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Cosmology for the Curious
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Delia Perlov
Alex Vilenkin
COSMOLOGY
FOR THE CURIOUS
Cosmology for the Curious
Delia Perlov · Alex Vilenkin
Cosmology for the
Curious
Delia Perlov
Tufts University
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
Tis work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of
the material is concerned, specifcally the rights of translation, reprinting, reuse of illustrations, recitation,
broadcasting, reproduction on microflms 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.
Te use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does
not imply, even in the absence of a specifc statement, that such names are exempt from the relevant protective
laws and regulations and therefore free for general use.
Te 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. Te publisher remains neutral with regard to jurisdictional claims in
published maps and institutional afliations.
Printed on acid-free paper
Tis Springer imprint is published by Springer Nature
Te registered company is Springer International Publishing AG
Te registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Alex Vilenkin
Tufts University
Medford, MA, USA
To the memory of Allen Everett and Leonard Schwartz
vii
We would like to express our sincere thanks to the Springer publishing team,
and especially to Angela Lahee. Angela has been extremely helpful, accommodating 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 ofering
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. Tanks also to Natalie Perlov for drawing several fgures 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.
Acknowledgements
ix
Part I Te Big Bang and the Observable Universe
1 A Historical Overview 3
1.1 The Big Cosmic Questions 3
1.2 Origins of Scientifc Cosmology 4
1.3 Cosmology Today 7
2 Newton’s Universe 13
2.1 Newton’s Laws of Motion 13
2.2 Newtonian Gravity 16
2.3 Acceleration of Free Fall 19
2.4 Circular Motion and Planetary Orbits 20
2.5 Energy Conservation and Escape Velocity 22
2.6 Newtonian Cosmology 26
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
3.3 Einstein’s Postulates 39
3.4 Simultaneity 41
3.5 Time Dilation 42
3.6 Length Contraction 44
3.6.1 Speeding Muons 45
3.7 E = mc2 46
3.8 From Space and Time to Spacetime 47
3.9 Causality in Spacetime 51
Contents
x Contents
4 The Fabric of Space and Time 59
4.1 The Astonishing Hypothesis 60
4.2 The Geometry of Space 63
4.2.1 Euclidean Geometry 63
4.2.2 Non-Euclidean Geometry 66
4.3 Curved Space 67
4.3.1 The Curvature of Surfaces 67
4.3.2 The Curvature of Three-Dimensional
Space 70
4.4 The General Theory of Relativity 72
4.5 Predictions and Tests of General Relativity 75
4.5.1 Light Defection and Gravitational
Lensing 75
4.5.2 Gravitational Time Dilation 77
4.5.3 Black Holes 77
4.5.4 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
6.2 Measuring Velocities 99
6.3 Measuring Distances 101
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
7.5 Cosmological Redshift 116
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
Contents xi
9 Dark Matter and Dark Energy 131
9.1 The Average Mass Density of the Universe
and Dark Matter 131
9.2 Dark Energy 136
9.3 The Fate of the Universe—Again 140
10 The Quantum World 143
10.1 Quantum Discreteness 143
10.2 Quantum Indeterminism 145
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
11.2 Thermal Radiation 158
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
12.1 Cosmic Structure 175
12.2 Assembling Structure 179
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
13.3 Stellar Nucleosynthesis 193
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
14.2.1 The Particles 206
14.2.2 The Forces 206
14.3 Symmetry Breaking 208
14.4 The Early Universe Timeline 211
xii Contents
14.5 Physics Beyond the Standard Model 213
14.5.1 Unifying the Fundamental Forces 213
14.6 Vacuum Defects 215
14.6.1 Domain Walls 216
14.6.2 Cosmic Strings 217
14.6.3 Magnetic Monopoles 220
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 Infation 235
16.1 Solving the Flatness and Horizon Problems 235
16.2 Cosmic Infation 236
16.2.1 The False Vacuum 236
16.2.2 Exponential Expansion 238
16.3 Solving the Problems of the Big Bang 240
16.3.1 The Flatness Problem 240
16.3.2 The Horizon Problem 241
16.3.3 The Structure Formation Problem 242
16.3.4 The Monopole Problem 242
16.3.5 The Expansion and High Temperature
of the Universe 242
16.4 Vacuum Decay 243
16.4.1 Boiling of the Vacuum 243
16.4.2 Graceful Exit Problem 244
16.4.3 Slow Roll Infation 245
16.5 Origin of Small Density Fluctuations 247
16.6 More About Infation 249
16.6.1 Communication in the Infating
Universe 249
16.6.2 Energy Conservation 250
Contents xiii
17 Testing Infation: Predictions and Observations 255
17.1 Flatness 255
17.2 Density Fluctuations 256
17.3 Gravitational Waves 260
17.4 Open Questions 264
18 Eternal Infation 269
18.1 Volume Growth and Decay 269
18.2 Random Walk of the Infaton Field 271
18.3 Eternal Infation via Bubble Nucleation 274
18.4 Bubble Spacetimes 275
18.5 Cosmic Clones 279
18.6 The Multiverse 281
18.7 Testing the Multiverse 284
18.7.1 Bubble Collisions 284
18.7.2 Black Holes from the Multiverse 285
19 String Theory and the Multiverse 291
19.1 What Is String Theory? 292
19.2 Extra Dimensions 294
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
20.1.1 Neutron Mass 302
20.1.2 Strength of the Weak Interaction 303
20.1.3 Strength of Gravity 303
20.1.4 The Magnitude of Density Perturbations 303
20.2 The Cosmological Constant Problem 304
20.2.1 The Dynamic Quantum Vacuum 304
20.2.2 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
xiv Contents
21.4 Predicting the Cosmological Constant 316
21.4.1 Rough Estimate 317
21.4.2 The Distribution 317
21.5 The Measure Problem 319
21.6 The Doomsday Argument and the Future
of Our Civilization 321
21.6.1 Large and Small Civilizations 322
21.6.2 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
22.2.1 Where Does This Leave Us? 330
22.2.2 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
23.2.1 Euclidean Time 337
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
24.1.1 What Do We Know? 343
24.1.2 Cosmic Infation 344
24.2 The Multiverse 345
24.2.1 Bubble Universes 345
24.2.2 Other Disconnected Spacetimes 346
24.2.3 Levels of the Multiverse 346
24.2.4 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
Part I
The Big Bang and the Observable Universe
3
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 of deep into thought, wondering: Is the universe
fnite or infnite? Has it existed forever? If not, when and how did it come
into being? Will it ever end? How do we humans ft 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. Ten he woke up and cracked the egg open with an ax.
Te light part of the egg foated 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 feas in his hair transmuted into humans.
Te prospect of being a descendant of feas 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 frst place?” Similar types of questions also arise in the context of scientifc cosmology. Even if we claim to know what happened at the beginning of the universe, you can always ask: And what happened before that?
1
A Historical Overview
© Springer International Publishing AG 2017
D. Perlov and A. Vilenkin, Cosmology for the Curious,
DOI 10.1007/978-3-319-57040-2_1
4 1 A Historical Overview
Tere 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. Tus, 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.
1.2 Origins of Scientifc Cosmology
Te idea that the universe can be rationally understood is at the foundation of all scientifc knowledge. Tis concept is now commonplace, but in
Ancient Greece more than 20 centuries ago it was a daring hypothesis. Te
Greek philosopher Tales (6th century BC) suggested that all of Nature’s
variety could be understood from a few basic principles, without the intervention 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.” Tis line of thought was further developed by Epicurus
(3rd century BC), who argued that complex order, including living organisms, evolved in a natural way, by random collisions and rearrangements
of atoms, without any purpose or intelligent design. Epicurus asserted that
atoms occasionally experience small random “swerves” from their rectilinear
motion. He believed that these deviations from strict determinism were necessary to explain the existence of free will. Epicurus taught that the universe
is infnite and that our Earth is just one of countless worlds that constantly
form and decay in an infnite space (Fig. 1.1).
Another important direction of thought originated with Pythagoras (6th
century BC), who believed that mathematical relations were at the heart of
all physical phenomena. Pythagoras was the frst to call the heavens cosmos,
which means order. He suggested that the Earth, the Sun, and other celestial bodies are perfect spheres and move in perfect circles around a central
fre, which cannot be seen by human eyes. Tink about how diferent this is
from the random aggregates of atoms envisioned by Epicurus!
In the 4th century BC, Plato and then Aristotle proposed more elaborate
versions of this picture, placing the Earth at the center of the universe, with