Delia Perlov Alex Vilenkin COSMOLOGY FOR THE CURIOUS www.com Cosmology for the Curious www.com Delia Perlov · Alex Vilenkin Cosmology for the Curious www.com Delia Perlov Alex Vilenkin Tufts University Tufts University Medford, MA, USA Medford, MA, USA ISBN 978-3-319-57038-9 ISBN 978-3-319-57040-2 (eBook) DOI 10.1007/978-3-319-57040-2 Library of Congress Control Number: 2017938144 © Springer International Publishing AG 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.
The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland www.com To the memory of Allen Everett and Leonard Schwartz www.com Acknowledgements We would like to express our sincere thanks to the Springer publishing team, and especially to Angela Lahee.
Angela has been extremely helpful, accom- modating and patient at each step of the way. We would like to thank the following people for reading some or all of the manuscript and offering useful feedback: Jose Blanco-Pillado, Peter Jackson, Jim Kernohan, Levon Pogosian, Michael Schneider and Brian Sinskie. A special thank you to Ken Olum for his extensive comments. Thanks also to Natalie Perlov for draw- ing several figures in the book, and to Gayle Grant and Caroline Merighi at Tufts University for their administrative help.
DP: I wish to thank my husband Larry, my children Natalie, Alexa and Chloe, my mother Glenda, sister Heidi, and my late father Leonard for continued support and interest in this project. AV: It would have been hard to get to the end of this project without the support I had from my wife Inna. I thank her for her patience, advice, and for the wonderful cuisine that kept up my spirits.com Contents Part I The Big Bang and the Observable Universe 1 A Historical Overview 3 1.1 The Big Cosmic Questions 3 1.2 Origins of Scientific Cosmology 4 1.3 Cosmology Today 7 2 Newton’s Universe 13 2.1 Newton’s Laws of Motion 13 2.3 Acceleration of Free Fall 19 2.4 Circular Motion and Planetary Orbits 20 2.5 Energy Conservation and Escape Velocity 22 2.7 Olbers’ Paradox 27 3 Special Relativity 31 3.1 The Principle of Relativity 31 3.2 The Speed of Light and Electromagnetism 35 3.8 From Space and Time to Spacetime 47 3.9 Causality in Spacetime 51 ix www.com x Contents 4 The Fabric of Space and Time 59 4.1 The Astonishing Hypothesis 60 4.2 The Geometry of Space 63 4.2 Non-Euclidean Geometry 66 4.1 The Curvature of Surfaces 67 4.2 The Curvature of Three-Dimensional Space 70 4.4 The General Theory of Relativity 72 4.5 Predictions and Tests of General Relativity 75 4.1 Light Deflection and Gravitational Lensing 75 4.2 Gravitational Time Dilation 77 4.4 Gravitational Waves 78 5 An Expanding Universe 83 5.1 Einstein’s Static Universe 83 5.2 Problems with a Static Universe 86 5.3 Friedmann’s Expanding Universe 89 6 Observational Cosmology 97 6.1 Fingerprints of the Elements 98 6.4 The Birth of Extragalactic Astronomy 105 7 Hubble’s Law and the Expanding Universe 109 7.1 An Expanding Universe 110 7.2 A Beginning of the Universe? 113 7.3 The Steady State Theory 114 7.4 The Scale Factor 115 7.6 The Age of the Universe 117 7.7 The Hubble Distance and the Cosmic Horizon 118 7.8 Not Everything is Expanding 120 8 The Fate of the Universe 125 8.1 The Critical Density 125 8.2 The Density Parameter 128 www.com Contents xi 9 Dark Matter and Dark Energy 131 9.1 The Average Mass Density of the Universe and Dark Matter 131 9.3 The Fate of the Universe—Again 140 10 The Quantum World 143 10.3 The Wave Function 148 10.4 Many Worlds Interpretation 151 11 The Hot Big Bang 155 11.1 Following the Expansion Backwards in Time 155 11.3 The Hot Big Bang Model 161 11.4 Discovering the Primeval Fireball 162 11.5 Images of the Baby Universe 165 11.6 CMB Today and at Earlier Epochs 168 11.7 The Three Cosmic Eras 170 12 Structure Formation 175 12.3 Watching Cosmic Structures Evolve 180 12.4 Primordial Density Fluctuations 182 12.5 Supermassive Black Holes and Active Galaxies 183 13 Element Abundances 187 13.1 Why Alchemists Did Not Succeed 187 13.2 Big Bang Nucleosynthesis 189 13.4 Planetary System Formation 194 13.5 Life in the Universe 196 14 The Very Early Universe 201 14.1 Particle Physics and the Big Bang 201 14.2 The Standard Model of Particle Physics 205 14.4 The Early Universe Timeline 211 www.com xii Contents 14.5 Physics Beyond the Standard Model 213 14.1 Unifying the Fundamental Forces 213 14.7 Baryogenesis 220 Part II Beyond the Big Bang 15 Problems with the Big Bang 227 15.1 The Flatness Problem: Why is the Geometry of the Universe Flat? 227 15.2 The Horizon Problem: Why is the Universe so Homogeneous? 229 15.3 The Structure Problem: What is the Origin of Small Density Fluctuations? 232 15.4 The Monopole Problem: Where Are They? 232 16 The Theory of Cosmic Inflation 235 16.1 Solving the Flatness and Horizon Problems 235 16.1 The False Vacuum 236 16.3 Solving the Problems of the Big Bang 240 16.1 The Flatness Problem 240 16.2 The Horizon Problem 241 16.3 The Structure Formation Problem 242 16.4 The Monopole Problem 242 16.5 The Expansion and High Temperature of the Universe 242 16.1 Boiling of the Vacuum 243 16.2 Graceful Exit Problem 244 16.3 Slow Roll Inflation 245 16.5 Origin of Small Density Fluctuations 247 16.6 More About Inflation 249 16.1 Communication in the Inflating Universe 249 16.2 Energy Conservation 250 www.com Contents xiii 17 Testing Inflation: Predictions and Observations 255 17.4 Open Questions 264 18 Eternal Inflation 269 18.1 Volume Growth and Decay 269 18.2 Random Walk of the Inflaton Field 271 18.3 Eternal Inflation via Bubble Nucleation 274 18.7 Testing the Multiverse 284 18.2 Black Holes from the Multiverse 285 19 String Theory and the Multiverse 291 19.1 What Is String Theory? 292 19.3 The Energy Landscape 295 19.4 String Theory Multiverse 296 19.5 The Fate of Our Universe Revisited 297 20 Anthropic Selection 301 20.1 The Fine Tuning of the Constants of Nature 302 20.2 Strength of the Weak Interaction 303 20.3 Strength of Gravity 303 20.4 The Magnitude of Density Perturbations 303 20.2 The Cosmological Constant Problem 304 20.1 The Dynamic Quantum Vacuum 304 20.2 Fine-Tuned for Life? 305 20.3 The Anthropic Principle 307 20.4 Pros and Cons of Anthropic Explanations 309 21 The Principle of Mediocrity 313 21.1 The Bell Curve 313 21.2 The Principle of Mediocrity 314 21.3 Obtaining the Distribution by Counting Observers 315 www.com xiv Contents 21.4 Predicting the Cosmological Constant 316 21.5 The Measure Problem 319 21.6 The Doomsday Argument and the Future of Our Civilization 321 21.1 Large and Small Civilizations 322 21.2 Beating the Odds 323 22 Did the Universe Have a Beginning? 327 22.1 A Universe that Always Existed? 327 22.2 The BGV Theorem 329 22.1 Where Does This Leave Us? 330 22.2 A Proof of God? 331 23 Creation of Universes from Nothing 333 23.1 The Universe as a Quantum Fluctuation 333 23.2 Quantum Tunneling from “Nothing” 336 23.3 The Multiverse of Quantum Cosmology 338 23.4 The Meaning of “Nothing” 339 24 The Big Picture 343 24.1 The Observable Universe 343 24.1 What Do We Know? 343 24.2 Other Disconnected Spacetimes 346 24.3 Levels of the Multiverse 346 24.4 The Mathematical Multiverse and Ockham’s Razor 347 24.3 Answers to the “Big Questions” 350 24.4 Our Place in the Universe 351 Appendix A 353 Further Reading 361 Index 365 www.com Part I The Big Bang and the Observable Universe www.com 1 A Historical Overview 1.1 The Big Cosmic Questions Cosmology is the study of the origin, nature and evolution of our universe. Its practitioners strive to describe cosmic history in quantitative detail, using the language of modern physics and abstract mathematics.
Yet, at its core, our cosmological knowledge is the answer to a few fundamental questions. Have you ever drifted off deep into thought, wondering: Is the universe finite or infinite? Has it existed forever? If not, when and how did it come into being? Will it ever end? How do we humans fit into the grand scheme of things? All ancient and modern cultures have developed creation stories where at least some of these questions have been addressed. In one of the Chinese creation myths, the universe begins as a black egg containing a sleeping giant, named Pan Gu. He slept for 18,000 years and grew while he slept.
Then he woke up and cracked the egg open with an ax. The light part of the egg floated up to form the sky, while the heavy part stayed down and formed the Earth. Pan Gu remained in the middle and continued to grow, pushing the sky and the Earth further apart. When Pan Gu died, his breath became the wind, his eyes the Sun and the Moon, his sweat turned into rain, and the fleas in his hair transmuted into humans.
The prospect of being a descendant of fleas may not be fully satisfying, but perhaps an even more objectionable aspect of this story is that it does not address the obvious question: “Where did the black egg come from in the first place?” Similar types of questions also arise in the context of sci- entific cosmology. Even if we claim to know what happened at the begin- ning of the universe, you can always ask: And what happened before that? © Springer International Publishing AG 2017 3 D. Vilenkin, Cosmology for the Curious, DOI 10.com 4 1 A Historical Overview There is also a limit to how far we can see in space, so how can we know what lies beyond? For a long time it seemed as though we would never know the answers to the “big” cosmic questions. Thus, cosmologists focused mostly on the part of the universe that could be directly observed, leaving it to philosophers and theologians to argue about the great mysteries.
We shall see, however, that due to remarkable developments in cosmology over the last few decades, we now have answers, that we have reason to believe, to at least some of the big questions.2 Origins of Scientific Cosmology The idea that the universe can be rationally understood is at the founda- tion of all scientific knowledge. This concept is now commonplace, but in Ancient Greece more than 20 centuries ago it was a daring hypothesis. The Greek philosopher Thales (6th century BC) suggested that all of Nature’s variety could be understood from a few basic principles, without the inter- vention of gods. He believed that the primary element of matter was water.
Two centuries later, Democritus advocated that all matter was made up of tiny, eternal, indivisible particles, called atoms, which moved and collided with one another in empty space. He stated: “Nothing exists except atoms and empty space.