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Grand Unified Models and Cosmology Grand Unified Models and Cosmology Rachel JEANNEROT Department of Applied Mathematics and Theoretical Physics Silver Street, Cambridge CB3 9EW, UK and Newnham College, Sidgwick avenue, Cambridge CB3 9DF, UK September 1996 arXiv:hep-ph/0604270v1 28 Apr 2006 A dissertation submitted for the degree of Doctor of Philosophy at the University of Cambridge. Declaration Apart from chapter 1, in which background material is reviewed, and chapter 2, which is the result of work in collaboration with Dr Anne-Christine Davis, the work presented in this dissertation is my own and includes no material which is the outcome of work done in collaboration. The work is original, and has not been submitted for any other degree, diploma, or other qualification. The results of Chapters 2, 3 and 4 have been published as three separate papers in Physical Review D [1, 2, 3]. The results of Chapter 5 have been published in Phys. Rev. Lett. [4]. Acknowledgements I am grateful to my supervisor, Dr Nick Manton, for helpful discussions and advice. I would like to thank Dr A-C. Davis. I would especially like to thank Professor Qaisar Shafi for his help and his continuous interest in my work. I would like to thank Professor Brandon Carter for his contagious enthusiasm and for discussions. I would like to thank Dr Robert Caldwell for discussions. I would like to thank everybody in my department and everybody in the d´epartement d’astrophysique relativiste et cosmologie at the Observatoire de Paris in Meudon. I would like to thank my friend Fr´ed´eric, for his patience and his care. I would like to thank my family. I would like to thank all my friends in and outside Cambridge, without whom I wouldn’t have been able to finish my Ph.D. Finally, I would like to thank Newnham College for financial support and also Trinity College. Summary The cosmological consequences of particle physics grand unified theories (GUTs) are studied. Cosmological models are implemented in realistic particle physics models. Models consistent from both particle physics and cosmological considerations are selected. After a brief introduction to the big-bang cosmology and to the particle physics standard model, the ideas of grand unification, supersymmetry, topological defects and inflation are in- troduced. Special emphasis is given to the physics of massive neutrinos and to supersymmetric GUTs. The elastic and inelastic scattering of fermions off cosmic strings arising in a nonsuper- symmetric SO(10) model are first studied. It is then shown that the presence of supersymmetry does not affect the conditions for topological defect formation. By studying the impact of the spontaneous symmetry breaking patterns from supersymmetric SO(10) down to the standard model on the standard cosmology, through the formation of topological defects, and by requiring that the model be consistent with proton lifetime measurements, it is shown that there are only three patterns consistent with observations. Using this analysis, a specific model is built. It gives rise to a false vacuum hybrid inflationary scenario which solves the monopole problem. At the end of inflation, cosmic strings form. It is argued that this type of inflationary scenario is generic in supersymmetric SO(10) models. Finally, a new mechanism for baryogenesis is descri- bed. This works in unified theories with rank greater or equal to five which contain an extra gauge U(1)B L symmetry, with right-handed neutrinos and B L cosmic string, i.e. cosmic − − strings which form at the B L breaking scale, where B and L are baryon and lepton numbers. − KALIAYEV,´egar´e. Je ne pouvais pas pr´evoir... Des enfants, des enfants surtout. As-tu regard´edes enfants? Ce regard grave qu’ils ont parfois... Je n’ai jamais pu soutenir ce regard... Une seconde auparavant, pourtant, dans l’ombre, au coin de la petite place, j’´etais heureux. Quand les lanternes de la cal`eche ont commenc´e`abriller au loin, mon coeur s’est mit `abattre de joie, je te le jure. Il battait de plus en plus fort `amesure que le roulement de la cal`eche grandissait. Il faisait tant de bruit en moi. J’avais envie de bondir. Je disais “ oui, oui ”...Tu comprends? Il quitte Stepan du regard et reprend son atti- tude affaiss´ee. J’ai couru vers elle. C’est `ace moment que je les ai vus. Ils ne riaient pas, eux. Ils se tenaient tout droit et regar- daient dans le vide. Comme ils avaient l’air triste! Perdus dans leurs habits de parade, les mains sur les cuisses, le buste raide de chaque cˆot´ede la porti`ere! Je n’ai pas vu la grande duchesse. Je n’ai vu qu’eux. S’ils m’avaient re- gard´e, je crois que j’aurais lanc´ela bombe. Pour ´eteindre au moins ce regard triste. Mais ils regardaient toujours devant eux. Il l`eve les yeux vers les autres. Silence. Plus bas encore. Alors je ne sais pas ce qui s’est pass´e. Mon bras est devenu faible. Mes jambes tremblaient. Une seconde apr`es, il ´etait trop tard. (Silence. Il regarde `aterre.) Dora, ai-je rˆev´e, il m’a sembl´eque les cloches sonnaient `ace moment l`a? Albert CAMUS, Les justes, ACTE II. Contents 1 Introduction 1 1.1 Particle physics and the standard cosmology . ........... 1 1.2 Massiveneutrinos................................ .... 9 1.2.1 Introduction .................................. 9 1.2.2 Majoranaparticles .. .. .. .. .. .. .. .. .. 10 1.2.3 Majorana mass terms and the see-saw mechanism . ...... 10 1.2.4 Quantisedfermionsfields . 13 1.3 Supersymmetry................................... 14 1.3.1 Motivation ................................... 14 1.3.2 Constructing supersymmetric Lagrangians . ......... 15 2 Scattering off an SO(10) cosmic string 18 2.1 Introduction.................................... 18 2.2 AnSO(10)string.................................. 20 2.3 Scattering of fermions from the abelian string . ............ 22 2.3.1 The scattering cross-section . ...... 22 2.3.2 Theequationsofmotion. 23 2.3.3 Theexternalsolution . .. .. .. .. .. .. .. .. 24 2.3.4 Theinternalsolution. 25 2.3.5 Matchingatthestringcore . 26 2.3.6 Thescatteringamplitude . 27 2.4 Theelasticcross-section . ....... 27 2.5 Theinelasticcross-section . ........ 28 2.6 The second quantised cross-section . ......... 30 2.7 Conclusions ..................................... 31 3 Constraining supersymmetric SO(10) models through cosmology 32 3.1 Introduction.................................... 32 3.2 Breakingdowntothestandardmodel . ...... 33 ix x CONTENTS 3.3 Topological defect formation in supersymmetric models .............. 35 3.3.1 Defect formation in supersymmetric models . ........ 35 3.3.2 Hybriddefects ................................. 35 3.4 Inflation in supersymmetricSO(10) models . ......... 37 3.5 SU(5) as intermediate scale . ...... 38 3.5.1 Breaking via SU(5) U(1)X ......................... 38 × 3.5.2 BreakingviaSU(5).............................. 39 3.5.3 Breaking via SU(5) U(1) .......................... 39 × 3.5.4 Breaking via SU(5) Z2 ............................ 40 × g 3.6 Patterns with a left-right intermediate scale . ............. 41 3.6.1 Domain walls in left-right models . ...... 41 3.6.2 Breaking via 4c2L2R .............................. 42 3.6.3 Breaking via 3c2L2R1B L ........................... 44 − 3.7 Breaking via 3c2L1R1B L ............................... 46 − 3.8 Breaking directly down to the standard model . .......... 47 3.9 Conclusions ..................................... 48 4 Supersymmetric SO(10) model with inflation and cosmic strings 52 4.1 Introduction.................................... 52 4.2 Inflation in supersymmetricSO(10) models . ......... 53 4.3 The supersymmetric SO(10) model and the standard cosmology.......... 56 4.4 Modelbuilding ................................... 57 4.4.1 Ingredients ................................... 57 4.4.2 Thesuperpotential. .. .. .. .. .. .. .. .. 58 4.5 Theinflationaryepoch . .. .. .. .. .. .. .. .. 60 4.6 Formationofcosmicstrings . ...... 63 4.6.1 Generalproperties . .. .. .. .. .. .. .. .. 63 4.6.2 Nosuperconductingstrings . 64 4.7 Observationalconsequences . ....... 65 4.7.1 Temperature fluctuations in the CBR . 65 4.7.2 Darkmatter .................................. 67 4.7.3 Largescalestructure. 68 4.8 Conclusions ..................................... 69 5 New Mechanism for Leptogenesis 70 5.1 Introduction.................................... 70 5.2 Unified theories with B L cosmicstrings...................... 72 − 5.3 Right-handed neutrino zero modes in B L cosmicstrings . 72 − 5.4 Leptogenesis via decaying cosmic string loops . ............ 74 5.5 Conclusions ..................................... 78 CONTENTS xi 6 Conclusions and perspectives 79 A Brief review of SO(10) 83 B Scattering amplitude calculations 85 B.1 Theexternalsolution. .. .. .. .. .. .. .. .. ..... 85 B.2 Theinternalsolution. .. .. .. .. .. .. .. .. ..... 86 B.3 Thematchingconditions. ..... 87 C Minimising the superpotential 89 Chapter 1 Introduction 1.1 Particle physics and the standard cosmology The particle physics standard model and theories beyond, such as grand unified theories or supersymmetry, are essential ingredients for any successful description of the evolution of the universe from very early time until today. Particle physics is particularly necessary for the understanding of the very early universe. It is also the only way to solve some cosmological problems, such as the baryon asymmetry of the universe or the dark matter problem. Particle physics also plays an important role in inflationary cosmology. This thesis is interested in this interplay between particle physics and cosmology. In this introductory chapter, we
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