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" Qualitative analysis of cosmological models "
R. J. van den Hoogen
A. A. Coley
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Latin Dissertation
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English
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| Record Number
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1113472
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TLpq304244295
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| Main Entry
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A. A. Coley
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R. J. van den Hoogen
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| Title & Author
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Qualitative analysis of cosmological models\ R. J. van den HoogenA. A. Coley
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| College
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Dalhousie University (Canada)
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| Date
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1995
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| student score
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1995
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| Degree
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Ph.D.
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| Page No
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223
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| Abstract
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It is proven that if one desires self-similar asymptotic limit points in spatially homogeneous cosmological models, then dimensionless equations of state are necessary. The converse is also true; it is proven that dimensionless equations of state imply self-similar asymptotic limit points. These results are subsequently used in the investigation of various cosmological models. Dimensionless equations of state and a set of dimensionless, expansion-normalized variables are used to reduce the dimension of the system describing the evolution of spatially homogeneous imperfect fluid cosmological models. Since the resulting system is an autonomous system of ordinary differential equations, dynamical systems techniques can be used to determine its qualitative behaviour. In particular, viscous fluid Bianchi type V models with heat conduction are analyzed and compared using both the Eckart and the 'Truncated' Israel-Stewart theories of irreversible thermodynamics, and Friedmann-Robertson-Walker models with bulk viscosity are studied and compared using both 'Truncated' and the 'Full' Israel-Stewart theories of irreversible thermodynamics. Furthermore, the dynamical system describing the evolution of the viscous fluid isotropic curvature models is given. The qualitative behaviours of the first order Eckart theory can be very different from the qualitative behaviours of the second order Israel-Stewart theories. It is found that in the Eckart theory the anisotropic Bianchi type I and V models always isotropize, however, the same is not true in the second order Israel-Stewart theories where it is shown that they need not isotropize. It is also found that bulk viscous inflation is possible in all of these theories. Finally, it is demonstrated that there can be more entropy produced in the Truncated Israel-Stewart theory than in the Eckart theory. The only scalar field models that allow self-similar asymptotic limit points are those in which the potential is either of exponential form or zero. Using the property that the dynamical system describing the spatially homogeneous models can be rewritten in terms of dimensionless variables, a class of spatially homogeneous models are investigated. A general result pertaining to the isotropization and inflation of Bianchi models with an exponential potential is obtained. It is found that the only Bianchi models that can possibly inflate and isotropize when usdk\sp2>2usd are those of Bianchi types, I, V, VII or IX. One of the criteria that breaks the self-similarity condition is the existence of a scalar field with a non-exponential potential. In isotropic and spatially homogeneous models with a quadratic potential, it is shown that oscillatory behaviour is possible. A survey of various models exhibiting this oscillatory behaviour is given and examples demonstrating this oscillatory behaviour, are found. Also, a qualitative analysis of a cosmological model arising from a soft-inflationary scenario is done and the asymptotic behaviour is determined.
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entropy
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equations of state
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Mathematics
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Pure sciences
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