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Dissertations / Theses on the topic 'Cosmology Mathematical models'
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1
Hervik, Sigbjørn. "Mathematical cosmology : Bianchi models, asymptotics and extra dimensions." Thesis, University of Cambridge, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.616093.
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Campbell, Robert Alan. "Inhomogeneous conformal cosmological models /." Title page, contents and summary only, 1985. http://web4.library.adelaide.edu.au/theses/09PH/09phc1888.pdf.
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Dechant, Pierre-Philippe. "Models of the early universe." Thesis, University of Cambridge, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.609618.
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Ng, Shao-Chin Cindy. "Cosmological models with quintessence : dynamical properties and observational constraints." Title page, table of contents and abstract only, 2001. http://web4.library.adelaide.edu.au/theses/09PH/09phn5758.pdf.
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Bibliography: leaves 100-106. Studies different models of "quintessence", in particular, a quintessence arising from an ultra-light pseudo Nambu-Goldstone boson. Overviews dynamical properties for these models using phase-space analyses to study attractor and tracker solutions. Studies high-redshift type Ia supernovae constraints on these models. Studies the impact of a simple phenomenological model for supernovae luminosity evolution on the PNGB models and the potentials of a future supernovae data set to discriminate the PNGB models over the other quintessence models. Studies gravitational lensing statistics of high luminosity quasars upon the quintessence models.
5
Luo, Xianghui 1983. "Symmetries of Cauchy Horizons and Global Stability of Cosmological Models." Thesis, University of Oregon, 2011. http://hdl.handle.net/1794/11543.
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ix, 111 p.This dissertation contains the results obtained from a study of two subjects in mathematical general relativity. The first part of this dissertation is about the existence of Killing symmetries in spacetimes containing a compact Cauchy horizon. We prove the existence of a nontrivial Killing symmetry in a large class of analytic cosmological spacetimes with a compact Cauchy horizon for any spacetime dimension. In doing so, we also remove the restrictive analyticity condition and obtain a generalization to the smooth case. The second part of the dissertation presents our results on the global stability problem for a class of cosmological models. We investigate the power law inflating cosmological models in the presence of electromagnetic fields. A stability result for such cosmological spacetimes is proved. This dissertation includes unpublished co-authored material.
Committee in charge: James Brau, Chair; James Isenberg, Advisor; Paul Csonka, Member; John Toner, Member; Peng Lu, Outside Member
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Foster, Scott. "Singularity structure of scalar field cosmologies /." Title page, contents and abstract only, 1996. http://web4.library.adelaide.edu.au/theses/09PH/09phf757.pdf.
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Howell, Eric John. "The characterization and temporal distribution of cosmological gravitational wave treatments." University of Western Australia. School of Physics, 2009. http://theses.library.uwa.edu.au/adt-WU2010.0095.
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[Truncated abstract] As gravitational wave detectors approach sensitivities that will allow observations to become routine, astrophysics lies on the cusp of an exciting new era. Potential sources will include transients such as merging neutron stars and black holes, supernova explosions or the engines that power gamma-ray bursts. This thesis will be devoted to the astrophysical gravitational wave background signal produced by cosmological populations of such transient signals. Particular attention will be devoted to the observation-time dependence imposed on the individual sources that accumulate to produce a gravitational wave background signal. The ultimate aim is to determine what information is encoded in the temporal evolution of such a signal. To lay the foundations for further investigation, the stochastic gravitational wave background signal from neutron star birth throughout the Universe has been calculated. In view of the uncertainties in both the single-source emissions and source rate histories, several models of each are employed. The results show that that the resulting signals are only weakly dependent on the source-rate evolution model and that prominent features in the single-source spectra can be related to the background spectra. In comparison with previous studies, the use of relativistic single-source gravitational wave waveforms rather than Newtonian models and a more slowly evolving source-rate density results in a 1 { 2 order of magnitude reduction in signal. ... A comparison with the more commonly used brightness distribution of events shows that when applying both methods to a data stream containing a background of Gaussian distributed false alarms, the brightness distribution yielded lower standard errors, but was biased by the false alarms. In comparison, a fitting procedure based on the time evolution of events was less prone to errors resulting from false alarms, but as fewer events contributed to the data, had a lower resolution. In further support of the time dependent signature of transient events, an alternative technique is fiapplied to the same source population. In this case, the local rate density is probed by measuring the statistical compatibility of the filtered data against synthetic time dependent data. Although this method is not as compact as the fitting procedure, the rate estimates are compatible. To further investigate how the observation time dependence of transient populations can be used to constrain global parameters, the method is applied to Swift long gamma-ray burst data. By considering a distribution in peak °ux rather than a gravitational wave amplitude, gamma-ray bursts can be considered as a surrogate for resolved gravitational wave transients. For this application a peak °ux{observation time relation is described that takes the form of a power law that is invariant to the luminosity distribution of the sources. Additionally, the method is enhanced by invoking time reversal invariance and the temporal cosmological principle. Results are presented to show that the peak °ux{observation time relation is in good agreement with recent estimates of source parameters. Additionally, to show that the intrinsic time dependence allows the method to be used as a predictive tool, projections are made to determine the upper limits in peak °ux of future gamma-ray burst detections for Swift.
8
Osano, Bob Otieno. "Beyond the standard model of cosmology : a perturbative approach." Doctoral thesis, University of Cape Town, 2007. http://hdl.handle.net/11427/4918.
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Includes abstract.Includes bibliographical references (p. 171-185).
This 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.
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Delbem, Nilton Flávio [UNESP]. "Introdução matemática aos modelos cosmológicos." Universidade Estadual Paulista (UNESP), 2010. http://hdl.handle.net/11449/94340.
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Made available in DSpace on 2014-06-11T19:27:09Z (GMT). No. of bitstreams: 0
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delbem_nf_me_rcla.pdf: 885461 bytes, checksum: 9ba35dff1d53b0378c1e134087c575b7 (MD5)Universidade Estadual Paulista (UNESP)
Esta dissertação tem a proposta de organizar, discutir e apresentar de maneira precisa os conceitos matemáticos de variedade diferenciável e de tensores envolvidos no estudo da Cosmologia sob o ponto de vista da Teoria da Relatividade Geral para o modelo de Friedmann-Lemaître-Robertson-Walker. Busca-se assim apresentar um texto didático que possa ser utilizado tanto nos cursos de graduação em Matemática como de Física para uma disciplina optativa de Introdução Matemática à Cosmologia
The goal of this dissertation is to organize and discuss in a rigorous way the mathematical concepts of manifolds and tensors needed to the study of Cosmology and the Friedmann-Lemaître-Robertson-Walker model under the point of view of the General Relativity. In this way, this dissertation was written as textbook that could be used in an undergraduate course of Physics and Mathematics
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Delbem, Nilton Flávio. "Introdução matemática aos modelos cosmológicos /." Rio Claro : [s.n.], 2010. http://hdl.handle.net/11449/94340.
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Orientador: Wladimir SeixasBanca: Manoel Borges Ferreira Neto
Banca: Henrique Lazari
Resumo: Esta dissertação tem a proposta de organizar, discutir e apresentar de maneira precisa os conceitos matemáticos de variedade diferenciável e de tensores envolvidos no estudo da Cosmologia sob o ponto de vista da Teoria da Relatividade Geral para o modelo de Friedmann-Lemaître-Robertson-Walker. Busca-se assim apresentar um texto didático que possa ser utilizado tanto nos cursos de graduação em Matemática como de Física para uma disciplina optativa de Introdução Matemática à Cosmologia
Abstract: The goal of this dissertation is to organize and discuss in a rigorous way the mathematical concepts of manifolds and tensors needed to the study of Cosmology and the Friedmann-Lemaître-Robertson-Walker model under the point of view of the General Relativity. In this way, this dissertation was written as textbook that could be used in an undergraduate course of Physics and Mathematics
Mestre
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Gebbie, Timothy John. "Fluid and gas models in FLRW and almost FLRW universes." Master's thesis, University of Cape Town, 1996. http://hdl.handle.net/11427/17936.
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Includes bibliographical references.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.
12
Mustapha, Nazeem. "Aspects of a spherically symmetric model of the post-decoupling universe." Master's thesis, University of Cape Town, 1997. http://hdl.handle.net/11427/17524.
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Bibliography: pages 84-88.The central aim of this thesis is to consider aspects of the spherically symmetric Lemaitre-Tolman-Bondi (LTB) solution as a model of the post-decoupling universe. To do this comprehensively is a massive task and is not our aim here. Indeed, far from it, we will concentrate on select instances of this programme and attempt in some places to indicate possibilities for further study. There are many solutions of the EFE which satisfy what we consider to be 'reasonable criteria' for a cosmology and others that do not. The LTB solution may be accepted as a reasonable cosmological model because ■ It allows non-empty solutions. ■ It allows expanding solutions. ■ It has a homogeneous and isotropic limit. ■ It allows for inhomogeneity.
13
Fay, Stéphane. "Cosmologies spatialement homogènes en théories tenseur-scalaires." Phd thesis, Université Paris-Diderot - Paris VII, 2004. http://tel.archives-ouvertes.fr/tel-00008063.
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Cette thèse étudie les modèles cosmologiques homogènes mais anisotropes en théories tenseur-scalaire. Son but est de déterminer les propriétés que doivent avoir ces théories afin que ces modèles possèdent asymptotiquement les caractéristiques dynamiques de notre Univers actuel ou apportent une réponse à certains de ses problèmes comme ceux de la constante cosmologique. La première partie de la thèse est consacrée à une introduction historique et à une justification physique des théories tenseur-scalaires de la gravitation et des modèles cosmologiques anisotropes. La seconde partie détaille les notions mathématiques nécessaires à la compréhension de cette thèse, à savoir la classification des cosmologies anisotropes et l'écriture des équations de champs dans le formalisme Lagrangien et Hamiltonien. La troisième partie est composée d'une série de sept articles montrant comment l'on peut parvenir à contraindre les théories tenseur-scalaires à l'aide de solutions exactes, en exigeant que l'Univers possède certains comportements dynamiques (expansion, inflation, etc), soit dépourvu de singularité ou possède une symétrie de Noether. Dans la quatrième partie, le processus d'isotropisation des modèles anisotropes est étudié en détail pour de nombreuses classes de théories tenseur-scalaires. Des contraintes nécessaires à l'isotropisation, les comportements asymptotiques des fonctions métriques et du potentiel au voisinage de cet état sont déterminés et le phénomène de quintessence analysé. Un lien entre les champs scalaires quintessents qui pourraient peupler notre Univers et la matière noire dans les galaxies (1 article) est montré. Les six articles à l'origine de ce chapitre sont reproduits dans la sixième partie qui tient lieu d'appendice. Nous concluons dans la cinquième partie.
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Holgersson, David. "Lanczos potentialer i kosmologiska rumtider." Thesis, Linköping University, Department of Mathematics, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-2582.
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We derive the equation linking the Weyl tensor with its Lanczos potential, called the Weyl-Lanczos equation, in 1+3 covariant formalism for perfect fluid Bianchi type I spacetime and find an explicit expression for a Lanczos potential of the Weyl tensor in these spacetimes. To achieve this, we first need to derive the covariant decomposition of the Lanczos potential in this formalism. We also study an example by Novello and Velloso and derive their Lanczos potential in shear-free, irrotational perfect fluid spacetimes from a particular ansatz in 1+3 covariant formalism. The existence of the Lanczos potential is in some ways analogous to the vector potential in electromagnetic theory. Therefore, we also derive the electromagnetic potential equation in 1+3 covariant formalism for a general spacetime. We give a short description of the necessary tools for these calculations and the cosmological formalism we are using.
15
Rainsford, Tamath Jane. "Newtonian and post-Newtonian cosmology / Tamath Rainsford." 2000. http://hdl.handle.net/2440/19818.
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Includes bibliographical references (leaves 168-179).xiii, 179 leaves ; 30 cm.
Title page, contents and abstract only. The complete thesis in print form is available from the University Library.
Finds that the post-Newtonian approximation seems to be a better approximation of the general relativistic theory than the standard Newtonian theory.
Thesis (Ph.D.)--Adelaide University, Dept. of Physics and Mathematical Physics, 2001
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Rainsford, Tamath Jane. "Newtonian and post-Newtonian cosmology / Tamath Rainsford." Thesis, 2000. http://hdl.handle.net/2440/19818.
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Includes bibliographical references (leaves 168-179).xiii, 179 leaves ; 30 cm.
Finds that the post-Newtonian approximation seems to be a better approximation of the general relativistic theory than the standard Newtonian theory.
Thesis (Ph.D.)--Adelaide University, Dept. of Physics and Mathematical Physics, 2001
17
Kgathi, Matome Abiel. "Cosmologies with causal bulk viscosity." Thesis, 1996. https://hdl.handle.net/10539/26146.
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A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg,
in fulfilment of the requirements for the degree of Doctor of Philosophy.
JohannesburgIn this thesis we investigate the evolution of viscous FRW cosmological models for two different constitutive equations for the bulk viscous pressure a, namely (Abbreviation abstract)
Andrew Chakane 2018
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Ng, Shao-Chin Cindy. "Cosmological models with quintessence : dynamical properties and observational constraints / Shao-Chin Cindy Ng." Thesis, 2001. http://hdl.handle.net/2440/21740.
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Bibliography: leaves 100-106.v, 107 leaves : ill. ; 30 cm.
Studies different models of "quintessence", in particular, a quintessence arising from an ultra-light pseudo Nambu-Goldstone boson. Overviews dynamical properties for these models using phase-space analyses to study attractor and tracker solutions. Studies high-redshift type Ia supernovae constraints on these models. Studies the impact of a simple phenomenological model for supernovae luminosity evolution on the PNGB models and the potentials of a future supernovae data set to discriminate the PNGB models over the other quintessence models. Studies gravitational lensing statistics of high luminosity quasars upon the quintessence models.
Thesis (Ph.D.)--University of Adelaide, Dept. of Physics and Mathematical Physics, 2001
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Foster, Scott. "Singularity structure of scalar field cosmologies / Scott Foster." Thesis, 1996. http://hdl.handle.net/2440/18744.
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Errata inserted opposite p.177.Bibliography: p. 173-177.
x, 177 p. : ill. ; 30 cm.
The classical dynamical structure of cosomological models in which the matter content of the universe consists of a scalar field with arbitrary non-negative potential is analyzed in full. (abstract)
Thesis (Ph.D.)--University of Adelaide, Dept. of Physics and Mathematical Physics, 1996?
20
Okabe, Takahide. "Spatially-homogeneous Vlasov-Einstein dynamics." 2008. http://hdl.handle.net/2152/18198.
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The influence of matter described by the Vlasov equation, on the evolution of anisotropy in the spatially-homogeneous universes, called the Bianchi cosmologies, is studied. Due to the spatial-homogeneity, the Einstein equations for each Bianchi Type are reduced to a set of coupled ordinary differential equations, which has Hamiltonian form with the metric components being the canonical coordinates. In the vacuum Bianchi cosmologies, it is known that a curvature potential, which comes from the symmetries of the three-dimensional Lie groups, determines the basic properties of the evolution of anisotropy. In this work, matter potentials are constructed for Vlasov matter. They are obtained by first introducing a new matter action principle for the Vlasov equation, in terms of a conjugate pair of functions, and then enforcing the symmetry to obtain a reduction. This yields an expression for the matter potential in terms of the phase space density, which is further reduced by assuming cold streaming matter. Some vacuum Bianchi cosmologies and Type I with Vlasov matter are compared. It is shown that the Vlasov-matter potential for cold streaming matter results in qualitatively distinct dynamics from the well-known vacuum Bianchi cosmologies.text
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Ericksson, Geoffery Brian. "The isotropic singularity in cosmological models." Phd thesis, 2002. http://hdl.handle.net/1885/148635.
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Moodley, Darell. "Bayesian analysis of cosmological models." Thesis, 2010. http://hdl.handle.net/10413/5865.
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In this thesis, we utilise the framework of Bayesian statistics to discriminate between models
of the cosmological mass function. We first review the cosmological model and the formation
and distribution of galaxy clusters before formulating a statistic within the Bayesian framework,
namely the Bayesian razor, that allows model testing of probability distributions. The Bayesian
razor is used to discriminate between three popular mass functions, namely the Press-Schechter,
Sheth-Tormen and normalisable Tinker models. With a small number of particles in the simulation,
we find that the simpler model is preferred due to the Occam’s razor effect, but as the size of
the simulation increases the more complex model, if taken to be the true model, is preferred. We
establish criteria on the size of the simulation that is required to decisively favour a given model
and investigate the dependence of the simulation size on the threshold mass for clusters, and
prior probability distributions. Finally we outline how our method can be extended to consider
more realistic N-body simulations or be applied to observational data.Thesis (M.Sc.)-University of KwaZulu-Natal, Westville, 2010.
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Naidoo, Ramsamy. "Cosmological models and the deceleration parameter." Thesis, 1992. http://hdl.handle.net/10413/5819.
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In this thesis we utilise a form for the Hubble constant first proposed by Berman
(1983) to study a variety of cosmological models. In particular we investigate the
Robertson-Walker spacetimes, the Bianchi I spacetime, and the scalar-tensor theory
of gravitation of Lau and Prokhovnik (1986). The Einstein field equations with variable
cosmological constant and gravitational constant are discussed and the Friedmann
models are reviewed. The relationship between observation and the Friedmann
models is reviewed. We present a number of new solutions to the Einstein
field equations with variable cosmological constant and gravitational constant in the
Robertson-Walker spacetimes for the assumed form of the Hubble parameter. We explicitly
find forms for the scale factor, cosmological constant, gravitational constant,
energy density and pressure in each case. Some of the models have an equation of
state for an ideal gas. The gravitational constant may be increasing in certain regions
of spacetime. The Bianchi I spacetime, which is homogeneous and anisotropic,
is shown to be consistent with the Berman (1983) law by defining a function which
reduces to the scale factor of Robertson-Walker. We illustrate that the scalar-tensor
theory of Lau and Prokhovnik (1986) also admits solutions consistent with the Hubble
variation proposed by Berman. This demonstrates that this approach is useful
in seeking solutions to the Einstein field equations in general relativity and alternate
theories of gravity.Thesis (M.Sc.)-University of Natal, 1992.
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Moodley, Kavilan. "Aspects of spherically symmetric cosmological models." Thesis, 1998. http://hdl.handle.net/10413/3909.
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In this thesis we consider spherically symmetric cosmological models when the shear
is nonzero and also cases when the shear is vanishing. We investigate the role of
the Emden-Fowler equation which governs the behaviour of the gravitational field.
The Einstein field equations are derived in comoving coordinates for a spherically
symmetric line element and a perfect fluid source for charged and uncharged matter.
It is possible to reduce the system of field equations under different assumptions to
the solution of a particular Emden-Fowler equation. The situations in which the
Emden-Fowler equation arises are identified and studied. We analyse the Emden-Fowler
equation via the method of Lie point symmetries. The conditions under which
this equation is reduced to quadratures are obtained. The Lie analysis is applied to
the particular models of Herlt (1996), Govender (1996) and Maharaj et al (1996) and
the role of the Emden-Fowler equation is highlighted. We establish the uniqueness
of the solutions of Maharaj et al (1996). Some physical features of the Einstein-Maxwell
system are noted which distinguishes charged solutions. A charged analogue
of the Maharaj et al (1993) spherically symmetric solution is obtained. The Gutman-Bespal'ko
(1967) solution is recovered as a special case within this class of solutions
by fixing the parameters and setting the charge to zero. It is also demonstrated
that, under the assumptions of vanishing acceleration and proper charge density,
the Emden-Fowler equation arises as a governing equation in charged spherically
symmetric models.Thesis (M.Sc.)-University of Natal, Durban, 1998.
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Boero, Ezequiel Fernando. "Lentes gravitacionales y modelos geométricos para el estudio de sistemas astrofı́sicos en el contexto cosmológico." Doctoral thesis, 2017. http://hdl.handle.net/11086/5841.
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Tesis (Doctor en Física)--Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía, Física y Computación, 2017.En esta tesis se abordan tres temáticas principales: el uso de modelos geométricos para la descripción de sistemas astrofísicos, el desarrollo de un nuevo formalismo en la teoría de lentes gravitacionales que extiende ideas de trabajos previos al contexto cosmológico y, por último, la cuestión de cómo realizar promedios en el marco de la relatividad general. Uno de los motivos principales que persigue este trabajo es el de discutir la forma en que el estudio del contenido de materia en el Universo es abordado. En particular, aquí indagamos nuevas posibilidades de descripción de la fenomenología asociada al problema de la masa faltante presentando nuevas herramientas desde el área de la teoría de lentes gravitacionales débiles sobre un espaciotiempo de fondo cosmológico. Las mismas permiten un modelado mucho más general de la geometría de la lente que aquellas que son habitualmente consideradas y se basan esencialmente en una concepción Newtoniana de la distribución de materia.
This doctorate thesis deals with three main topics: the use of geometric models for the description of astrophysical systems, the development of a new formalism within the theory of gravitational lensing which improves and generalize previous ideas already presented to the cosmological context and, finally the problem of how to perform averages in the conceptual framework of general relativity. One of the main motivation of this work is to discuss the way in which the study of the matter content in the Universe is addressed. In particular, here we investigate new possibilities of description of the phenomenology related to the missing mass problem. We present new tool from the subject of weak gravitational lensing over a cosmological background spacetime. Such tools allow a much more general modelling of the lens geometry than those that are usually considered and which are based essentially on a Newtonian concepton of the matter distribution.