Geometry of deformed special relativity
- Authors: Sixaba, Vuyile
- Date: 2018
- Subjects: Special relativity (Physics) , Quantum gravity , Quantum theory , Geometry , Heisenberg uncertainty principle
- Language: English
- Type: text , Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10962/59478 , vital:27615
- Description: We undertake a study of the classical regime in which Planck's constant and Newton's gravitational constant are negligible, but not their ratio, the Planck mass, in hopes that this could possibly lead to testable quantum gravity (QG) effects in a classical regime. In this quest for QG phenomenology we consider modifications of the standard dispersion relation of a free particle known as deformed special relativity (DSR). We try to geometrize DSR to find the geometric origin of the spacetime and momentum space. In particular, we adopt the framework of Hamilton geometry which is set up on phase space, as the cotangent bundle of configuration space in order to derive a purely phase space formulation of DSR. This is necessary when one wants to understand potential links of DSR with modifications of quantum mechanics such as Generalised Uncertainty Principles. It is subsequently observed that space-time and momentum space emerge naturally as curved and intertwined spaces. In conclusion we mention examples and applications of this framework as well as potential future developments.
- Full Text:
- Date Issued: 2018
- Authors: Sixaba, Vuyile
- Date: 2018
- Subjects: Special relativity (Physics) , Quantum gravity , Quantum theory , Geometry , Heisenberg uncertainty principle
- Language: English
- Type: text , Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10962/59478 , vital:27615
- Description: We undertake a study of the classical regime in which Planck's constant and Newton's gravitational constant are negligible, but not their ratio, the Planck mass, in hopes that this could possibly lead to testable quantum gravity (QG) effects in a classical regime. In this quest for QG phenomenology we consider modifications of the standard dispersion relation of a free particle known as deformed special relativity (DSR). We try to geometrize DSR to find the geometric origin of the spacetime and momentum space. In particular, we adopt the framework of Hamilton geometry which is set up on phase space, as the cotangent bundle of configuration space in order to derive a purely phase space formulation of DSR. This is necessary when one wants to understand potential links of DSR with modifications of quantum mechanics such as Generalised Uncertainty Principles. It is subsequently observed that space-time and momentum space emerge naturally as curved and intertwined spaces. In conclusion we mention examples and applications of this framework as well as potential future developments.
- Full Text:
- Date Issued: 2018
Cosmological structure formation using spectral methods
- Authors: Funcke, Michelle
- Date: 2016
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10962/2969 , vital:20348
- Description: Numerical simulations are becoming an increasingly important tool for understanding the growth and development of structure in the universe. Common practice is to discretize the space-time using physical variables. The discreteness is embodied by considering the dynamical variables as fields on a fixed spatial and time resolution, or by constructing the matter fields by a large number of particles which interact gravitationally (N-body methods). Recognizing that the physical quantities of interest are related to the spectrum of perturbations, we propose an alternate discretization in the frequency domain, using standard spectral methods. This approach is further aided by periodic boundary conditions which allows a straightforward decomposition of variables in a Fourier basis. Fixed resources require a high-frequency cut-off which lead to aliasing effects in non-linear equations, such as the ones considered here. This thesis describes the implementation of a 3D cosmological model based on Newtonian hydrodynamic equations in an expanding background. Initial data is constructed as a spectrum of perturbations, and evolved in the frequency domain using a pseudo-spectral evolution scheme and an explicit Runge-Kutta time integrator. The code is found to converge for both linear and non-linear evolutions, and the convergence rate is determined. The correct growth rates expected from analytical calculations are recovered in the linear case. In the non-linear model, we observe close correspondence with linear growth and are able to monitor the growth on features associated with the non-linearity. High-frequency aliasing effects were evident in the non-linear evolutions, leading to a study of two potential resolutions to this problem: a boxcar filter which adheres to“Orszag’s two thirds rule” and an exponential window function, the exponential filter suggested by Hou and Li [1], and a shifted version of the exponential filter suggested, which has the potential to alleviate high frequency- ripples resulting from the Gibbs’ phenomenon. We found that the filters were somewhat successful at reducing aliasing effects but that the Gibbs’ phenomenon could not be entirely removed by the choice of filters.
- Full Text:
- Date Issued: 2016
- Authors: Funcke, Michelle
- Date: 2016
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10962/2969 , vital:20348
- Description: Numerical simulations are becoming an increasingly important tool for understanding the growth and development of structure in the universe. Common practice is to discretize the space-time using physical variables. The discreteness is embodied by considering the dynamical variables as fields on a fixed spatial and time resolution, or by constructing the matter fields by a large number of particles which interact gravitationally (N-body methods). Recognizing that the physical quantities of interest are related to the spectrum of perturbations, we propose an alternate discretization in the frequency domain, using standard spectral methods. This approach is further aided by periodic boundary conditions which allows a straightforward decomposition of variables in a Fourier basis. Fixed resources require a high-frequency cut-off which lead to aliasing effects in non-linear equations, such as the ones considered here. This thesis describes the implementation of a 3D cosmological model based on Newtonian hydrodynamic equations in an expanding background. Initial data is constructed as a spectrum of perturbations, and evolved in the frequency domain using a pseudo-spectral evolution scheme and an explicit Runge-Kutta time integrator. The code is found to converge for both linear and non-linear evolutions, and the convergence rate is determined. The correct growth rates expected from analytical calculations are recovered in the linear case. In the non-linear model, we observe close correspondence with linear growth and are able to monitor the growth on features associated with the non-linearity. High-frequency aliasing effects were evident in the non-linear evolutions, leading to a study of two potential resolutions to this problem: a boxcar filter which adheres to“Orszag’s two thirds rule” and an exponential window function, the exponential filter suggested by Hou and Li [1], and a shifted version of the exponential filter suggested, which has the potential to alleviate high frequency- ripples resulting from the Gibbs’ phenomenon. We found that the filters were somewhat successful at reducing aliasing effects but that the Gibbs’ phenomenon could not be entirely removed by the choice of filters.
- Full Text:
- Date Issued: 2016
Observational cosmology with imperfect data
- Authors: Bester, Hertzog Landman
- Date: 2016
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: http://hdl.handle.net/10962/463 , vital:19961
- Description: We develop a formalism suitable to infer the background geometry of a general spherically symmetric dust universe directly from data on the past lightcone. This direct observational approach makes minimal assumptions about inaccessible parts of the Universe. The non-parametric and Bayesian framework we propose provides a very direct way to test one of the most fundamental underlying assumptions of concordance cosmology viz. the Copernican principle. We present the Copernicus algorithm for this purpose. By applying the algorithm to currently available data, we demonstrate that it is not yet possible to confirm or refute the validity of the Copernican principle within the proposed framework. This is followed by an investigation which aims to determine which future data will best be able to test the Copernican principle. Our results on simulated data suggest that, besides the need to improve the current data, it will be important to identify additional model independent observables for this purpose. The main difficulty with current data is their inability to constrain the value of the cosmological constant. We show how redshift drift data could be used to infer its value with minimal assumptions about the nature of the early Universe. We also discuss some alternative applications of the algorithm.
- Full Text:
- Date Issued: 2016
- Authors: Bester, Hertzog Landman
- Date: 2016
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: http://hdl.handle.net/10962/463 , vital:19961
- Description: We develop a formalism suitable to infer the background geometry of a general spherically symmetric dust universe directly from data on the past lightcone. This direct observational approach makes minimal assumptions about inaccessible parts of the Universe. The non-parametric and Bayesian framework we propose provides a very direct way to test one of the most fundamental underlying assumptions of concordance cosmology viz. the Copernican principle. We present the Copernicus algorithm for this purpose. By applying the algorithm to currently available data, we demonstrate that it is not yet possible to confirm or refute the validity of the Copernican principle within the proposed framework. This is followed by an investigation which aims to determine which future data will best be able to test the Copernican principle. Our results on simulated data suggest that, besides the need to improve the current data, it will be important to identify additional model independent observables for this purpose. The main difficulty with current data is their inability to constrain the value of the cosmological constant. We show how redshift drift data could be used to infer its value with minimal assumptions about the nature of the early Universe. We also discuss some alternative applications of the algorithm.
- Full Text:
- Date Issued: 2016
A study of spherical solutions in chameleon scalar-tensor theories
- Authors: Mohapi, Neo
- Date: 2014
- Subjects: Scalar field theory , Equivalence principle (Physics) , General relativity (Physics) , Bosons , Dark energy (Astronomy) , Galactic dynamics
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5428 , http://hdl.handle.net/10962/d1013315
- Description: The equivalence principle has proven to be central to theories of gravity, with General Relativity being the simplest and most elegant theory to embody the principle. Most alternative theories of gravity struggle to satisfy the principle and still be distinct from GR. Extensions of cosmological and quantum theories question the irrefutably of the equivalence at every scale. The possibility of an equivalence principle violation at galactic scales would be an exciting prospect. In this thesis, we will carefully examine the equivalence principle through the study of chameleon scalar-tensor theories, this will include solutions for hypothetical stars known as boson stars. Such theories find varied application, especially in cosmology, where they model dark energy and inflation. The AWE hypothesis, is an instance of this. It is a nonuniversally coupled model in which violations of the equivalence principle on galactic scales may be apparent. We investigate spherically symmetric and static solutions within the framework of this theory. The constraints obtained from galactic rotation curves results in values of the couplings that show no significant violation of the equivalence principle or values consistent with a theory of dark energy
- Full Text:
- Date Issued: 2014
- Authors: Mohapi, Neo
- Date: 2014
- Subjects: Scalar field theory , Equivalence principle (Physics) , General relativity (Physics) , Bosons , Dark energy (Astronomy) , Galactic dynamics
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5428 , http://hdl.handle.net/10962/d1013315
- Description: The equivalence principle has proven to be central to theories of gravity, with General Relativity being the simplest and most elegant theory to embody the principle. Most alternative theories of gravity struggle to satisfy the principle and still be distinct from GR. Extensions of cosmological and quantum theories question the irrefutably of the equivalence at every scale. The possibility of an equivalence principle violation at galactic scales would be an exciting prospect. In this thesis, we will carefully examine the equivalence principle through the study of chameleon scalar-tensor theories, this will include solutions for hypothetical stars known as boson stars. Such theories find varied application, especially in cosmology, where they model dark energy and inflation. The AWE hypothesis, is an instance of this. It is a nonuniversally coupled model in which violations of the equivalence principle on galactic scales may be apparent. We investigate spherically symmetric and static solutions within the framework of this theory. The constraints obtained from galactic rotation curves results in values of the couplings that show no significant violation of the equivalence principle or values consistent with a theory of dark energy
- Full Text:
- Date Issued: 2014
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