Cosmology for the Curious

This book is a gentle introduction for all those wishing to learn about modern views of the cosmos. Our universe originated in a great explosion – the big bang. For nearly a century cosmologists have studied the aftermath of this explosion: how the universe expanded and cooled down, and how galaxies were gradually assembled by gravity. The nature of the bang itself has come into focus only relatively recently. It is the subject of the theory of cosmic inflation, which was developed in the last few decades and has led to a radically new global view of the universe. Students and other interested readers will find here a non-technical but conceptually rigorous account of modern cosmological ideas - describing what we know, and how we know it. One of the book's central themes is the scientific quest to find answers to the ultimate cosmic questions: Is the universe finite or infinite? Has it existed forever? If not, when and how did it come into being? Will it ever end? The book is based on the undergraduate course taught by Alex Vilenkin at Tufts University. It assumes no prior knowledge of physics or mathematics beyond elementary high school math. The necessary physics background is introduced as it is required. Each chapter includes a list of questions and exercises of varying degree of difficulty. This new edition includes hints for answering the questions and exercises, as well as extensions to the discussions on dark matter, quantum cosmology. A new chapter summarizing the standard cosmological model has also been added. Preface Acknowledgements Contents Part I The Big Bang and the Observable Universe 1 A Historical Overview 1.1 The Big Cosmic Questions 1.2 Origins of Scientific Cosmology 1.3 Cosmology Today 2 Newton’s Universe 2.1 Newton’s Laws of Motion 2.2 Newtonian Gravity 2.3 Acceleration of Free Fall 2.4 Circular Motion and Planetary Orbits 2.5 Energy Conservation and Escape Velocity 2.6 Newtonian Cosmology 2.7 Olbers’ Paradox 3 Special Relativity 3.1 The Principle of Relativity 3.2 The Speed of Light and Electromagnetism 3.3 Einstein’s Postulates 3.4 Simultaneity 3.5 Time Dilation 3.6 Length Contraction 3.6.1 Speeding Muons 3.7 E = mc2 3.8 From Space and Time to Spacetime 3.9 Causality in Spacetime 4 The Fabric of Space and Time 4.1 The Astonishing Hypothesis 4.2 The Geometry of Space 4.2.1 Euclidean Geometry 4.2.2 Non-Euclidean Geometry 4.3 Curved Space 4.3.1 The Curvature of Surfaces 4.3.2 The Curvature of Three-Dimensional Space 4.4 The General Theory of Relativity 4.5 Predictions and Tests of General Relativity 4.5.1 Light Deflection and Gravitational Lensing 4.5.2 Gravitational Time Dilation 4.5.3 Black Holes 4.5.4 Gravitational Waves 4.6 Underlying Simplicity 5 An Expanding Universe 5.1 Einstein’s Static Universe 5.2 Problems with a Static Universe 5.3 Friedmann’s Expanding Universe 6 Observational Cosmology 6.1 Fingerprints of the Elements 6.2 Measuring Velocities 6.3 Measuring Distances 6.4 The Birth of Extragalactic Astronomy 7 Hubble’s Law and the Expanding Universe 7.1 An Expanding Universe 7.2 A Beginning of the Universe? 7.3 The Steady State Theory 7.4 The Scale Factor 7.5 Cosmological Redshift 7.6 The Age of the Universe 7.7 The Hubble Distance and the Cosmic Horizon 7.8 Not Everything is Expanding 8 The Fate of the Universe 8.1 The Critical Density 8.2 The Density Parameter 9 Dark Matter and Dark Energy 9.1 The Average Mass Density of the Universe and Dark Matter 9.2 Dark Energy 9.3 The Fate of the Universe—Again 10 The Quantum World 10.1 Quantum Discreteness 10.2 Quantum Indeterminism 10.3 The Wave Function 10.4 Many Worlds Interpretation 11 The Hot Big Bang 11.1 Following the Expansion Backwards in Time 11.2 Thermal Radiation 11.3 The Hot Big Bang Model 11.4 Discovering the Primeval Fireball 11.5 Images of the Baby Universe 11.6 CMB Today and at Earlier Epochs 11.7 The Three Cosmic Eras 12 Structure Formation 12.1 Cosmic Structure 12.2 Assembling Structure 12.3 Watching Cosmic Structures Evolve 12.4 Primordial Density Fluctuations 12.5 Supermassive Black Holes and Active Galaxies 13 Element Abundances 13.1 Why Alchemists Did Not Succeed 13.2 Big Bang Nucleosynthesis 13.3 Stellar Nucleosynthesis 13.4 Planetary System Formation 13.5 Life in the Universe 14 The Very Early Universe 14.1 Particle Physics and the Big Bang 14.2 The Standard Model of Particle Physics 14.2.1 The Particles 14.2.2 The Forces 14.3 Symmetry Breaking 14.4 The Early Universe Timeline 14.5 Physics Beyond the Standard Model 14.5.1 Exotic Dark Matter 14.5.2 Unifying the Fundamental Forces 14.6 Vacuum Defects 14.6.1 Domain Walls 14.6.2 Cosmic Strings 14.6.3 Magnetic Monopoles 14.7 Baryogenesis Part II Beyond the Big Bang 15 Problems with the Big Bang 15.1 The Flatness Problem: Why is the Geometry of the Universe Flat? 15.2 The Horizon Problem: Why is the Universe so Homogeneous? 15.3 The Structure Problem: What is the Origin of Small Density Fluctuations? 15.4 The Monopole Problem: Where Are They? 16 The Theory of Cosmic Inflation 16.1 Solving the Flatness and Horizon Problems 16.2 Cosmic Inflation 16.2.1 The False Vacuum 16.2.2 Exponential Expansion 16.3 Solving the Problems of the Big Bang 16.3.1 The Flatness Problem 16.3.2 The Horizon Problem 16.3.3 The Structure Formation Problem 16.3.4 The Monopole Problem 16.3.5 The Expansion and High Temperature of the Universe 16.4 Vacuum Decay 16.4.1 Boiling of the Vacuum 16.4.2 Graceful Exit Problem 16.4.3 Slow Roll Inflation 16.5 Origin of Small Density Fluctuations 16.6 More About Inflation 16.6.1 Communication in the Inflating Universe 16.6.2 Energy Conservation 17 Testing Inflation: Predictions and Observations 17.1 Flatness 17.2 Density Fluctuations 17.3 Gravitational Waves 17.4 Open Questions 18 Eternal Inflation 18.1 Volume Growth and Decay 18.2 Random Walk of the Inflaton Field 18.3 Eternal Inflation via Bubble Nucleation 18.4 Bubble Spacetimes 18.5 Cosmic Clones 18.6 The Multiverse 18.7 Testing the Multiverse 18.7.1 Bubble Collisions 18.7.2 Black Holes from the Multiverse 19 String Theory and the Multiverse 19.1 What Is String Theory? 19.2 Extra Dimensions 19.3 The Energy Landscape 19.4 String Theory Multiverse 19.5 The Fate of Our Universe Revisited 20 Anthropic Selection 20.1 The Fine Tuning of the Constants of Nature 20.1.1 Neutron Mass 20.1.2 Strength of the Weak Interaction 20.1.3 Strength of Gravity 20.1.4 The Magnitude of Density Perturbations 20.2 The Cosmological Constant Problem 20.2.1 The Dynamic Quantum Vacuum 20.2.2 Fine-Tuned for Life? 20.3 The Anthropic Principle 20.4 Pros and Cons of Anthropic Explanations 21 The Principle of Mediocrity 21.1 The Bell Curve 21.2 The Principle of Mediocrity 21.3 Obtaining the Distribution by Counting Observers 21.4 Predicting the Cosmological Constant 21.4.1 Rough Estimate 21.4.2 The Distribution 21.5 The Measure Problem 21.6 The Doomsday Argument and the Future of Our Civilization 21.6.1 Large and Small Civilizations 21.6.2 Beating the Odds 22 Did the Universe Have a Beginning? 22.1 A Universe that Always Existed? 22.2 The BGV Theorem 22.2.1 Where Does This Leave Us? 22.2.2 A Proof of God? 23 Creation of Universes from Nothing 23.1 The Universe as a Quantum Fluctuation 23.2 Quantum Tunneling from “Nothing” 23.2.1 Euclidean Time 23.3 The Hartle-Hawking No-Boundary Proposal 23.4 The Multiverse of Quantum Cosmology 23.5 The Meaning of “Nothing” 24 The Big Picture 24.1 The Observable Universe 24.1.1 What Do We Know? 24.1.2 Cosmic Inflation 24.2 The Multiverse 24.2.1 Bubble Universes 24.2.2 Other Disconnected Spacetimes 24.2.3 Levels of the Multiverse 24.2.4 The Mathematical Multiverse and Ockham’s Razor 24.3 Answers to the “Big Questions” 24.4 Our Place in the Universe Appendix A A.1 The Friedmann Equation A.2 Solutions in Different Cosmic Epochs A.3 Radiation Era A.4 Matter Era A.5 Vacuum Dominated Era A.6 Inflation A.7 Flatness Problem Appendix B B.1 The Standard Model of Cosmology—ΛCDM B.1.1 A Closer Look at the Best-Fit Parameters for ΛCDM B.2 The Hubble Constant Tension B.2.1 Early Dark Energy Further Reading Relativity and Quantum Physics Index "This book is an introductory text for all those wishing to learn about modern views of the cosmos. Our universe originated in a great explosion--the big bang. For nearly a century cosmologists have studied the aftermath of this explosion: how the universe expanded and cooled down, and how galaxies were gradually assembled by gravity. The nature of the bang itself has come into focus only relatively recently. It is the subject of the theory of cosmic inflation, which was developed in the last few decades and has led to a radically new global view of the universe. Students and other interested readers will find here a non-technical but conceptually rigorous account of modern cosmological ideas - describing what we know, and how we know it. One of the book's central themes is the scientific quest to find answers to the ultimate cosmic questions: Is the universe finite or infinite? Has it existed forever? If not, when and how did it come into being? Will it ever end? The book is based on the undergraduate course taught by Alex Vilenkin at Tufts University. It assumes no prior knowledge of physics or mathematics beyond elementary high school math. The necessary physics background is introduced as it is required. Each chapter includes a list of questions and exercises of varying degree of difficulty"--Back cover.