A little inflation at the cosmological QCD phase transition [Elektronische Ressource] / put forward by Moritz Tillmann Boeckel

Boeckel

Sujets

• Physik

Informations

• Publié par: ruprecht-karls-universitat_heidelberg
• Publié le: 01 janvier 2011
• Nombre de lectures: 35
• Langue: Deutsch
• Poids de l'ouvrage: 2 Mo

Extrait

Dissertation
submitted to the
Combined Faculties of the Natural Sciences and Mathematics
of the Ruperto-Carola-University of Heidelberg. Germany
for the degree of
Doctor of Natural Sciences
Put forward by
Moritz Tillmann Boeckel
born in: Friedberg(Hessen), Germany
thOral examination: June 8 2011A Little Inflation at the
Cosmological QCD Phase Transition
Referees: Professor Ju¨rgen Schaffner-Bielich
Professor Michael G. SchmidtTopic in German
In dieser Dissertation untersuche ich ein neues Szenario welches im fru¨hen Uni-
versum fu¨r die Quantenchromodynamik (QCD) einen starken Phasenu¨bergang er-
ster Ordnung bei nicht verschwindender Baryonendichte erm¨oglicht und diskutiere
m¨ogliche beobachtbare Konsequenzen. Nach Einfu¨hrungen in wichtige Aspekte
der zugrunde liegenden Felder der QCD und der Kosmologie diskutiere ich die
M¨oglichkeiteinerkurzeninflation¨arenPhaseamkosmologischenQCDPhasenu¨ber-
gang. Ein starker Baryogenese-Mechanismus is notwendig um die ben¨otigte Bary-
onasymmetrie der Gr¨oßenordung eins voraussetzen zu k¨onnen, eine M¨oglichkeit
w¨are dabei die sogenannte Affleck-Dine Baryogenese die ebenfalls diskutiert wird.
Die zweite Kernannahme dieses ”kleine Inflation”-Szenarios ist ein quasistabiler
QCD-Vacuumzustand der eine kurze Periode der exponentiallen Expansion verur-
sacht unddabeidasVerh¨altnis vonBaryonenzuPhotonenaufdenHeute beobach-
tetenWertverdu¨nnt. DiekosmologischenAuswirkungesindunteranderemeinedi-
rekte Modifikation der primordialen Dichtefluktuationen bis zu einer Massenskala
¨der dunklen Materie von M ∼ 1M , eine Anderung in der spektralen Stei-med ⊙
6gung bis zu M ∼ 10 M , Produktion von starken primordialen Magnetfeldernmax ⊙
und eines Gravitationswellen-Spektrums das von zuku¨nftigen Pulsarlaufzeit-Gra-
vitationswellen-Detektoren beobachtet werden k¨onnte.
Topic in English
In this thesis I explore a new scenario that allows for a strong first order phase-
transition ofquantum chromodynamics (QCD)atnon-negligible baryon density in
the early universe and its possible observable consequences. After an introduction
to important aspects of the underlying fields of QCD and cosmology I discuss the
possibility of a short inflationary phase at the cosmological QCD phase transition.
A strong mechanism for baryogenesis is needed to start out with a baryon asym-
metry of order unity, e.g. as provided by Affleck-Dine baryogenesis which is also
discussed within the thesis. The second main assumption for this ”little inflation”
scenario is a quasistable QCD-vacuum state that leads to a short period of expo-
nential expansion consequently diluting the net baryon to photon ratio to today’s
observed value. The cosmological implications are among other things direct ef-
fects on primordial density fluctuations up to length scales corresponding to an
enclosed dark matter mass of M ∼ 1M , change in the spectral slope up tomed ⊙
6M ∼ 10 M , production of strong primordial magnetic fields and a gravita-max ⊙
tional wave spectrum that could be observed by future pulsar timing gravitational
wave detectors.Acknowledgements
I would like to thank all the people who have directly or indirectly supported me
during the last three and a half years and without whom this work could not have
been completed.
First of all I would like to thank my professor Ju¨rgen Schaffner-Bielich for sup-
portingandsupervising my doctoralthesis. Thebasic ideasthatleadtothisthesis
were developed with him during many interesting discussions and without his con-
tinuous support the thesis could not have taken shape.
Furthermore I want to thank our compact stars and cosmology group for a warm
and pleasant working atmosphere. I would like to thank Irina Sagert, Giuseppe
Pagliara, Andreas Lohs, Debarati Chatterjee, Simon Weissenborn, Bruno Mintz
and Basil Sa’d. Special thanks go to the two other cosmo-guys Rainer Stiele
and Simon Schettler for countless discussions about many problems related to the
thesis. I am also very grateful to Matthias Hempel for numerous chats about com-
plicated topics that often helped a lot in improving my understanding.
I am indebted to my second supervisor professor Michael Schmidt for interesting
discussions about the thesis and related topics.
Tina Straße cannot be thanked enough for always being a good friend next door
whenever I was in need of one. Additional thanks go to her, Soniya Savant and
Sandeep Botla for making our Dossenhome such a great place to live. I also want
to thank Ilja Doroschenko for many laughs and unfortunately far too few encoun-
ters in the last years. Furthermore I want to thank all the other people that made
my time in Heidelberg unforgettable, most importantly Florian Marhauser, Julia
Schaper, Katja Weiß and Florian Freundt.
And last but not least I am deeply gratefulto my parents and my siblings fortheir
love, support and encouragement throughout the years. They always had an open
ear and were ready to help in any situation.Contents
1 Introduction 7
2 QCD 13
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2 Noethers Theorem and Conserved Currents . . . . . . . . . . . . . . 18
2.3 Chiral Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3.1 Chiral Transformations . . . . . . . . . . . . . . . . . . . . . 21
2.4 PCAC-relation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.5 Goldberger-Treiman Relation . . . . . . . . . . . . . . . . . . . . . 26
2.6 Linear σ-Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.7 The Bag-Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.8 Scale Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.9 Trace Anomaly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.10 Dilaton Quark Meson Model . . . . . . . . . . . . . . . . . . . . . . 41
2.10.1 Lagrangian and Basic Thermodynamics . . . . . . . . . . . . 41
2.10.2 Vacuum energy and the trace anomaly . . . . . . . . . . . . 45
2.10.3 Diagonalizing the mass matrix . . . . . . . . . . . . . . . . . 46
2.10.4 Pressure and Equation of State . . . . . . . . . . . . . . . . 48
3 Cosmology 53
3.1 The homogeneous and isotropic FLRW-universe . . . . . . . . . . . 55
3.1.1 FLRW-metric and the Friedmann equations . . . . . . . . . 62
3.1.2 Thermal history of the early universe . . . . . . . . . . . . . 65
3.2 Inflation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.2.1 The flatness problem . . . . . . . . . . . . . . . . . . . . . . 68
3.2.2 The horizon problem . . . . . . . . . . . . . . . . . . . . . . 70
3.2.3 The solution: Inflation . . . . . . . . . . . . . . . . . . . . . 71
3.3 Structure Formation . . . . . . . . . . . . . . . . . . . . . . . . . . 77
53.3.1 Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.3.2 Types of perturbations . . . . . . . . . . . . . . . . . . . . . 77
3.3.3 Gauge transformations . . . . . . . . . . . . . . . . . . . . . 79
3.3.4 Gauge invariant formalism . . . . . . . . . . . . . . . . . . . 80
3.3.5 Uniform expansion gauge . . . . . . . . . . . . . . . . . . . . 81
3.3.6 Analytic Solutions . . . . . . . . . . . . . . . . . . . . . . . 82
3.4 Baryogenesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.4.1 Electroweak Baryogenesis . . . . . . . . . . . . . . . . . . . 87
3.4.2 Baryogenesis via Leptogenesis . . . . . . . . . . . . . . . . . 88
3.4.3 Affleck-Dine Baryogenesis . . . . . . . . . . . . . . . . . . . 88
4 A Little Inflation 95
4.1 QCD Phase Transition in Cosmology . . . . . . . . . . . . . . . . . 97
4.2 Baryon asymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4.2.1 Baryon Asymmetry . . . . . . . . . . . . . . . . . . . . . . . 100
4.2.2 Chemical Potentials and the Duration of Inflation . . . . . . 100
4.3 Nucleation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
4.4 Structure Formation . . . . . . . . . . . . . . . . . . . . . . . . . . 110
4.4.1 Analytic Solutions . . . . . . . . . . . . . . . . . . . . . . . 111
4.4.2 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . 115
4.5 Dark Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
4.6 Magnetic Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
4.7 Gravitational Waves . . . . . . . . . . . . . . . . . . . . . . . . . . 127
5 Conclusion and Outlook 131
6 Appendix 137
6.1 Dilaton Quark Meson Model - Details . . . . . . . . . . . . . . . . . 139
6.1.1 Speed of Sound . . . . . . . . . . . . . . . . . . . . . . . . . 139
6.1.2 Diagonalizing the Mass Matrix . . . . . . . . . . . . . . . . 141
6.2 Structure Formation . . . . . . . . . . . . . . . . . . . . . . . . . . 142
6.2.1 Additional Results . . . . . . . . . . . . . . . . . . . . . . . 142Chapter 1
Introduction
79
The standard models of cosmology and particles physics provide excellent descrip-
tions of the universe from an early stage up to the present day. In the last two
decades a wealth of observations has confirmed many predictions of the theory
hot big bang while on the other hand opening up many new questions, for ex-
ample about the nature of dark matter and dark energy. However, there are still
s