Non-minimal Higgs inflation and frame dependence in cosmology:
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| Format: | Thesis Book |
| Language: | English German |
| Published: |
2012
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Zsfassung in dt. und engl. Sprache |
| Physical Description: | VI, 270 S. graph. Darst. |
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| 245 | 1 | 0 | |a Non-minimal Higgs inflation and frame dependence in cosmology |c vorgelegt von Christian Friedrich Steinwachs |
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Record in the Search Index
| _version_ | 1804149696779780096 |
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| adam_text | IMAGE 1
C O N T E N T S
1 INTRODUCTION 1
2 COSMOLOGY 4
2.1 GENERAL RELATIVITY 4
2.1.1 SYMMETRY REDUCTION C
2.2 FRIEDMANN-ROBCRTSOII-WALKCR UNIVERSE 7
2.2.1 PHYSICAL VERSUS COMOVING DISTANCE 8
2.2.2 CONFORMAL TIME 9
2.2.3 FRICDMANN EQUATIONS 10
2.2.4 EPOCHS OF THE UNIVERSE 12
2.2.5 OBSERVABLE QUANTITIES 14
2.3 INFLATION 15
2.3.1 QUALITATIVE PRELIMINARY CONSIDERATIONS 15
2.3.2 SCALAR FIELD MODEL OF INFLATION 18
2.3.3 DE SITTER SPACE 20
2.3.4 SLOW-ROLL INFLATION 22
2.4 COSMOLOGICAL PERTURBATIONS 24
2.4.1 GENERATION OF DENSITY FLUCTUATIONS: BASIC MECHANISM . . . . 24
2.4.2 DECOMPOSITION OF DIFFERENT TYPES OF FLUCTUATIONS 26
2.4.3 QUANTIZATION OF FLUCTUATIONS 29
2.5 HORIZON CROSSING AND OBSERVABLE QUANTITIES 32
2.5.1 SLOW-ROLL POWER SPECTRUM 35
2.5.2 COSMOLOGICAL PARAMETERS DURING SLOW-ROLL 37
3 STANDARD M O D E L 3 9
3.1 GAUGE THEORIES 41
3.1.1 ELECTROMAGNETIC INTERACTION /EM(1) 42
3.1.2 STRONG INTERACTION SU C( I) 46
3.1.3 ELECTROWEAK INTERACTION S U L ( 2 ) X C/Y W(L) 50
3.2 MASSES OF ELEMENTARY PARTICLES 54
3.2.1 MASSIVE FERMIONS IN THE STANDARD MODEL ? 54
3.2.2 THE MASSLESS STANDARD MODEL LAGRANGIAN 56
3.2.3 SPONTANEOUS SYMMETRY BREAKING 58
3.2.4 HIGGS MECHANISM AND THE GENERATION OF MASSES 62
HTTP://D-NB.INFO/1026814715
IMAGE 2
IV
CONTENTS
4 EFFECTIVE A C T I O N A N D RENORMALIZATION G R O U P 6 7
4.1 CLASSICAL FIELD THEORY AND DIMENSIONAL ANALYSIS 67
4.2 DIVERGENCES, REGULARIZATION AND RENORMALIZATION 69
4.3 RENORMALIZATION GROUP 72
4.3.1 ILLUSTRATIVE EXAMPLES 72
4.3.2 GELL-MANN-LOW EQUATIONS 73
4.3.3 RELATION BETWEEN COUNTERTERMS AND BETA FUNCTIONS 76
4.4 PATH INTEGRAL AND EFFECTIVE ACTION 78
4.4.1 FADDEEV-POPOV-METHOD 82
4.5 GENERALIZED SCHWINGER-DEWITT ALGORITHM 86
4.5.1 REDUCTION ALGORITHM FOR MINIMAL OPERATORS 87
4.5.2 DIMENSIONAL REGULARIZATION AND THE CI2 COEFFICIENT 91
4.5.3 RECURSION RELATION AND COINCIDENCE LIMITS 91
5 ONE-LOOP C O S M O L O G Y AND FVAME D E P E N D E N C E 9 3
5.1 MINIMALLY COUPLED SINGLE FIELD IN THE EINSTEIN FRAME 94
5.1.1 CALCULATION OF THE FLUCTUATION OPERATOR 94
5.1.2 CALCULATION OF THE MINIMAL OPERATOR 99
5.1.3 RESULTS 101
5.1.4 COMPARISON WITH T HOOFT AND VELTMAN 106
5.2 NON-MINIMAL O(N) MULTIPLET IN THE JORDAN FRAME 106
5.2.1 SECOND VARIATION AND MINIMAL OPERATOR 107
5.2.2 ONE-LOOP DIVERGENCES IN THE JORDAN FRAME: THE RESULT; . . . 113
5.2.3 CHECKS AND COMPARISON WITH KNOWN RESULTS 120
5.3 COSMOLOGICAL DEBATE;: JORDAN FRAME VERSUS EINSTEIN FRAME 125 5.3.1
TRANSITION BETWEEN THE FRAMES 127
5.3.2 FRAME DEPENDENCE OF QUANTUM CORRECTIONS 132
5.3.3 GEOMETRICAL EFFECTIVE ACTION 138
5.4 CONCLUSIONS 142
6 N O N - M I N I M A L H I G G S INFLATION 1 4 3
6.1 MOTIVATION FOR A NOIL-MINIMAL COUPLING 144
6.1.1 MINIMAL HIGGS INFLATION 144
6.1.2 NON-MINIMAL HIGGS INFLATION 145
6.1.3 BEYOND GENERAL RELATIVITY 145
6.2 THE STANDARD MODEL HIGGS BOSON AS THE INFLATON 147
6.2.1 MATTER SECTOR 148
6.2.2 GRAVITON-SCALAR SECTOR 149
6.2.3 S-FACTOR SUPPRESSION 151
6.2.4 ORIGIN OF SUPPRESSION AND GOLDSTONE CONTRIBUTIONS 153
6.3 ^ COSMOLOGICAL ASPECTS OF THE MODEL 154
6.3.1 SLOW-ROLL DYNAMICS IN THE JORDAN FRAME 154
6.3.2 EFFECTIVE POTENTIAL AND SLOW-ROLL IN THE EINSTEIN FRAME . . . 157
IMAGE 3
CONTENTS V
6.3.3 COSMOLOGICAL PARAMETERS IN NON-MINIMAL HIGGS INFLATION . . 159 6.4
HIGGS INFLATION AND RENORMALIZATION GROUP 161
6.4.1 HIGGS INFLATION A T THE ELCCTROWEAK SCALE 161
6.4.2 RENORMALIZATION GROUP IMPROVEMENT 1G2
6.4.3 DIAGRAMMATIC INSERTION TECHNIQUE OF S-FACT.ORS 164
0.4.4 R.UNNING POTENTIAL A T THE INFLATIONARY SCALE 168
6.5 NUMERICAL ANALYSIS 171
6.5.1 EXACT NUMERICAL SOLUTIONS OF THE RG IMPROVED MODEL . . . 172 6.5.2
DISCUSSION OF NUMERICAL RESULTS 175
6.6 VALIDITY OF THE MODEL: NATURALNESS AND UNITARITY 181
6.6.1 RUNNING CUT-OFF 181
6.6.2 SCALE-INVARIANCE AND SHIFT-SYMMETRY 184
6.7 EXTENSIONS AND MODIFICATIONS 188
6.7.1 VARIANTS OF HIGGS INFLATION 188
6.7.2 INDUCED GRAVITY AND NON-MINIMAL HIGGS INFLATION 188
6.8 CONCLUSIONS 189
7 QUANTUM C O S M O L O G Y 1 9 4
7.1 CONCEPTUAL QUESTIONS 194
7.1.1 OBSERVATIONS AND SPECULATIONS 194
7.1.2 DECOHERENCE AND THE EVERETT, MANY-WORLDS INTERPRETATION . . 196
7.1.3 ETERNAL INFLATION AND MULTIVERSES 203
7.2 BOUNDARY CONDITIONS OF THE COSMOS 204
7.2.1 TUNNELLING CONDITION IN MINISUPCRSPACE 205
7.2.2 BEYOND THE MINISUPCRSPACE TREATMENT 209
7.2.3 PATH INTEGRAL FOR THE MICROCANONICAL STATISTICAL SUM . . . . 212
7.3 QUANTUM ORIGIN OF THE UNIVERSE IN THE HIGGS INFLATION SCENARIO . .
216 7.4 CONCLUSIONS 221
8 S U M M A R Y AND O U T L O O K 2 2 3
A R I E M A N N CURVATURE TENSOR 2 2 6
B VARIATIONS AND DERIVATIVES 2 2 8
B.L COVARIANT DIFFERENTIATION IN GENERAL RELATIVITY 228
B.2 FUNCTIONAL DERIVATIVE 228
B.3 LIE DERIVATIVE 229
B.4 VARIATION OF METRIC QUANTITIES 230
C Y O U N G TABLEAUX FOR 5(7(3) 232
D SYNGE S WORLD FUNCTION 235
D . L DERIVATIVES OF THE WORLD FUNCTION 236
IMAGE 4
VI
CONTENTS
D.2 DENSITIES AND DETERMINANTS 230
D.3 THE PARALLEL PROPAGATOR 237
D.4 FIELD CURVATURE 239
D.5 COINCIDENCE LIMITS 240
E C O R R E C T I O N S T O T H E I N I T I A L V A L U E S O F A A N D
Y T 2 4 2
F T R A N S F E R E Q U A T I O N S 2 4 3
G G R A D I E N T S T R U C T U R E S 2 4 5
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| dewey-sort | 3523.1 |
| dewey-tens | 520 - Astronomy and allied sciences |
| discipline | Physik |
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| institution | BVB |
| language | English German |
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| spelling | Steinwachs, Christian Friedrich Verfasser (DE-588)1025132254 aut Non-minimal Higgs inflation and frame dependence in cosmology vorgelegt von Christian Friedrich Steinwachs 2012 VI, 270 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Zsfassung in dt. und engl. Sprache Köln, Univ., Diss., 2012 (DE-588)4113937-9 Hochschulschrift gnd-content DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025432841&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Steinwachs, Christian Friedrich Non-minimal Higgs inflation and frame dependence in cosmology |
| subject_GND | (DE-588)4113937-9 |
| title | Non-minimal Higgs inflation and frame dependence in cosmology |
| title_auth | Non-minimal Higgs inflation and frame dependence in cosmology |
| title_exact_search | Non-minimal Higgs inflation and frame dependence in cosmology |
| title_full | Non-minimal Higgs inflation and frame dependence in cosmology vorgelegt von Christian Friedrich Steinwachs |
| title_fullStr | Non-minimal Higgs inflation and frame dependence in cosmology vorgelegt von Christian Friedrich Steinwachs |
| title_full_unstemmed | Non-minimal Higgs inflation and frame dependence in cosmology vorgelegt von Christian Friedrich Steinwachs |
| title_short | Non-minimal Higgs inflation and frame dependence in cosmology |
| title_sort | non minimal higgs inflation and frame dependence in cosmology |
| topic_facet | Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025432841&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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