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Abstract Generalized Natural Inflation and The ABSTRACT Title of dissertation: GENERALIZED NATURAL INFLATION AND THE QUEST FOR COSMIC SYMMETRY BREAKING PATTERS Simon Riquelme Doctor of Philosophy, 2018 Dissertation directed by: Professor Zackaria Chacko Department of Physics We present a two-field model that generalizes Natural Inflation, in which the inflaton is the pseudo-Goldstone boson of an approximate symmetry that is spon- taneously broken, and the radial mode is dynamical. Within this model, which we designate as \Generalized Natural Inflation”, we analyze how the dynamics fundamentally depends on the mass of the radial mode and determine the size of the non-Gaussianities arising from such a scenario. We also motivate ongoing research within the coset construction formalism, that aims to clarify how the spontaneous symmetry breaking pattern of spacetime, gauge, and internal symmetries may allow us to get a deeper understanding, and an actual algebraic classification in the spirit of the so-called \zoology of con- densed matter", of different possible \cosmic states", some of which may be quite relevant for model-independent statements about different phases in the evolution of our universe. The outcome of these investigations will be reported elsewhere. GENERALIZED NATURAL INFLATION AND THE QUEST FOR COSMIC SYMMETRY BREAKING PATTERNS by Simon Riquelme Dissertation submitted to the Faculty of the Graduate School of the University of Maryland, College Park in partial fulfillment of the requirements for the degree of Doctor of Philosophy 2018 Advisory Committee: Professor Zackaria Chacko, Chair/Advisor Professor Richard Wentworth, Dean's Representative Professor Theodore Jacobson Professor Rabinda Mohapatra Professor Raman Sundrum A mis padres, Kattya y Luis. ii Acknowledgments It is a pleasure to acknowledge my adviser, Dr. Zacharia Chacko, for be- lieving in me, even during times where everything pointed to the real possibility of desertion. It has been quite nice to learn how to learn from such a great field theorist. Despite not being as productive as one may expect, especially when considering how competitive the \market" is out there, I have learned a lot of physics during these years, and I am taking with me lessons I will never forget and surely apply in my future original research. In this vein, I also acknowledge having had the possibility of attending world-class lectures taught by Professors Ted Jacobson and Raman Sundrum. I have had the great chance of meeting very bright young researchers includ- ing Prateek Agrawal, Peizhi Du, Anton de la Fuente, Sungwoo Hong, Soubhik Kumar, Rashmish Mishra, and Chris Verhaaren. I learned something from all of them, and for that I am thankful. I thank my good friend Matt Severson for all the good times talking about physics and enjoying good old punk rock together. He will be missed. I am grateful to my family, my parents, my sister, my grandmothers. They are me, and I am them. I thank my sisters and brothers of life, the friends of my old self, and the ones I met in the way. They are too many to name, but they surely know who they are. Finally, I thank University of Maryland, my home during all these years. I will miss every corner of this great place, and I hope and know that I will come back here several times during my lifetime. iii Table of Contents Dedication ii Acknowledgments iii List of Tables vi List of Figures vii 1 Introduction1 1.1 Some Lucubrations... .1 1.2 ... And Some Facts . .8 2 The Inflationary Paradigm 12 2.1 Why Do We Need Cosmic Inflation? A Quick Roadmap . 12 2.1.1 The Horizon Problem . 16 2.1.2 Cosmic Inflation . 17 2.1.3 Cosmological \Free Lunch": Primordial Perturbations . 21 3 The Effective Field Theory of Inflation 23 3.1 Spontaneous Symmetry Breaking . 23 3.1.1 SSB of Global Symmetries . 23 3.1.2 SSB of Gauge Symmetries . 27 3.2 Symmetry Breaking in Cosmology . 30 3.2.1 Broken Time Translations . 30 3.2.2 Intermission I: Adiabatic Fluctuations . 32 3.2.3 Exploring the EFT of Inflation . 35 3.2.4 EFT Construction in the Unitary Gauge . 40 3.2.4.1 Universal Part of the Action . 43 3.2.4.2 Higher-Order Terms . 44 3.2.4.3 Stueckelberg Trick for the EFT of Inflation . 45 4 Generalized Natural Inflation 50 4.1 Motivation . 50 4.2 The Inflationary Background . 54 4.2.1 Multifield Inflation . 54 4.2.2 The Model . 55 4.2.3 EFT for the Slowly-Rolling Field θ ............. 60 4.2.3.1 Small Radial Displacement . 62 4.2.3.2 Big Radial Displacement . 62 4.2.4 Intermission II: Vacuum Fluctuations, Curvature Perturba- tions, Gravitational Waves . 64 4.2.5 Semi-analytical Approach . 68 4.3 Inflationary Perturbations in the GNI Model . 71 iv 2 2 4.3.1 Meff H Regime . 74 4.3.1.1 Effective Theory for the Adiabatic (Inflaton) Fluc- tuation . 74 4.3.1.2 Non-Gaussianities . 77 2 2 4.3.2 Meff ∼ H Regime . 87 4.3.2.1 The Single-Field EFT Breaks Down . 87 4.3.2.2 Non-Gaussianities . 94 2 2 4.3.2.3 Comments on the Meff H Regime . 98 4.4 Discussion and Conclusions . 99 5 Cosmological Cosets 102 5.1 Phenomenological Lagrangians: SSB of Internal Global Symmetries as a Warm-Up . 102 5.1.1 Generalities . 102 5.1.2 The Non-linear Realization . 105 5.1.3 Invariant Lagrangians . 107 5.2 The General Case: Local (Gauge) Internal and Spacetime Symmetries . 111 5.2.1 Review of a Generalized Coset Construction . 111 5.2.2 Gauging Some Symmetries: The General Case and GR as an Example . 115 5.2.3 Inverse Higgs Constraints . 118 5.2.4 Some Relevant Examples . 120 5.2.4.1 Membranes . 120 5.2.4.2 Perfect Superfluid . 125 5.3 Coset Construction of the EFT of Inflation . 130 6 Concluding Remarks 139 A In-In Formalism and Equilateral Bispectra 142 B Effective Single-Field Theory Regime 150 C Slow-Roll Approximation Consistency 153 Bibliography 158 v List of Tables 4.1 Couplings of the Model as a Function of the Speed of Sound and the Mass of the Heavy Mode . 70 4.2 Sizes of Non-Gaussianities as a Function of the Speed of Sound . 85 vi List of Figures 1.1 The Purity of Fields . .2 1.2 Pie Chart of Our Universe . .9 1.3 Our Best Theory So Far . .9 2.1 Horizon Problem . 17 2.2 Inflationary Solution to the Horizon Problem . 18 3.1 Evolution of Curvature Perturbations . 34 3.2 Higgs Mechanism . 40 4.1 Deformed Mexican Hat . 57 4.2 (ns; r)-Plane for Generalized Natural Inflation . 70 4.3 Sizes of Non-Gaussianities Associated With Cubic Operators . 83 4.4 Sizes of Observable Non-Gaussianities . 84 4.5 \Feynman Rules" for the Interaction Hamiltonian H int ...... 89 4.6 Leading (Tree-Level) Diagrams for the 2, 3 and 4-Point Functions of the Curvature Perturbation in QSF Inflation Models . 93 6.1 Constraints on Inflation Models from Planck 2018 . 139 vii Chapter 1 Introduction 1.1 Some Lucubrations... 1 The question of \Why is there anything at all?", or, \Why is there some- thing rather than nothing?" 2 has been raised by many great philosophers, including Gottfried Wilhelm Leibniz [2], Martin Heidegger [3,4] and Ludwig Wittgenstein [5]. It is of such importance, that Heidegger himself called it the fundamental question of metaphysics. For those of us who often forget what the word metaphysics is supposed to mean, the encyclopedia of our era, Wikipedia, may enlighten us: \Metaphysics is a branch of philosophy that explores the nature of being, exis- tence, and reality. Metaphysics seeks to answer, in a `suitably abstract and fully general manner', the questions: 1. What is there? 2. And what is it like? Topics of metaphysical investigation include existence, objects and their proper- ties, space and time, cause and effect, and possibility." It is reasonable to feel somehow overwhelmed when faced to all these highbrow concepts. Our natural instinct of looking for some firm ground compels us to drop the prefix \meta" and consider the definition of physics itself: 1Warning: the reader who is mainly interested in getting a quick glimpse on what this dissertation is about, may want to skip these \lucubrations" altogether, and jump directly to section 1.2. 2A little more \down to earth" but in the same vein kind of question has been addressed lately by Nima Arkani-Hamed and others, namely \Why is there a macroscopic universe?" [1]. Watch also this. 1 \Physics is the natural science that studies matter and its motion and behavior through space and time and that studies the related entities of energy and force. Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves." You see, we could spend our whole lives arguing about the deep meaning and \fundamentality" of each of the words entering in both definitions, which surely are definitions themselves, and to be honest, we do not know if there is ever an ending to such an endeavor. In some sense, this task seems analogous to the in- sipid discussion of how \pure" a field is compared to others, as the little cartoon in Figure 1.1 tries to suggest. Figure 1.1: The purity of fields. We are not interested (or, for that matter, trained to) delve ourselves into the deep waters of Leibniz, Heidegger, Wittgenstein, and many others. Let us just make an act of faith and trust that Sean Carroll is doing a good job \defending the flag of physics" in that trench [6].
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