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Cosmic Acceleration: Past and Present

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Cosmic Acceleration: Past and Present COSMIC ACCELERATION: PAST AND PRESENT A Dissertation Presented to the Faculty of the Graduate School of Cornell University in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy by Nishant Agarwal May 2011 c 2011 Nishant Agarwal ALL RIGHTS RESERVED COSMIC ACCELERATION: PAST AND PRESENT Nishant Agarwal, Ph.D. Cornell University 2011 Our Universe has an exciting history of accelerated expansion. Following its in- ception in an event known as the big bang, the Universe underwent a phase of exponential expansion called inflation. Although precise observations of the cos- mic microwave background (CMB) radiation and large-scale structure support the inflationary paradigm, the absence of a firm physical mechanism for inflation has led to a plethora of theoretical embarkments attempting to understand its genesis. Inflation lasted only for a fraction of a second, but observations suggest that thir- teen billion years after inflation, the Universe began accelerating once again. This acceleration, which continues till date, is attributed to a mysterious component, dubbed dark energy, that fills up our Universe and accounts for almost 73% of the total energy density in the Universe. In this thesis we study and develop models of inflation and dark energy, in the light of current observations. We begin, in Chapter 1, with a detailed introduction to cosmic acceleration, and discuss various models of inflation and dark energy that have been studied in the literature in the recent years. In Chapter 2, we discuss how a hierarchy of Hubble flow parameters, extended to include the evolution of the inflationary sound speed, can be applied to compare a general, single-field inflationary action with cosmological observational data. In Chapter 3, we study the six-field dynamics of D3-brane inflation for a general scalar potential on the conifold, finding simple, universal behavior, such as a power law dependence for the probability of Ne e-folds of inflation. Subsequent chapters study modifications to the theory of gravity in an attempt to understand dark energy. In Chapter 4, we establish the dynamical attractor behavior in scalar-tensor theories of gravity, providing a powerful framework to analyze such theories, predicting common evolutionary characteristics that can be compared against cosmological constraints. Chapter 5 develops a cascading cosmology framework in order to study the cosmological implications of a six- dimensional (6D) theory of gravity. We find that cascading cosmology can indeed lead to an accelerating Universe. Finally, in Chapter 6, we study the issue of ghostlike instabilities in the cascading framework, and propose a mechanism to obtain flat brane and bulk solutions. We conclude in Chapter 7 with a discussion of the main results presented in this thesis. BIOGRAPHICAL SKETCH Nishant Agarwal was born in 1984 in a beautiful village called Maun in the South- ern African country of Botswana. Shortly after, his family moved to Gaborone. He had his early education in Northside Primary School there. When he was seven years old, his family moved to India, and he completed his schooling from Oxford Senior Secondary School in New Delhi. In 2001 he joined St. Stephen's College in the University of Delhi for a bache- lor's degree in physics. On completing his under-graduation in 2004, he went to the Indian Institute of Technology at Kanpur to pursue a master's degree in physics. In 2006 he came to the U.S.A. to begin his graduate studies in cosmology at the Department of Astronomy in Cornell University. iii To, my family. iv ACKNOWLEDGEMENTS I would like to begin by thanking my advisor Rachel Bean for her incessant support through the years of my Ph.D. She has always given me the freedom to explore the exciting field of cosmology, while her guidance has prevented me from ever getting lost in its complexities. I admire the expanse and depth of her knowledge in cosmology, and thank her for all of her patience and encouragement. I also thank her for building extremely enjoyable collaborations from which I have benefitted immensely. It has been a great pleasure to work with her for my Ph.D. I have been fortunate to work with the most amazing people in the course of my research. I would like to thank Justin Khoury and Mark Trodden, who have so greatly influenced my understanding of theoretical physics. I thank them for a wonderful collaboration filled with enthusiasm and opportunity, and for all of their hospitality during my visits to the University of Pennsylvania. I would also like to thank Liam McAllister for an exciting opportunity to work on string cosmology. I thank him and Gang Xu for their patient and thorough guidance in string theory. Gang's imperturbable zeal made research all the more enjoyable and I thank her for the countless discussions that we have had in order to remove any discrepancies between our results. I also thank my other collaborators | Pankaj Jain, John Ralston, Douglas McKay, and Archana Kamal (who is also my wife) | my work with whom is not included as a part of this thesis. Pankaj introduced me to the exciting field of pseudoscalar-photon mixing while I was studying for my master's degree in physics in India. I have learned a lot in cosmology from him and thank him for a great collaboration. I thank my committee members | David Chernoff, Eanna Flanagan, and Terry Herter | for their interest in my research, their patience during my presentations, v and their brilliant questions that have helped me better understand my work. I am also thankful to have had great office-mates and friends like Istvan Laszlo, without whom life in Cornell would not have been half as much fun. Coming back to my wife, Archana | without her this thesis would just not have been possible. She has always been there for me with all of her love, care, and support, and has helped maintain sanity in life at crazy times. She has helped me through discussions in every project, and also as a collaborator in some of my research. I would also like to express my heartfelt gratitude towards my parents for all of their love and affection and for their rigid support throughout my career. My sister has always been an inspiration for me and I have many times just wanted to be like her. Without her support I would possibly not be doing Astronomy at all. My brother-in-law has guided me not only professionally but also personally and I can not imagine how I would have achieved anything without his support. My brother, who has taught me how to excel without ever panicking, has always been there for any help I have ever needed. I dedicate this thesis to my family. vi TABLE OF CONTENTS Biographical Sketch . iii Dedication . iv Acknowledgements . .v Table of Contents . vii List of Tables . .x List of Figures . xi 1 Introduction 1 1.1 Inflation . .4 1.1.1 Evidence in support of inflation . .4 1.1.2 The physics of inflation . .6 1.1.3 Models of inflation . 11 1.2 Dark energy . 15 1.2.1 Observational evidence for dark energy . 15 1.2.2 The physics of dark energy . 18 1.2.3 Dark energy models . 20 2 General, single-field inflation 27 2.1 Introduction . 27 2.2 The Hubble flow formalism . 29 2.3 Primordial perturbations . 32 2.3.1 Calculating the power spectrum . 32 2.3.2 Scalar and tensor perturbation initial conditions . 34 2.3.3 Calculating the primordial power spectrum . 36 2.4 Observable predictions of inflation . 40 2.4.1 Monte-Carlo simulations of inflationary trajectories . 41 2.4.2 Constraints from cosmological observational data . 45 2.4.3 Reconstruction of viable inflationary trajectories . 50 2.5 Conclusions . 51 3 D-brane inflation 61 3.1 Introduction . 61 3.2 Review of warped D-brane inflation . 63 3.3 Methodology . 68 3.3.1 Setup . 68 3.3.2 Constructing an ensemble of potentials . 70 3.3.3 Initial conditions . 72 3.3.4 Parameters summarized . 73 3.4 Results for the homogeneous background . 74 3.4.1 The probability of inflation . 74 3.4.2 An analytic explanation of the exponent α = 3 . 80 3.4.3 Dependence on initial conditions . 81 vii 3.4.4 The DBI effect . 84 3.5 Towards the primordial perturbations . 87 3.5.1 Angular kinetic energy and bending trajectories . 87 3.5.2 Single-field treatment of the perturbations . 90 3.6 Conclusions . 94 4 Scalar-tensor theories of dark energy 98 4.1 Introduction . 98 4.2 Cosmic evolution . 100 4.2.1 Evolution in the Einstein frame . 100 4.2.2 Evolution in the Jordan frame . 101 4.2.3 The Einstein frame vs. Jordan frame perspectives . 102 4.2.4 The form of the scalar potential . 104 4.3 Dynamical critical points . 105 4.3.1 Jordan frame autonomous phase plane equations . 105 4.3.2 Einstein frame autonomous phase plane equations . 107 4.3.3 Mapping between the Einstein and Jordan frame phase planes108 4.3.4 Critical points and calculating their stability . 109 4.4 Solving the autonomous phase plane equations . 112 4.4.1 The critical points . 112 4.4.2 Comparison with other dynamical analysis of f(R) and cou- pled CDM theories . 118 4.4.3 Stability criteria for the dynamical attractors . 119 4.4.4 Classification of F (Φ)R scalar-tensor theories . 124 4.4.5 Criteria for viable models with saddle acceleration . 129 4.5 Conclusions . 130 5 Cascading cosmology 133 5.1 Introduction . 133 5.2 A proxy theory for cascading gravity .
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