Browsing by Author "Clarkson, Chris"

Now showing 1 - 9 of 9
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    A covariant approach to gravitational lensing
    (2004) De Swardt, Bonita; Dunsby, Peter K S; Clarkson, Chris
    The 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.
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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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    General relativistic electrodynamics with applications in cosmology and astrophysics
    (2005) Betschart, Gerold; Dunsby, Peter K S; Marklund, Mattias; Clarkson, Chris; Zunckel, Caroline; Servin, Martin; Tsagas, Christos
    Includes bibliographical references.
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    The influence of structure formation on the evolution of the universe
    (2013) Umeh, Obinna; Clarkson, Chris; Ellis, GFR
    The next generation of telescopes will usher in a new era of precision cosmology capable of determining key parameters of a cosmological model to percent level and beyond. For this to be effective, the theoretical model must be understood to at least the same level of precision. A range of subtle physical spacetime effcts remain to be explored theoretically, for example, the effect of backreaction on cosmological observables. A good understanding of this effect is paramount given that it is a consequence of any space-time theory of gravity. We provide a comprehensive study of this effect from the perspective of geometric averaging on a hyper-surface and averaging on the celestial sphere. We concentrate on Friedmann-Lemaitre-Robertson-Walker spacetime with small perturbation up to non-linear order . This enables us to quantify by how much this effect could change the standard model interpretation of the universe. We study in great detail key parameters of the standard model, Hubble rate, deceleration parameter and area distance.
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    Non-linear effects in the universe
    (2009) Lu, Hui-Ching; Clarkson, Chris
    One of the distinct trends in modern cosmology is in testing its theoretical aspects against the high precision data available in recent years. Although the standard cosmological model has already shown certain satisfactory results in matching the data from observations of the Cosmic Microwave Background and Large Scale Structure, we are by far unable to be convinced of its ability in describing the complete nature of the universe. Therefore, detailed study has to be done in the theory of higher order cosmological perturbation to enable us the ability in describing the non-linear aspects of the universe.
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    On the evolution of large-scale structure in a cosmic void
    (2014) February, Sean Phillip; Clarkson, Chris; Ellis, GFR
    Future large-scale structure surveys are expected to pin-down the properties of dark energy significantly more by mapping the cosmic web to unprecedented precision. To take advantage of such state-of-the-art technologies, the evermore accurate modelling of structure formation is absolutely necessary. While relativistic linear and non-relativistic (Newtonian) non-linear effects have been well established (although improvements are still being made), a fairly unexplored area is the impact of relativistic, non-linear effects on structure formation. As an attempt in this direction, we consider linear perturbations of a Lemaître-Tolman-Bondi (LTB) spacetime. LTB models are spherically symmetric but inhomogeneous exact dust solutions to the Einstein field equations. They are known to accommodate most observations of the background universe without dark energy. In this work we present a new numerical code to solve the set of coupled partial differential equations that describe the evolution of the (polar) perturbations, test it in the case of a Hubble-scale LTB void, and demonstrate its excellent stability and convergence. We then explore the solutions for a variety of generic initial conditions. The variable that closely resembles the Newtonian potential is shown to excite propagating (tensor) as well as rotational (vector) modes at the percent-level. Comparing our results to that which ignores the full coupling, we estimate percent-level corrections to the amplitude of the galaxy correlation function when only the scalar degrees of freedom are included. In addition, we showed that the anisotropic correlation function can nevertheless be used as a test of the Copernican Principle. Note that our code has applications to other scenarios as well in which spherical symmetry is a good approximation, such as the lensing of gravitational waves by intervening halos/voids.
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    Relativistic corrections to weak lensing convergence
    (2016) Andrianomena, Sambatra Hagatiana; Clarkson, Chris
    A fundamental issue in modern science is the dark energy problem - the apparent accelerating expansion of the universe. Many cosmological observations of the Cosmic Microwave Background (CMB), Baryon Acoustic Oscillation (BAO) and weak lensing have been carried out to try to understand the nature of this repulsive dark force. With the advent of advanced experiments like the Square Kilometer Array we enter the era of precision cosmology where measurements of effects such as weak lensing will be achieved at a sub percent level, implying strong constraints on dark energy. The full picture of weak lensing includes linear and non-linear correction terms to its standard formula. In this thesis we address the questions: Are some of these effects detectable? Under which conditions can we safely neglect them such that the analysis of future weak lensing observations is not biased? Induced by gravity, peculiar velocity of galaxies can potentially be used to probe the growth of structure in our universe. Peculiar velocities induce a lensing-like effect, which we consider as Doppler magnification. By developing new statistical tools which are based on Doppler magnification, we investigate the dark energy problem. These new statistical probes also enable us to explore the viability of other theories that attempt to account for the apparent acceleration of the cosmic expansion by modifying Einstein's General Relativity.
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    Rendering dark energy void
    (2009) February, Sean Phillip; Clarkson, Chris
    The current model of cosmology, the Friedman-Lemaitre-Robertson-Valker model, assumes that the universe is approximately homogeneous and isotropic on very large scales. Further assuming flatness and dark energy in the form of Einstein's cosmological constant A then implies that the latter contributes roughly 73% of the total energy of the universe, cold dark matter (CD'I) 23SiC, and baryons, the matter we are made, only 4%.
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    Topics in relativistic cosmology: Cosmology on the past lightcone and in modified gravitation
    (2018) Elmardi, Maye Y A; Clarkson, Chris; Larena, Julien
    The lightcone gauge is a set of what are called the observational coordinates adapted to our past lightcone. We develop this gauge by producing a perturbed spacetime metric that describes the geometry of our past lightcone where observations are usually obtained. We then connect the produced observational metric to the perturbed Friedmann-Lemaître-Robertson-Walker metric in the standard general gauge or what is the so-called 1+3 gauge. We derive the relations between these perturbations of spacetime in the observational coordinates and those perturbations in the standard metric approach, as well as the dynamical equations for the perturbations in observational coordinates. We also calculate the observables in the lightcone gauge and rederive them in terms of Bardeen potentials to first order. A verification is made of the observables in the perturbed lightcone gauge with those in the standard gauge. The advantage of the method developed is that the observable relations are simpler than in the standard formalism. We use the perturbed lightcone gauge in galaxy surveys and galaxy number density contrast. The significance of the new gauge is that by considering the null-like light propagations, the calculations are much simpler since angular deviations are not considered. Standard cosmology based on General Relativity is generally believed to have serious shortcomings, such as the unexplained issues of dark matter and dark energy. As a remedy, many alternative theories of gravitation have been proposed over the years, one of which is ƒ(R) gravity. We explore classes of irrotational-fluid cosmological models in the context of ƒ(R) gravity in an attempt to put some theoretical and mathematical restrictions on the form of the ƒ(R) gravitational Lagrangian. In particular, we investigate the consistency of the linearised dust models for shear-free cases as well as in the limiting cases when either the gravito-magnetic or gravito-electric components of the Weyl tensor vanish. We also discuss the existence and consistency of classes of non-expanding irrotational spacetimes in ƒ(R)-gravity. Furthermore, we explore exact ƒ(R) gravity solutions that mimic Chaplygin-gas inspired ΛCDM cosmology. Starting with the original, generalized and modified Chaplygin gas equations of state, we reconstruct the forms of ƒ(R) Lagrangians. The resulting solutions are generally quadratic in the Ricci scalar, but have appropriate ΛCDM solutions in limiting cases. These solutions, given appropriate initial conditions, can be potential candidates for scalar field-driven early universe expansion (in ation) and dark energy-driven late-time cosmic acceleration.