Turbulent reheating after cosmological inflation
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1 Research Collection Doctoral Thesis Turbulent reheating after cosmological inflation Author(s): Micha, Raphael Publication Date: 2004 Permanent Link: Rights / License: In Copyright - Non-Commercial Use Permitted This page was generated automatically upon download from the ETH Zurich Research Collection. For more information please consult the Terms of use. ETH Library
2 Diss. ETH No Turbulent Reheating after Cosmologieal Inflation A dissertation submitted to the Swiss Federal Instituteof TechnologyZürich for the degree of Doctor of Natural Sciences presented by Raphael Micha Dipl.-Phys. University of Heidelberg, Germany born on February 22, 1974 Citizen of Germany accepted on the recommendation of Prof. Dr. Gian Michele Graf, examiner Prof. Dr. Igor I. Tkachev, co-examiner Dr. ChristophSchmid, co-examiner Zürich, 2004
3 known is Abstract In this dissertation we study, analytically and with lattice simulations, the reheating after cosmologieal Inflation, i.e the decay of the coherent inflaton field and the relaxation of the resulting stochastic classical wave-fields. We identify three different stages of these processes. - The initial stage characterizedby linear insta- - as preheating bilities and exponentiallygrowing fluetuation fields. Although this process excites large field variances and oecupation numbers, it transfers only a small fraction of the initial inflaton energy to fluctuations in the physically relevant case of sufficiently large couplings with acceptably large reheating tempera ture. Preheating ends, when large created fluctuations effectively terminate the linear instabilities, while nonlinear scattering processes start to dominate and eventually randomize the field distributions. As a new result we identify the prompt second stage of the reheating of bosons as a driven turbulence. We find that this process transfers a major fraction of energy from the coherent inflaton field towards large particle momentaof the fluetuation fields. The turbulent flow in this regime is generally characterizedby a linear growth of the fluetuation energy. We classify the longish third stage of reheating as a free turbulence. It appears as soon as the fluetuation fields contain essentially the entire energy density. During the turbulent stages, the evolutionofthe particle distribution functions is self-similar. We obtained these general results by use of the kinetic theory of wave turbulence. They are confirmed qualitatively and quantitativelyby our nu merical lattice simulations for specific modeis of chaotic inflation. On basis of our findings we discuss analytically the asymptotics of the relaxation process at late times. We find analytical estimates of reheating time and temperaturein terms of coupling constants and initial inflaton am plitude. We find eoineidence with perturbative estimates from the literature, provided that the asymptotical evolutionis characterizedby a free turbulence of fluetuation fields. The results and methods, which have been developed, are universal and
4 VI allow for a straightforwardapplication and generalization Systems in and outside of cosmology and astroparticle physics. to field theoretical
5 Zusammenfassung In dieser Dissertation studieren wir, analytisch und mit Gittersimulatio nen, das Reheating nach der kosmologischen Inflation, d.h. den Zerfall des ursprünglich kohärenten Inflatonfeldes und die Relaxation der resultieren den stochastischen, klassischenwellenfelder. Wir identifizieren drei unter schiedliche Phasen dieser Prozesse. Deren erste, das sogenannte Preheating, ist durch lineare Instabilitäten und exponentiellwachsendefluktuationsfeldercharakterisiert. Obwohl dieser Prozess grosse Varianzen und Besetzungszahlen erregt, vermag er nur einen kleinen Anteil der ursprünglichen Inflatonenergie in Fluktuationen zu trans ferieren, wenn man den physikalischrelevanten Fall hinreichend grosserkop plungskonstanten und Reheatingtemperaturen betrachtet. Das Preheating ended, sobald die erzeugten grossen Feldfluktuationen die linearen Insta bilitäten effektiv beenden, wobei nichtlineare Streuprozesse dominant wer den, welche letztendlich die Feldverteilungen chaotisieren. Als ein neues Resultat identifizieren wir die prompte zweite Phase des Reheatings als eine erregte Turbulenz. Wir zeigen, dass dieser Prozess den grösseren Anteil der Energie vom kohärenten Inflaton in Richtung grosser Teilchenimpulse der Fluktuationsfeldertransferiert. Der turbulente Fluss in diesem Regime ist generell charakteriziert durch ein lineares Wachstum der in der konformen Zeit. Fluktuationsenergie Wir klassifizierendie langwierigedritte Phase des Reheatingsals eine freie Turbulenz. Diese entsteht, sobald die Fluktuationsfelderim wesentlichen die gesamte Energiedichte besetzen. Wärend der turbulenten Phasen ist die Entwicklungder Teilchenverteilungfunktionenselbstähnlich. Diese generellenresultate erhalten wir mit Hilfe der kinetischetheorie der Wellenturbulenz. Sie werden quantitativ wie qualitativ durch unsere numerischengittersimulationen spezieller Modelleder chaotischen Inflation bestätigt. AufGrundlage unserer Ergebnisse diskutierenwir die Asymptotik des Re laxationsprozessesfür späte Zeiten. Wir finden analytische Abschätzungen für Dauer und Temperatur des Reheatings als Funktion von Kopplungskonvn
6 VUl stanten und der ursprünglicher Inflatonamplitude. Wir finden Übereinstim mungen mit perturbativen Abschätzungen aus der Literatur für den Fall, dass die asymptotische Entwicklungdurch eine Freie Turbulenz der Fluktu ationsfelder gegeben ist. Die Resultate und die Methoden, welche ermittelt bzw. entwickeltwur den, sind universell und erlauben eine direkte Anwendung und Verallge meinerung auf feldtheoretische Systeme in und ausserhalb der Kosmologie und Astroteilchenphysik.
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