Browsing by Author "Dunsby, Peter K S"
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- ItemOpen AccessBeyond the standard model of cosmology : a perturbative approach(2007) Osano, Bob Otieno; Dunsby, Peter K S; Clarkson, C AThis thesis concerns higher order perturbations of the standard model of cosmology. The theme is addressed in two distinct research areas. The first area deals with linear perturbations of Bianchi type I model filled with dust whose flow is irrotational, and which is an analogue to second order perturbations about the standard model. We investigate both density perturbations and gravitational waves in the shear dominated and the matter dominated regimes. We find that whereas the analysis of the perturbations in the matter dominated regime recovers the standard FLRW results, the analysis of perturbations in the shear dominated regime reveals that density perturbations and gravitational waves decouple only when the background shear is locally rotational symmetric.
- ItemOpen AccessCosmic electromagnetic fields due to perturbations in the gravitational field(American Physical Society, 2012) Mongwane, Bishop; Dunsby, Peter K S; Osano, Otieno BobWe use non-linear gauge-invariant perturbation theory to study the interaction of an inflation produced seed magnetic field with density and gravitational wave perturbations in an almost Friedmann-Lemaˆıtre-Robertson-Walker (FLRW) spacetime with zero spatial curvature. We compare the effects of this coupling under the assumptions of poor conductivity, perfect conductivity and the case where the electric field is sourced via the coupling of velocity perturbations to the seed field in the ideal magnetohydrodynamic (MHD) regime, thus generalizing, improving on and correcting previous results. We solve our equations for long wavelength limits and numerically integrate the resulting equations to generate power spectra for the electromagnetic field variables, showing where the modes cross the horizon. We find that the interaction can seed Electric fields with non-zero curl and that the curl of the electric field dominates the power spectrum on small scales, in agreement with previous arguments.
- ItemOpen AccessCosmological dynamics of exponential gravity(2007) Abdelwahab, Mohamed Elshazli Sirelakhatim; Dunsby, Peter K SThe objective of this thesis is to explore several hotly debated current issues in modern cosmology, with a focus on f(R) gravity. In chapter 1 we present a review of modern theoretical cosmology. We begin by introducing some fundamental cosmological concepts, followed by a discussion of the field equations of general relativity, which underlie both the behavior of global cosmological models and the isolated gravitating systems such as stars, black holes and galaxies. In particular we focus on the solutions for the Friedmann-Robertson-Walker Universe. Next we present a detailed discussion of the dark matter problem. Astrophysical observations indicate that the two components account for 25% of the total mass/energy of the observable Universe. We then present the big bang model, which represents the current standard model for the origin and the evolution of the Universe. In our discussion we introduce the inflationary scenario in some detail; specifically we present an example of quadratic inflation to demonstrate how this scenario provides a solution to some of the problems with the standard model. Next we discussed the dark energy model, which as been introduced to address the late-time acceleration problem. We then present the quintessence model, which as been proposed to address the coincidence and the magnitude problems. We conclude this chapter by a detailed discussion of the higher order theories of gravity with a particular we focus on f(R)-gravity, which is based on the idea of introducing corrections to the Einstein-Hilbert action that are negligible in the early Universe and only become effective at late times when the Ricci curvature R decreases. In our discussion we indicate how these corrections can be interpreted as an effective fluid of purely geometrical origin; we also discuss the phase space and stability of deSitter space in f(R) gravity.
- ItemOpen AccessA covariant approach to gravitational lensing(2004) De Swardt, Bonita; Dunsby, Peter K S; Clarkson, ChrisThe main focus of this thesis is to study the properties of null geodesics in general relativistic models. This thesis is divided into two parts. In the first part, we introduce the (1+3)-covariant approach which will be used in our study of null geodesics and their applications to gravitational lensing. The dynamics of the null congruence can be better understood through the propagation and constraint equations in the direction of the congruence. Thus, we derive these equations after describing the geomentry of a ray. We also derive a general from of the null geodesic deviation equation (NGDE) which can be used in any given space-time. Various applications of this equation are studied, including its role in determining area-distance relations in an Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmological model. We also use the NGDE in deriving a covariant form of the angle of deflection, showing its versatile applications in gravitational lensing theory.
- ItemOpen AccessCovariant perturbations in f (R) - gravity of multi-component fluid cosmologies(2009) Gidelew, Amare Abebe; Dunsby, Peter K SWe study the evolution of scalar cosmological perturbations in the 1+3 Covariant Gauge-Invariant formalism for generic f(R) theories of gravity. Working in the energy frame of the total matter, we give a complete set equations describing the evolution of matter and curvature fluctuations for a multi-fluid cosmological medium. We then specialize to a radiation-dust fluid described by barotropic equations of state. We apply the perturbation equations around a background solution of Rⁿ gravity and look at exact solutions for scales much smaller and much larger than the Hubble radius.
- ItemOpen AccessExploring the cosmological dynamics of a viable theory for ƒ(R)-gravity(2014) Kandhai, Sulona; Dunsby, Peter K SA viable theory for ƒ(R) gravity, the Hu-Sawicki (HS) model, is considered from a dynamical systems perspective. The case for which n=1, c₁=1 is treated, and qualitative information regarding the phase space of this model is extracted. Several stable de Sitter equilibrium points are identified, as well as an unstable "matter-like" point and solution orbits which resemble the ACDM evolution are presented. The expansion history produced by integration of the dynamical system of the HS model is compared with that of ACDM. It is found that while the HS model can produce the desired behaviour in the appropriate regime, this occurs at the expense of ACDM values of the observational parameters.
- ItemOpen AccessFluid and gas models in FLRW and almost FLRW universes(1996) Gebbie, Timothy John; Ellis, George F R; Maartens, Roy; Dunsby, Peter K SRecently 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.
- ItemOpen AccessGeneral relativistic electrodynamics with applications in cosmology and astrophysics(2005) Betschart, Gerold; Dunsby, Peter K S; Marklund, Mattias; Clarkson, Chris; Zunckel, Caroline; Servin, Martin; Tsagas, ChristosIncludes bibliographical references.
- ItemOpen AccessProblems in cosmology and numerical relativity(2015) Mongwane, Bishop; Dunsby, Peter K SA generic feature of most inflationary scenarios is the generation of primordial perturbations. Ordinarily, such perturbations can interact with a weak magnetic field in a plasma, resulting in a wide range of phenomena, such as the parametric excitation of plasma waves by gravitational waves. This mechanism has been studied in different contexts in the literature, such as the possibility of indirect detection of gravitational waves through electromagnetic signatures of the interaction. In this work, we consider this concept in the particular case of magnetic field amplification. Specifically, we use non-linear gauge-in variant perturbation theory to study the interaction of a primordial seed magnetic field with density and gravitational wave perturbations in an almost Friedmann-Lemaıtre-Robertson- Walker (FLRW) spacetime with zero spatial curvature. We compare the effects of this coupling under the assumptions of poor conductivity, perfect conductivity and the case where the electric field is sourced via the coupling of velocity perturbations to the seed field in the ideal magnetohydrodynamic (MHD) regime, thus generalizing, improving on and correcting previous results. We solve our equations for long wavelength limits and numerically integrate the resulting equations to generate power spectra for the electromagnetic field variables, showing where the modes cross the horizon. We find that the interaction can seed Electric fields with non-zero curl and that the curl of the electric field dominates the power spectrum on small scales, in agreement with previous arguments. The second focus area of the thesis is the development a stable high order mesh refinement scheme for the solution of hyperbolic partial differential equations. It has now become customary in the field of numerical relativity to couple high order finite difference schemes to mesh refinement algorithms. This approach combines the efficiency of local mesh refinement with the robustness and accuracy of higher order methods. To this end, different modifications of the standard Berger-Oliger adaptive mesh refinement a logarithm have been proposed. In this work we present a new fourth order convergent mesh refinement scheme with sub- cycling in time for numerical relativity applications. One of the distinctive features of our algorithm is that we do not use buffer zones to deal with refinement boundaries, as is currently done in the literature, but explicitly specify boundary data for refined grids instead. We argue that the incompatibility of the standard mesh refinement algorithm with higher order Runge Kutta methods is a manifestation of order reduction phenomena which is caused by inconsistent application of boundary data in the refined grids. Indeed, a peculiar feature of high order explicit Runge Kutta schemes is that they behave like low order schemes when applied to hyperbolic problems with time dependent Dirichlet boundary conditions. We present a new algorithm to deal with this phenomenon and through a series of examples demonstrate fourth order convergence. Our scheme also addresses the problem of spurious reflections that are generated when propagating waves cross mesh refinement boundaries. We introduce a transition zone on refined levels within which the phase velocity of propagating modes is allowed to decelerate in order to smoothly match the phase velocity of coarser grids. We apply the method to test problems involving propagating waves and show a significant reduction in spurious reflections.
- ItemOpen AccessReview of current radiometer technology with suggestions for future South African satellites(2012) Calder-Potts, George; Inggs, Michael; Dunsby, Peter K SGiven that South Africa is an emerging space nation, in a continent of emerging space nations and economies, several technologies need to be developed to progress the space program into a viable and sustainable endeavour. The three main areas of space technology are communications, navigation and remote sensing. Earth science is strongly reliant on the third of these areas for obtaining global scientific data, on a suitable temporal/spatial scale. One of the forms of electro-magnetic remote sensing is microwave radiometry. This dissertation presents a short review of currently available space-faring radiometer technologies and applications, which are then discussed in the context of today's South Africa. For instance Passive Microwave Radiometers (PMR) in the L-Band have huge implications in Soil Moisture (SM) and Sea Salinity (SSS), which in turn affect the global climate, and are being investigated by current and soon to launch missions such as Aquarius, SMOS and SMAP. Multi-frequency radiometers are used to classify various other aspects of Earth's surface-atmosphere system. The structure of this dissertation is to introduce the concepts of radiometry with a review of current and future radiometers from literature (up to November 2011). The user communities, current and possible, are also analysed. There is a discussion of South Africa's history, needs and presence in space, along with possible constraints on a future South African instrument going to space. A technology demonstrator passive microwave radiometer, for SM and Sea Surface Temperature (SST) along with some atmospheric correction channels, is presented. Synergy with data obtained from other instruments, such as an Infra-Red (IR) sounder, is also discussed.
- ItemOpen AccessA study of solutions and perturbations of spherically symmetric spacetimes in fourth order gravity.(2013) Nzioki, Anne Marie; Dunsby, Peter K SIn this thesis we use the 1+1+2 covariant approach to General Relativity to study exact solutions and perturbations of rotationally symmetric spacetimes in f(R) gravity, one of the most widely studied classes of fourth order gravity. We begin by introducing f(R) theories of gravity and present the general equations for these theories. We investigate the problem of matching different regions of spacetime, shedding light on the problem of constructing realistic inhomogeneous cosmologies in the context of f(R) gravity. We also study strong lensing in these fourth order theories of gravity derive the lens mass and magnification for the gravitational lens system. We provide an extensive review of both the 1+3 and 1+1+2 covariant approaches to f(R) theories of gravity and give the full system of evolution, propagation and constraint equations of LRS spacetimes. We then determine the conditions for the existence of spherically symmetric vacuum solutions of these fourth order field equations and prove a Jebsen-Birkhoff like theorem for f(R) theories of gravity and the necessary conditions required for the existence of Schwarzschild solution in these theories.
- ItemOpen AccessTensors and Relativity Course(2014-08-22) Dunsby, Peter K SThis website contains lecture notes on Special and General Relativity, with a mathematical approach. The first part is exclusively dedicated to Special Relativity and its mathematical treatment using Tensors. The last four subjects go through General Relativity, explaining its principles, the effects of gravity and how to apply Tensors to the study of curvature of space. The topics in this resource include: Mathematical Tools and Linear Algebra and Tensors in General physics; General Relativity; Mathematics in relativity; Tensors in relativity; and Special relativity. The image used is Special Relativity by Wonderlane and is licensed under a Creative Commons Attribution license.
- ItemOpen AccessTopics in cosmology(2001) Hobbs, Claudia Stacey; Dunsby, Peter K SThis thesis contains two distinct parts: the first part introduces and explains the relevant theory and background necessary for the analytic work done on magnetized cosmological perturbations at the end of the first part. The second part discusses some issues related to observational cosmology. After an introductory chapter including an overview of the thesis, PART I starts with a discussion of the covariant approach to cosmology, introducing notation needed in the thesis. The covariant approach to perturbations is then discussed, and the basic inhomogeneity variables describing energy density, pressure and expansion pertubations are introduced. Their exact evolution equations are presented before being linearized about an FRW background.
- ItemOpen AccessTopics in modified gravity(2012) Abdelwahab, Mohamed Elshazli Sirelakhatim; Dunsby, Peter K SThe key element of modern cosmology is the assumption that the General Theory of Relativity (GR) is the correct theory of gravitation. It replaced the Newtonian theory of gravity which was presented in the Principia in 1687. The fundamental idea in GR is that gravity is a manifestation of the curvature of the spacetime, while in Newton’s theory gravity acts directly as a force between bodies. Many of the predictions of GR, such as the bending of star light by gravity and a tiny shift in the orbit of the planetMercury, have been quantitatively confirmed by experiment
- ItemOpen AccessTopics in stringy cosmology(2004) Goheer, Naureen; Dunsby, Peter K SThis thesis is composed of two distinct research topics. The first topic concerns Randall-Sundrum cosmological models, in particular their isotropization properties at early times. We first study the state space of inflationary braneworld models with exponential potential and identify the past and future attractors within the homogeneous state space. Our main result is that the isotropic high energy BDL model is the generic past attractor in the state space of FLRW braneworld models. In the state space of Bianchi I models both the BDL model and the inflationary anisotropic Kasner model are past attractors. We then address the question of isotropization using a different approach by studying the evolution of general inhomogeneous and anisotropic perturbations around the spatially flat FLRW braneworld background for three different energy regimes. Here we find that for the high energy braneworld background, the physically relevant anisotropic, inhomogeneous perturbations decay when approaching the initial singularity. We confirm the standard results for thelow energy limit: as in General Relativity, the anisotropy here grows in the past. We conclude that the initial singularity appears to be generically homogeneous and isotropic in the braneworld context.
- ItemOpen AccessWavelet analysis of geomagnetic jerks(2013) de Wit, Tjaart Cornelis; Dunsby, Peter K S; Kotzé, Pieter; Hulot, Gauthier; Gibert, DominiqueGeomagnetic jerks, or secular variation impulses, are abrupt changes in the slope of the first time derivative of the Earth's magnetic field. These changes occur on time scales of the order of a year. It has been demonstrated that the jerks might be more singular than previously supposed; their """"regularity"""" is closer to 1.5 than to 2. Although discovered over 30 years ago, geomagnetic jerks remain poorly understood. Their origin probably lies in the magnetohydrodynamics that is responsible for the maintenance of the Earth's magnetic field produced within the Earth's liquid and convecting core (through a so-called geo-dynamo process). A wavelet tool was programmed in MATLAB and a wavelet analysis applied to detect and characterize singular events, or jerks, in the time series made of monthly mean values of the east component of the geomagnetic field from 45 selected worldwide observatories. The analysis was first performed on various synthetic series made up of a """"main"""" signal of smooth variation intervals separated by singular events, a white noise and an """"external"""" signal made up of the sum of a few harmonic signals. Conditions, in which the singular events could be clearly isolated and their associated """"regularities"""" recovered, are highlighted. Geomagnetic jerks were detected globally in 1969, 1978, 1991 and 1999. Furthermore, geomagnetic jerks are also thought to have also occurred in 1901, 1913 and 1925, but due to the small number of observatories with long enough records to allow for detection during this period, their extent is unclear. Two further geomagnetic jerks were found to have occurred around 1937 and 1952, but due to these events not being detected by all the observatories with records covering this period, these events might not be of the same extent or origin. The results of the geomagnetic jerks detected here and the phase jumps detected in the Chandler wobble are compared and the remarkable coincidence highlighted. The spatio-temporal behaviour of jerks, for example where jerks arrive in the northern hemisphere before the southern hemisphere, is explored. Using k-means clustering, an antipodal relationship is proposed between regional trends in the time delay in the detection of geomagnetic jerks at the surface of the Earth. It is possible that this finding may shed some new light on the origin of geomagnetic jerks. The wavelet analysis was also used to investigate whether the nature of geomagnetic jerks could be classified into one of the following three categories: geomagnetic jerks are the result of some instability starting at the time of the jerk; geomagnetic jerks are the result of some continuous oscillations; that geomagnetic jerks possibly reflect a process ending at the time of the jerk. A startling pattern emerged that suggested that the 1969 jerk corresponded to an event starting at that time, the 1978 jerk corresponding to an event ending at that time, and lastly an event again starting in 1990. This implied that the 1969 and 1978 jerks might have been the result of a common phenomenon starting in 1969 and ending almost a decade later in 1978.