, where the latter is signifying timelessness unqualifiedly. For I show that Plato conceives of time and temporal passage as the imperfectly everlasting image (aiônios eikôn) of eternity whilst understanding eternity to be perfectly everlasting (diaiônios), since eternal Being is subject to no passage from its essential being. Only in this way can one explain how the temporality of Becoming is akin to—yet also distinguishable from—the extra-temporality of Being, and then again why it is that both should be thought of as durational. Hence the scholarly assumption that duration entails temporality, an assumption commonly encountered in modern thought, is foreign to Plato. Nor again does it make sense to speak of an ‘eternal present’ apart from everlastingness, and thence apart from duration. So as to clarify this twofold notion of everlastingness it has proven necessary for my argument to touch upon another controversy surrounding the cosmogony of the Timaeus, namely, whether the universe, the realm of Becoming, has had a beginning at some time in the remote past (i.e., at the very first moment of time) or has had no single beginning, at least in a temporal sense (i.e., that it will have come into being ‘always’ (aei)). Scholars have given various arguments for both of these readings. However, I argue that one can resolve this issue by more closely analysing the possible meanings of the verb gegonen (viz. ‘It has come into being’), which is said of the universe as well as time (Tim. 28b 7, 38b 6). With respect to gegonen, the temporal ambiguity of its perfect aspect means that it might refer to a past event in the immediate past no less than in the remote past. Hence one can speak of the generation of time and the universe as everlasting, as a process of genesis having no single, distinct beginning at a time or even in time, but infinitely many beginnings, extending from the infinite past into the ever-emerging present. And that gegonen is ambiguous between past and present time is shown by the cosmological argument at Tim. 28b 2-c 2 and the status of god relative to creation. All in all, this reveals that time, being generate, is a feature of Becoming, not Being. It also reveals that time and the universe need not have had a beginning at some first moment of time.