Browsing by Author "Maartens, Roy"

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    Exact non-equilibrium solutions of the Einstein-Boltzmann equations
    (1994) Wolvaardt, F P; Maartens, Roy
    In this thesis we use the exact solution of the Boltzmann equation, with a relaxation-time model of collisions, to find solutions of the Einstein-Boltzmann system of equations. A covariant harmonic decomposition of the distribution function is used to obtain exact results. The conditions imposed by the conservation of particle number and energy-momentum, and by the H-theorem are determined. The properties of exact truncated Boltzmann solutions with first and second order anisotropies are investigated. Exact entropy results are obtained for the solution with first order anisotropy, and the solution with second order anisotropy is shown to obey exact thermodynamics laws. The Einstein-Boltzmann equations with relaxation-time model of collisions are solved in FRW and Bianchi I spacetime. In FRW spacetime, a general anisotropic solution and an isotropic solution are obtained. The non-equilibrium anisotropic solution with arbitrary isotropic relaxation function has vanishing particle flux and an equilibrium energy-momentum tensor. Specific forms of the relaxation function permit tilted solutions and solutions with non-zero bulk viscosity. Exact entropy results are derived for the isotropic solution showing that the H-theorem is satisfied. The non-equilibrium isotropic solution has vanishing non-equilibrium pressures and fluxes. The FRW and Bianchi I solutions are used to demonstrate the generation of anisotropy in FRW cosmologies. A relaxation length model of collisions is introduced. This model is used to obtain solutions of the Einstein-Boltzmann equations in static spherically symmetric spacetime. In this static model, anisotropic pressure comes from the bulk viscosity.
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    Fluid and gas models in FLRW and almost FLRW universes
    (1996) Gebbie, Timothy John; Ellis, George F R; Maartens, Roy; Dunsby, Peter K S
    Recently the universe has been modeled in the covariant sense, in terms of fluid models and perturbations thereof, leading to Gauge Invariant Covariant (GIC) perturbations of these fluid models. It is well known that kinetic theory provides a physically sound and consistent description of the matter and radiation in the universe, so a perturbative theory of gas models using kinetic theory would be most helpful. This has been done to a large degree in the Gauge Invariant (GI) Bardeen approach to perturbation theory by studies of gases based on the relativistic Boltzmann equation. These treatments, however, were not fully covariant. The GI Bardeen approach is dependent on a co-ordinate choice, while in the full GIC perturbation theory full covariance is maintained along with gauge invariance by describing the theory in a particular set of perturbation variables that differ from the Bardeen choice but can be related to the Bardeen variables. The covariant formulation of the relativistic Boltzmann equation in terms of variables that are of use in the GIC theory for gases has been well described. In this thesis, I provide both a good introduction to the full GIC perturbation theory of a photon gas and matter fluid system in the linear theory as well as a solid grounding with respect to the exact FLRW fluid model upon which most of the original ideas and concepts of modern cosmology are based. The introduction to the exact FLRW model is done in the sense of the dynamical systems approach to cosmology which provides the easiest access to understanding the evolution of single and multi-fluid FLRW models.
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    Galaxy correlations and the BAO in a void universe: structure formation as a test of the Copernican Principle
    (IOP Publishing, 19) February, Sean; Clarkson, Chris; Maartens, Roy
    A suggested solution to the dark energy problem is the void model, where accelerated expansion is replaced by Hubble-scale inhomogeneity. In these models, density perturbations grow on a radially inhomogeneous background. This large scale inhomogeneity distorts the spherical Baryon Acoustic Oscillation feature into an ellipsoid which implies that the bump in the galaxy correlation function occurs at different scales in the radial and transverse correlation functions. We compute these for the first time, under the approximation that curvature gradients do not couple the scalar modes to vector and tensor modes. The radial and transverse correlation functions are very different from those of the concordance model, even when the models have the same average BAO scale. This implies that if void models are fine-tuned to satisfy average BAO data, there is enough extra information in the correlation functions to distinguish a void model from the concordance model. We expect these new features to remain when the full perturbation equations are solved, which means that the radial and transvers.
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    A study of potential calibrators using the KAT-7 radio telescope
    (2015) Kassaye, Ermias Abebe; Bassett, Bruce; Oozeer, Nadeem; Maartens, Roy; Romeel, Dave
    This thesis presents a study of potential calibrators observed by the Karoo Array Telescope (KAT-7). The KAT-7 is an engineering prototype for the coming sensitive array, the MeerKAT, one of the pathfinders for the Square Kilometre Array (SKA). This thesis plays a supporting role in the ongoing commissioning activities of the KAT-7, whose construction started in early 2008, and which has been undergoing engineering and science verifications since late 2010. This thesis has achieved the first steps towards identifying possible flux-density standards for short baseline interferometers such as the KAT-7. The systematic error for flux-density calibration at KAT-7 was estimated relative to 3C123, and it was found to be ~5% of the measured flux density. 18 (~47%) of the 38 sources were identified as good flux density calibrator candidates, for their Modulation Index (MI) and Variability Index (VI) values were less than 0.05 and all the sources in the field had less than 10% of the peak flux density of the calibrator candidate. One source (PKS J0837-1951), which showed low variability and hence appeared to be a good flux-density calibrator candidate (class A), was deemed to be not a good flux-density calibrator candidate because a strong confusing source was found within its primary beam. Eight sources had MI or VI values between 0.05 and 0.09 and may deserve further study as potential flux calibrator candidates. Five sources had MI or VI values greater than 0.09 suggesting significant variability while 17 sources had only one or two observations so their suitability as potential flux calibrator candidates could not be evaluated. In addition, we used another measure of variability, the de-biased modulation index, for our sources comparing the observed modulation indices against Monte Carlo simulations. The result showed that the values of Md are largely as expected and the uncertainties therefore not substantially underestimated.
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    Temperature anisotropies: covariant CMB anisotropies and nonlinear corrections
    (1999) Gebbie, Tim; Ellis, George; Maartens, Roy
    The questions I ask myself are generally all along the lines of "so where did all this structure come from?". I hoped that work in the CMB and its cosmological implications would give me insight into this. It is an adventure that is still young. I began my PhD with an investigation of some formal aspects of Ehlers-Ellis Relativistic Kinetic Theory in mind { the implications of the truncation conditions found in the exact theory. I ended up trying to calculate CMB anisotropies as an application of this beautiful and somewhat purist formalism. The Ehler-Ellis (1+3) Lagrangian approach to General Relativity (GR) and Relativistic Kinetic Theory (RKT) are apparently not well known nor well used and have only recently begun to show advantages over the more usual ADM and Bardeen perturbative approaches to astrophysical cosmology when combined with the Ellis Bruni perturbation theory.