Quantum fluctuations and cosmic inflation
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Date
2005-06-28
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Universität Dortmund
Abstract
Diese Doktorarbeit behandelt zwei Themengebiete: das inflationäre Störungsspektrum und die Vorerwärmungsphase im Anschluss an die Hybrid-Inflation. Quantenfluktuationen im inflationären Universum bilden einen natürlichen Mechanismus zur Erzeugung primordialer Störungen, aus denen kosmische Strukturen entstehen. In einem Teil der Arbeit präsentieren wir ein mathematisch kontrolliertes, semi-analytisches Näherungsverfahren zur Berechnung des inflationären Störungsspektrums für skalare und tensorielle Störungen. Detaillierte Berechnungen des Leistungsspektrums, des spektralen Index und anderer Observablen werden durchgeführt, zu führender und nächstführender Ordnung in einer uniformen Approximation sowie mit Fehlerschranken. Diese Berechnungen verzichten auf explizite 'slow-roll'-Annahmen. Zusammen mit einer einfach zu implementierenden Erweiterung der führenden Ordnung, welche wir aus dem detaillierten Verständnis nächstführender Ordnungen gewinnen, wird die ausgezeichnete Genauigkeit des Verfahrens uniformer Approximationen anhand verschiedener Beispiele demonstriert. Die Ergebnisse werden mit exakten numerischen Resultaten und der slow-roll-Näherung verglichen. Die vorgestellten Techniken sind zusammen mit den entwickelten Programmen von unmittelbarem Nutzen zur theoretisch präzisen Berechnung von primordialen Störungsspektren sowie der Einschränkung von einigen inflationären Modellen bzw. Modellparametern. Weiterhin werden einige Aspekte der Vorerwärmungsphase im Anschluss an die Inflation im Rahmen des sogenannten Hybrid-Modells detailliert untersucht. Die inflationäre Expansion endet in diesem Modell mit einem Phasenübergang eines symmetriebrechenden Feldes. Dieses symmetriebrechende Feld ist während der inflationären Phase in einem falschen Vakuumzustand gefangen und vollführt, dynamisch destabilisiert, einen Übergang zum wahren Vakuum. Indem eine Blasen-Resummation der Propagatoren formuliert wird, kann der wichtige Einfluss von Rückwirkungen der Quantenfluktuationen explizit berücksichtigt werden. Das Problem der Renormierung in einem System mit mehreren gekoppelten Kanälen wird gelöst. In detaillierten numerischen Simulationen wird so sehr zuverlässig der Phasenübergang nach der Hybrid-Inflation untersucht und die Bedeutung der Rückwirkungseffekte der Quantenfluktuationen herausgestellt.
This thesis addresses two topics: the inflationary perturbation spectrum and preheating after hybrid inflation. Quantum fluctuations in the inflationary universe provide a natural mechanism for the generation of primordial perturbations which seed the formation of cosmic structure. In this thesis we present a semi-analytical, and mathematically controlled, so-called uniform approximation. This approximation can be used for the calculation of scalar and tensor inflationary perturbations. Detailed calculations of the power spectra, the spectral indices and other observables are performed to leading and next-to-leading order in the uniform approximation, respectively. Explicit 'slow-roll' assumptions are avoided. A simple extension of the leading order, which is gained from the detailed understanding of the next-to-leading order, leads to excellent accuracy of the uniform approximation, which is demonstrated with several representative examples. The results are compared to standard slow-roll approximations as well as to exact numerical results. The techniques and numerical routines described here allow to calculate primordial perturbation spectra very efficiently with high precision and to constrain some models of inflation. Furthermore, this thesis provides a detailed analysis of some aspects of preheating after hybrid inflation. In the hybrid model the inflationary expansion is terminated by a phase transition of a symmetry-breaking field. During inflation this symmetry-breaking field is trapped in a false vacuum, becomes dynamically instable and performs a transition to the true vacuum. Herein the important influence of the back-reaction of quantum fluctuations is considered by using a bubble-resummation of the propagators. The problem of renormalization in a system of multiple and coupled fields is explicitly solved. The false vacuum transition after hybrid inflation, along with other physical observables, is analyzed with detailed numerical investigations reliably and the influence of back-reaction of quantum fluctuations is emphasized.
This thesis addresses two topics: the inflationary perturbation spectrum and preheating after hybrid inflation. Quantum fluctuations in the inflationary universe provide a natural mechanism for the generation of primordial perturbations which seed the formation of cosmic structure. In this thesis we present a semi-analytical, and mathematically controlled, so-called uniform approximation. This approximation can be used for the calculation of scalar and tensor inflationary perturbations. Detailed calculations of the power spectra, the spectral indices and other observables are performed to leading and next-to-leading order in the uniform approximation, respectively. Explicit 'slow-roll' assumptions are avoided. A simple extension of the leading order, which is gained from the detailed understanding of the next-to-leading order, leads to excellent accuracy of the uniform approximation, which is demonstrated with several representative examples. The results are compared to standard slow-roll approximations as well as to exact numerical results. The techniques and numerical routines described here allow to calculate primordial perturbation spectra very efficiently with high precision and to constrain some models of inflation. Furthermore, this thesis provides a detailed analysis of some aspects of preheating after hybrid inflation. In the hybrid model the inflationary expansion is terminated by a phase transition of a symmetry-breaking field. During inflation this symmetry-breaking field is trapped in a false vacuum, becomes dynamically instable and performs a transition to the true vacuum. Herein the important influence of the back-reaction of quantum fluctuations is considered by using a bubble-resummation of the propagators. The problem of renormalization in a system of multiple and coupled fields is explicitly solved. The false vacuum transition after hybrid inflation, along with other physical observables, is analyzed with detailed numerical investigations reliably and the influence of back-reaction of quantum fluctuations is emphasized.
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Keywords
Quantum Fluctuations, Inflation, Perturbations, Preheating, Hybrid Model, Nonequilibrium Quantum Field Theory, Inflationary Universe, Uniform Approximation, Primordial Power Spectra