Dissertationsubmitted to theCombined Faculties for the Natural Sciences and for Mathematicsof the Ruperto-Carola University of Heidelberg, Germanyfor the degree ofDoctor of Natural Sciencespresented byMaster of Science-Physics: Khamphee Karwanborn in: Bangkok, ThailandOral examination: 14.02.2006Fluctuations in a Quintessence UniverseReferees: Prof. Dr. Christof WetterichProf. Dr. Matthias BartelmannFluktuationen in einem Quintessenz-UniversumZusammenfassungWir diskutieren die Entwicklung und E ekte von Quintessenz uktuationen ineinem FRW und in ation arem Universum. Nachdem wir die Prinzipien der kos-mologischen St orungstheorie eingefuhrt haben, geben wir Entwicklungsgleichungenfur metrische, Materie- und Quintessenz uktuationen an. Wir verwenden diese Gle-ichungen, um die Entwicklung von Quin in einem FRW Uni-versum zu studieren. Die Fluktuationen in einem Exponentialpotentialmodell mitnicht-kanonischem kinetischen Term k onnen das CMB Leistungsspektrum bei niedri-gen Multipolen sowohl erh ohen als auch erniedrigen, vorausgesetzt das Quintessen-zfeld bleibt bis heute eingefroren. In unserer Analyse ben otigen wir keinen Mechanis-mus zur Verst arkung der Feld uktuationen. Um zu ub erprufen, ob das Quintessen-zfeld bis heute eingefroren sein kann, betrachten wir dessen Entwicklung w ahrendder In ation. W ahrend der In ation wird der Erwartungswert des Quintessen-zfeldes zu gr osseren Werten hin verschoben.
Dissertation submitted to the Combined Faculties for the Natural Sciences and for Mathematics of the Ruperto-Carola University of Heidelberg, Germany for the degree of Doctor of Natural Sciences
presented by Master of Science-Physics: Khamphee Karwan born in: Bangkok, Thailand Oral examination: 14.02.2006
Fluctuations in a Quintessence Universe
Referees: Prof. Dr. Christof Wetterich Prof. Dr. Matthias Bartelmann
Fluktuationen in einem Quintessenz-Universum Zusammenfassung WirdiskutierendieEntwicklungundEektevonQuintessenzuktuationenin einemFRWundinationaremUniversum.NachdemwirdiePrinzipienderkos-mologischenStorungstheorieeingefuhrthaben,gebenwirEntwicklungsgleichungen furmetrische,Materie-undQuintessenzuktuationenan.WirverwendendieseGle-ichungen,umdieEntwicklungvonQuintessenzuktuationenineinemFRWUni-versum zu studieren. Die Fluktuationen in einem Exponentialpotentialmodell mit nicht-kanonischemkinetischenTermkonnendasCMBLeistungsspektrumbeiniedri-genMultipolensowohlerhohenalsaucherniedrigen,vorausgesetztdasQuintessen-zfeldbleibtbisheuteeingefroren.InunsererAnalysebenotigenwirkeinenMechanis-muszurVerstarkungderFelduktuationen.Umzuuberprufen,obdasQuintessen-zfeldbisheuteeingefrorenseinkann,betrachtenwirdessenEntwicklungwahrend derInation.WahrendderInationwirdderErwartungswertdesQuintessen-zfeldeszugrosserenWertenhinverschoben.DadurchistderErwartungswertzu Beginn der Strahlungsdominierten Phase gross genug, um die Quintessenz bis heute eingefrorenzulassen.SchliesslichstudierenwirEinschrankungenandieEntwick-lung der Dunklen Energie durch Beobachtungsdaten. Wir verwenden hierzu eine Parametrisierung, welche von Wetterich vorgeschlagen wurde. Fluctuations in a Quintessence Universe
Abstract Inthisthesis,wediscusstheevolutionandeectsofquintessenceuctuationsin aFRWandinationaryuniverse.Afterintroducingthefundamentalideasofcos-mological perturbation theory, we give the evolution equations for metric, matter andquintessenceuctuations.Weusetheseequationstostudytheevolutionand eectsofquintessenceuctuationsinaFRWuniverse.Theuctuationsinanexpo-nential quintessence model with non-canonical kinetic term can suppress or enhance theCMBpowerspectrumatlowmultipoles,ifthequintessenceeldisfrozenuntil the present epoch. In our analysis, we do not need any mechanism for amplifying theelductuations.Tocheckwhetherthequintessenceeldcanbefrozenuntil thepresentepoch,weconsideritsevolutionduringination.Duringination,the meanvalueofthequintessenceeldisdriventowardsalargevaluebyitsquan-tumuctuations.Asaresult,thevalueofthequintessenceeldatthebeginning ofradiationdominationislargeenoughtokeepthequintessenceeldfrozenuntil the present epoch. Finally, we study observational constraints on the dark energy evolution using a parameterization proposed by Wetterich.
Observational Constraints on Dark 5.1 Dark Energy Parameterization . . 5.2 SNe Ia constraints . . . . . . . . 5.3 CMB plus LSS constraints . . . .
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CONTENTS
Chapter
1
Introduction
Before the 17th century, attempts to understand the universe were based on philo-sophicalpointofview.Thescienticperceptionsoftheuniversehavestartedafter Newton proposed the law of gravity. Because of the limits of observational informa-tions, those perceptions were not quite right. At the beginning of the 20th century, Einstein used the theory of general relativity to construct the model of the universe. Since people believed that the universe is static, Einstein introduced the cosmolog-ical constant to balance the gravitational attractive force due to the matter in the universe. In 1929, Hubble measured distance-redshift relation of galaxies and found that the redshift of light emitted from galaxies increases with their distance so the universe is expanding. Thus, the cosmological constant was not necessary because the Einstein equations can give rise to the expanding universe. Many theories for the expandinguniversewereproposedbutsomeofthemhavebeenfalsiedbycurrent observations. Recently the instruments and techniques for observing the universe have been improved and the picture of our universe is more clear than 20 years ago. Cosmology now is in the stage of “Modern Cosmology”. In this chapter, we will give a brief overview of cosmology. Observations currently suggest that the expansion of the universe is accelerat-ing at the present epoch [1]. Sincethe cosmological constant can give rise to the accelerating universe, it plays a crucial role in modern cosmology. However, the origin of the cosmological constant is mysterious because its magnitude is extremely small compared with the energy scale at the time when it should originate. This is the cosmological constant problem [2, 3]. Because of the cosmological constant problem, a mysterious form of energy, called dark energy, has been suggested [4]-[12] forexplainingtheacceleratedexpansionoftheuniverse.Theevolvingscalareld, i.e., quintessence, is a possible candidate for dark energy. The cosmological model is called Lambda Cold Dark Matter Model (CDM model) if the cosmological constant drives the accelerated expansion of the universe, and called Quintessence Cold Dark Matter Model (QCDM model) if quintessence drives the accelerated expansion. The