Quinta esencia con acoplamiento no mínimo a la materia oscura desde la perspectiva de los sistemas dinámicos
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Fecha
2008-07-02
Autores
González Morales, Dania
Nápoles Alvarez, Yunelsy
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Editor
Universidad Central “Marta Abreu” de Las Villas
Resumen
En esta tesis se investiga un modelo cosmológico de quintaesencia con acoplamiento no mínimo a la materia oscura. Se caracteriza el comportamiento asintótico del modelo hacia el pasado y hacia el futuro utilizando variables adecuadas en cada caso. Se demuestra que bajo determinadas condiciones sobre la función de acoplamiento y del potencial la densidad de energía del fluido de fondo y la energía cinética del campo escalar son despreciables en el futuro, dominando la energía potencial del campo escalar. De esta manera el universo evoluciona hacia una solución de vacío de tipo de de Sitter. Se demuestra que el campo escalar es casi siempre no acotado hacia el pasado (aunque no se excluye la posibilidad de que el campo escalar también diverja hacia el futuro). Asumiendo entonces algunas hipótesis de regularidad sobre el potencial y la función de acoplamiento, se construye e investiga un sistema dinámico apropiado para estudiar el comportamiento del modelo cerca de la singularidad inicial. Demostramos que para una clase muy general de modelos, la estructura asintótica de las soluciones en el pasado es simple y regular y que esta estructura es independiente de los detalles exactos del potencial, el acoplamiento y la materia de fondo presente. Adicionalmente se obtienen puntos críticos que corresponden a soluciones escalantes de gran importancia en cosmología.
In this thesis we investigate a quintessential cosmological model with non minimal coupling to dark matter. By considering appropriate variables we analyze qualitatively and characterize both past and future attractors. By considering well suited hypothesis on the potential and coupling functions we prove that the future attractor corresponds to the vacuum de Sitter ́s solution. Those solutions are characterized by negligible contributions of the kinetic and background energy densities to the total energy density. So, potential energy dominates. By using Hubble-normalized variables we find that the scalar field diverges into the past. This fact does not preclude the divergence of the scalar field towards the future. It is well-kown that in the initial singularity the scalar field diverges. So, in order to study the dynamics close to the initial singularity we must study that limit. With this purp ose we assume some regularity conditions on the potential and coupling function. We prove, for a general class of models, that the asymptotic structure of solutions towards the past is simple and regular. Also, it is independent on the feature s of the potential, the coupling function and the background matter. Additionally, we find the existence of scaling solutions in this limit. These solutions are of great importance in cosmology.
In this thesis we investigate a quintessential cosmological model with non minimal coupling to dark matter. By considering appropriate variables we analyze qualitatively and characterize both past and future attractors. By considering well suited hypothesis on the potential and coupling functions we prove that the future attractor corresponds to the vacuum de Sitter ́s solution. Those solutions are characterized by negligible contributions of the kinetic and background energy densities to the total energy density. So, potential energy dominates. By using Hubble-normalized variables we find that the scalar field diverges into the past. This fact does not preclude the divergence of the scalar field towards the future. It is well-kown that in the initial singularity the scalar field diverges. So, in order to study the dynamics close to the initial singularity we must study that limit. With this purp ose we assume some regularity conditions on the potential and coupling function. We prove, for a general class of models, that the asymptotic structure of solutions towards the past is simple and regular. Also, it is independent on the feature s of the potential, the coupling function and the background matter. Additionally, we find the existence of scaling solutions in this limit. These solutions are of great importance in cosmology.
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Palabras clave
Modelo Cosmológico de Quintaesencia, Acoplamiento no Mínimo, Comportamiento Asintótico, Materia Oscura, Campo Escalar, Sistemas Dinámicos