UNIVERSITY OF CALIFORNIA, SAN DIEGO Philosophical Implications of Inflationary Cosmology A Dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Philosophy by Casey David McCoy Committee in charge: Professor Craig Callender, Chair Professor Nancy Cartwright Professor Brian Keating Professor Kerry McKenzie Professor David Meyer 2016 Copyright Casey David McCoy, 2016 All rights reserved. The Dissertation of Casey David McCoy is approved, and it is acceptable in quality and form for publication on microfilm and electronically: Chair University of California, San Diego 2016 iii DEDICATION I dedicate this dissertation to the inquiring minds of St. John's College, who revealed to me a beautiful life of thought. iv EPIGRAPH The edge of evening...the long curve of people all wishing on the first star.... Always remember those men and women along the thousands of miles of land and sea. The true moment of shadow is the moment in which you see the point of light in the sky. The single point, and the Shadow that has just gathered you in its sweep... |T. Pynchon, Gravity's Rainbow v TABLE OF CONTENTS Signature Page................................... iii Dedication...................................... iv Epigraph......................................v Table of Contents.................................. vi Acknowledgements................................. viii Vita......................................... xi Abstract of the Dissertation............................ xii Introduction.....................................1 Chapter 1 Relativistic Cosmology....................... 15 1.1 Introduction.......................... 15 1.2 Cosmological Models..................... 17 1.2.1 Relativistic Spacetimes................ 19 1.2.2 Universe or Multiverse................ 23 1.2.3 Ranges of Applicability................ 27 1.3 Geometry of the Standard Big Bang Model......... 30 1.3.1 Symmetry Assumptions in Cosmology........ 31 1.3.2 Friedman-Robertson-Walker Spacetimes....... 34 1.3.3 Initial Value Formulation............... 42 1.3.4 Perturbed Friedman-Robertson-Walker Spacetimes 45 1.4 Singularities and Horizons.................. 50 1.4.1 Singularities in Cosmology.............. 51 1.4.2 Particle and Event Horizons............. 55 1.5 Cosmological Observations.................. 61 Chapter 2 Fine-Tuning Problems in Cosmology............... 67 2.1 Introduction.......................... 67 2.2 Problems in Big Bang Cosmology.............. 70 2.2.1 What Is The Horizon Problem?........... 72 2.2.2 What is the Flatness Problem?........... 79 2.3 Scientific Problems...................... 82 2.4 Inflation............................ 98 2.4.1 Classical Dynamics of Inflation........... 100 2.4.2 Inflation as a Solution to the Horizon Problem... 102 2.4.3 Inflation Implemented as a Scalar Field....... 106 vi 2.5 Fine-Tuning: From the Hot Big Bang to Inflation..... 110 2.5.1 Problems and Solutions................ 112 2.5.2 The Special Low Entropy State of the Universe.. 114 2.5.3 Fine-Tuning Problems in Inflationary Cosmology.. 119 Chapter 3 Likelihood in Physics........................ 128 3.1 Introduction.......................... 128 3.2 The Implementation of Probability in Physics....... 130 3.2.1 Measure in Classical Particle and Statistical Mechanics134 3.2.2 Covariant and Canonical Classical Field Theory.. 143 3.3 The Justification and Interpretation of Statistical Mechanical Probabilities.......................... 148 3.3.1 Kinds of Interpretation................ 149 3.3.2 Interpretation of Statistical Mechanics....... 154 3.3.3 Gibbsian Statistical Mechanics............ 157 3.3.4 Boltzmannian Statistical Mechanics......... 161 3.3.5 Justification of Measure............... 170 Chapter 4 The Generic Universe........................ 174 4.1 Introduction.......................... 174 4.2 General Problems of Objective Probability Measures.... 177 4.2.1 The Reference Class Problem............ 178 4.2.2 Interpretation of Cosmological Probabilities.... 184 4.2.3 Justification of Cosmological Likelihoods...... 187 4.3 Likelihood in the Solution Space of General Relativity... 191 4.4 Likelihood in FRW Spacetimes................ 200 4.4.1 The Gibbons-Hawking-Stewart Measure...... 200 4.4.2 The Flatness Problem................ 207 4.4.3 The Likelihood of Inflation in FRW spacetimes... 216 4.4.4 The Uniformity Problem............... 220 References...................................... 224 vii ACKNOWLEDGEMENTS I acknowledge and express my gratitude to the many people who contributed to the completion of this dissertation. There are a few people that deserve a special thanks: My greatest debt and gratitude go to my supervisor, Craig Callender, who encouraged me to take up inflation as a dissertation topic and provided invaluable guidance and suggestions throughout. His ability to master complex physics in his research while remaining resolutely focused on making important philosophical points and being engaging and accessible provides a model I have tried to emulate. I hope that this dissertation demonstrates his influence on my approach to philosophy. I would also like to thank Nancy Cartwright and Kerry McKenzie for serving on my committee. Reading Nancy's influential work is what brought me to the philosophy of science, and I feel very fortunate to have had her advice, guidance, and assistance during my time at UCSD. Although Kerry only joined my committee quite recently, she has been wonderfully open to discussing my ideas and has been a great source of encouragement and inspiration. It is a great pleasure to have such philosophers whom I admire so much as a part of my dissertation committee. Brian Keating and David Meyer deserve my hearty thanks for serving as committee members from outside the philosophy department. I am grateful to Brian in particular for the valuable role he played in the early stages of my dissertation, contributing significantly to my education in cosmology (I had a lot to learn about the subject!). I appreciated David's enthusiasm for my project and encouragement to share my results with his group in mathematics. If only I had been in San Diego over the last years, I would have been more easily able to take him up on his friendly offer! viii Due to his departure from San Diego for the green pastures of Switzerland, Christian W¨uthrich unfortunately had to leave my committee. However his contri- butions to my philosophical education and this project were many and great; I am deeply grateful for his dedication and willingness to reading and commenting on my earlier drafts. He also was always glad to dispense valuable professional advice, and served as a valuable model of a careful, thorough, and rigorous philosopher of physics. I also owe a great deal to Richard Dawid, who has been a tremendous influence on this dissertation as well as my general philosophical outlook. Richard generously offered his time during my stints in Vienna for regular discussions of his work and my dissertation. I will never forget the many pleasant afternoons discussing philosophy at the Caf´eEiles in one of the great cities of the world. He has also been an unflagging supporter of my fledgling career, for which I cannot thank him enough. Besides Richard, I would also like to express my appreciation to others I met during my time in Vienna, especially Dejan Makovic and the rest of the Vienna Forum for Analytic Philosophy. My subsequent time in Nijmegen also brought me into contact with wonderful colleagues. I especially thank Klaas Landsman and Fred Muller for their generous welcome and interest in my work. I feel incredibly fortunate to have gotten to know them while in the Netherlands. I also appreciate Klaas's enthusiasm for bringing a bunch of theoretical physicists together to talk philosophy, among whom I wish especially to thank Francesca Vidotto for being a great friend and a wonderful philosophical interlocutor. The Department of Philosophy at UCSD has been a wonderful place to study philosophy. I thank the many members of the faculty that have contributed to my ix development|a special thanks to Eric Watkins for going well beyond the call of duty in helping me along. I have been quite lucky also to have been in close enough proximity to UC Irvine to study with the several excellent philosophers of physics there too. I have learned a lot about philosophy and more from David Malament, who welcomed me into one of his courses and made a strong impression on my approach to philosophy. I would like to take this opportunity to thank him in particular. Finally I must acknowledge the many contributions and friendship of my fellow graduate students at UCSD, who have been a constant source of encouragement and support over the years. I recognize especially John Dougherty, with whom I have spoken more about philosophy than probably everyone else put together. My knowledge of physics, mathematics, philosophy, and far more would not be what it is if it were not for John. His patience in listening to my many (often random or confused) thoughts is just one way in which John has been a colleague without compare. Gil Hersch and Alex Marcellesi have been great friends and also willingly read a whole lot of my physics-heavy papers and forced me to make sense of it to them. Insofar as my work is accessible to a general audience, it is surely due to their helpful suggestions and discussion. Chapter 2 includes material that is published in McCoy, Casey. \Does infla- tion solve the hot big bang model's fine-tuning problems?" Studies in History and