Undergraduate Texts in Physics

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Claus Grupen

Astroparticle PhysicsSecond Edition

123

With Contribution by Dr. Tilo Stroh

Claus GrupenUniversität Siegen FB PhysikSiegen, Germany

ISSN 2510-411X ISSN 2510-4128 (electronic)Undergraduate Texts in PhysicsISBN 978-3-030-27341-5 ISBN 978-3-030-27339-2 (eBook)https://doi.org/10.1007/978-3-030-27339-2

1st edition: © Springer-Verlag Berlin Heidelberg 20052nd edition: © Springer Nature Switzerland AG 2020This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or partof 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 transmissionor information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilarmethodology now known or hereafter developed.The use of general descriptive names, registered names, trademarks, service marks, etc. in thispublication does not imply, even in the absence of a specific statement, that such names are exempt fromthe 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 thisbook are believed to be true and accurate at the date of publication. Neither the publisher nor theauthors or the editors give a warranty, expressed or implied, with respect to the material containedherein or for any errors or omissions that may have been made. The publisher remains neutral with regardto jurisdictional claims in published maps and institutional affiliations.

Cover illustration: Interaction of an energetic cosmic ray muon in the ALPEH experiment

This Springer imprint is published by the registered company Springer Nature Switzerland AGThe registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Muon shower in the ALEPH experiment at a depth of 125m underground

Preface to the Present Second English Edition(2020)

Nothing lasts, nothing is finished, and nothing is perfect.Alan Saporta

The first English edition of Astroparticle Physics was published in 2005. Eventhough the period of 14 years since the first edition of this book is short comparedto the recently determined age of the universe by the Planck satellite, a lot hashappened since 2005. In particular, there are new results in cosmology. The clas-sical Big Bang model is able to explain the flatness, the horizon, and the monopoleproblems. However, what happened in the first fractions of a second is stillunknown. What is bothering us is the still open problem of the dominance of darkmatter and dark energy. CP-violating effects are known in the field of particlephysics, but they are insufficient to explain the disappearance of antimatter. Resultsfrom the satellite experiment PAMELA and the AMS experiment on board theinternational space station ISS do find a surprisingly high positron excess at highenergies. But there is also the possibility that these positrons originate from neutronstars, quasars, or active galactic nuclei.

In particle physics, the discovery of the long-searched-for Higgs boson at theLarge Hadron Collider (LHC) at CERN in 2012 is certainly a highlight. With itsmass of 125GeV, this boson supports the Standard Model of particle physics. Onthe other hand, the non-observation of supersymmetric particles in the mass rangeof up to one TeV is somewhat disappointing. Supersymmetric particles were andstill are considered as dark-matter candidates. With gravitational microlensing onecan, however, ‘see’ the effect of dark matter in the Bullet Cluster, but this ‘seeing’ isa little indirect. So, the search for dark-matter particles still goes on.

A short flicker of hope for the detection of gravitational waves from the BigBang came from the BICEP experiment at the South Pole, but it soon crumbled intodust. The expected gravitational waves should exhibit a fingerprint of the polari-sation in the primordial cosmic background radiation, for which there seemed someevidence from BICEP. The polarisation of the cosmic blackbody radiation is,however, also influenced by cosmic dust, and the Planck satellite could not confirmBICEP’s result. On the other hand, the LIGO detector with its two Michelsoninterferometers was the first to find excellent evidence for gravitational waves in2015. This represented an unexpected real breakthrough. Up to the time of writing

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of this book 11 events were found, most of them dominated by mergers of twoblack holes, and one by a kilonova caused by a binary-neutron-star merger. Thetime structure of the gravitational-wave signals and the coincident measurementof the signals in two separate stations about 3000 kilometers apart providesexcellent support for the correctness of these findings. This detection of gravita-tional waves opens up a new window for an astronomy in addition to the obser-vation of celestial objects by electromagnetic radiation.

In cosmic rays the ICECUBE experiment found evidence for cosmogenic,high-energy neutrino events in the PeV range since 2013, at least one of themwhich possibly correlates with a radiation burst of a blazar residing in a galaxy at adistance of almost ten billion light-years. Therewith, also the neutrino astronomyenters the stage of astroparticle physics in the high-energy regime.

Also, new developments in detection techniques might gain additional scientificknowledge. For example, the radio measurements of high-energy cosmic raysprovide a cost-effective technique for the measurement of primary cosmic rays inthe range beyond 100 PeV in extensive air showers. The radio signal is believed tooriginate from geomagnetic synchrotron radiation. The pioneer experimentsLOPES and LOFAR have opened up a new detection window by radio astronomyin the field of high-energy astroparticle physics. Radio experiments with their 100%duty time can observe the sky all day, in contrast to fluorescence and Cherenkovtelescopes, which can only operate in cloudless and moonless nights. The SquareKilometre Array (SKA) presently under construction will be the most sensitiveradio telescope in the future, and could contribute to uncover the origin anddevelopment of our universe.

The Planck satellite with its excellent angular resolution of five arc minutes(COBE: 7 degrees, WMAP: 13.5 arc minutes) and increased sensitivity has mea-sured the cosmic background radiation in large detail, and has provided a set of newimportant cosmological parameters.

Compared to the first English edition we have added also new sections, like theone on extrasolar planets, which take into account new developments in astropar-ticle physics. Naturally, all chapters have been updated so that they present the mostrecent knowledge in this field.

The problem sections of the first edition of the book have also been updated andsome problems to new sections have been added.

I thank Prof. Dr. Glen Cowan for his important ideas and suggestions, in par-ticular, in the field of cosmology and the early universe, and for allowing me to usethese ideas from the first edition of this book. I also acknowledge the numerouscontributions of Dr. Tilo Stroh to the present edition, in particular, his successfulefforts to produce a high-quality appearance of this book.

Siegen, GermanySeptember 2019

Claus Grupen

viii Preface to the Present Second English Edition (2020)

Preface to the First English Edition (2005)

This book on astroparticle physics is the translation of the book on‘Astroteilchenphysik’ published in German by Vieweg,Wiesbaden, in the year 2000.It is not only a translation, however, but also an update. The young field ofastroparticle physics is developing so rapidly, in particular with respect to ‘newastronomies’ such as neutrino astronomy and the detailed measurements of cosmicbackground radiation, that these new experimental results and also new theoreticalinsights need to be included.

The details of the creation of the universe are not fully understood yet and it isstill not completely clear how the world will end, but recent results from supernovaeobservations and precise measurement of the primordial blackbody radiation seemto indicate with increasing reliability that we are living in a flat Euclidean universewhich expands in an accelerated fashion.

In the past couple of years, cosmology has matured from a speculative science toa field of textbook knowledge with precision measurements at the percent level.

The updating process has been advanced mainly by my colleague Dr. GlenCowan, who is lecturing on astroparticle physics at Royal Holloway College,London, and by myself. The chapter on ‘Cosmology’ has been rewritten, andchapters on ‘The Early Universe’, ‘Big Bang Nucleosynthesis’, ‘The CosmicMicrowave Background’, and ‘Inflation’ as well as a section on gravitationalastronomy have been added. The old chapter on ‘Unsolved Problems’ chapter on‘Dark Matter’, and part of it went into chapters on primary and secondary cosmicrays.

The book has been extended by a large number of problems related toastroparticle physics. Full solutions to all problems are given. To ease the under-standing of theoretical aspects and the interpretation of physics data, a mathematicalappendix is offered, where most of the formulae used are presented and/or derived.In addition, details on the thermodynamics of the early universe have been treatedin a separate appendix.

Professor Dr. Simon Eidelman from the Budker Institute of Nuclear Physics inNovosibirsk and Dipl.Phys. Tilo Stroh have carefully checked the problems andproposed new ones. Dr. Ralph Kretschmer contributed some interesting and very

ix

intricate problems. I have also received many comments from my colleagues andstudents in Siegen.

The technical aspects of producing the English version lay in the hands ofMs. Ute Smolik, Lisa Hoppe, and Ms. Angelika Wied (text), Dipl.Phys. StefanArmbrust (updating the figures), Dr. Glen Cowan and Ross Richardson (polishedmy own English translation), and M.Sc. Mehmet T. Kurt (helping with the editing).The final appearance of the book including many comments on the text, the figures,and the layout was accomplished by Dipl.Phys. Tilo Stroh and M.Sc. Nadir OmarHashim.

Without the help of these people, it would have been impossible for me tocomplete the translation in any reasonable time, if at all. In particular, I would liketo thank my colleague Prof. Dr. Torsten Fließbach, an expert on Einstein’s theory ofgeneral relativity, for his critical assessment of the chapter on cosmology and forproposing significant improvements. Also, the contributions by Dr. Glen Cowan onthe new insights into the evolution of the early universe and related subjects arehighly appreciated. Dr. Cowan has really added essential ingredients to the lastchapters of the book. Finally, Prof. Dr. Simon Eidelman, Dr. Armin Böhrer, andDipl.Phys. Tilo Stroh read the manuscript with great care and made invaluablecomments. I thank all my friends for their help in creating this English version ofmy book.

Siegen, February 2005 Claus Grupen

x Preface to the First English Edition (2005)

Preface to the German Edition

The field of astroparticle physics is not really a new one. Up until 1960, the physicsof cosmic rays essentially represented this domain. Elementary particle physics inaccelerators has evolved from the study of elementary particle processes in cosmicradiation. Among others, the first antiparticles (positrons) and the members of thesecond lepton generation (muons) were discovered in cosmic-ray experiments.

The close relationship between cosmology and particle physics was, however,recognized only relatively recently. Hubble’s discovery of the expanding universeindicates that the cosmos originally must have had a very small size. At suchprimeval times, the universe was a microworld that can only be described byquantum-theoretical methods of elementary particle physics. Today, particlephysicists try to recreate the conditions that existed in the early universe by usingelectron–positron and proton–antiproton collisions at high energies to simulate‘mini Big Bangs’.

The popular theories of elementary particle physics attempt to unify the varioustypes of interactions in the Standard Model. The experimental confirmation of theexistence of heavy vector bosons that mediate weak interactions (W þ ;W�; Z0), andprogress in the theoretical understanding of strong interactions seem to indicate thatone may be able to understand the development of the universe just after the BigBang. The high temperatures or energies that existed at the time of the Big Bangwill, however, never be reached in earthbound laboratories. This is why a symbiosisof particle physics, astronomy, and cosmology is only too natural. Whether this newfield is named astroparticle physics or particle astrophysics is more or less a matterof taste or the background of the author. This book will deal both with astrophysicsand elementary particle physics aspects. We will equally discuss the concepts ofastrophysics focusing on particles and particle physics using astrophysical methods.The guiding line is physics with astroparticles. This is why I preferred the termastroparticle physics over particle astrophysics.

After a relatively detailed historical introduction (Chap. 1) in which the mile-stones of astroparticle physics are mentioned, the basics of elementary particlephysics (Chap. 2), particle interactions (Chap. 3), and measurement techniques

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(Chap. 4) are presented. Astronomical aspects prevail in the discussion of accel-eration mechanisms (Chap. 5) and primary cosmic rays (Chap. 6). In these fields,new disciplines such as neutrino and gamma-ray astronomy represent a close link toparticle physics. This aspect is even more pronounced in the presentation of sec-ondary cosmic rays (Chap. 7). On the one hand, secondary cosmic rays have been agold mine for discoveries in elementary particle physics. On the other hand,however, they sometimes represent an annoying background in astroparticleobservations.

The highlight of astroparticle physics is surely cosmology (Chap. 8) in which thetheory of general relativity, which describes the macrocosm, is united with thesuccesses of elementary particle physics. Naturally, not all questions have beenanswered; therefore a final chapter is devoted to open and unsolved problems inastroparticle physics (Chap. 9).

The book tries to bridge the gap between popular presentations of astroparticlephysics and textbooks written for advanced students. The necessary basics fromelementary particle physics, quantum physics, and special relativity are carefullyintroduced and applied, without rigorous derivation from appropriate mathematicaltreatments. It should be possible to understand the calculations presented with theknowledge of basic A-level mathematics. On top of that, the basic ideas discussedin this book can be followed without referring to special mathematical derivations.

I owe thanks to many people for their help during the writing of this book.Dr. Armin Böhrer read the manuscript with great care. Ms. Ute Bender andMs. Angelika Wied wrote the text, and Ms. Claudia Hauke prepared the figures thatwere finalized by Dipl.Phys. Stefan Armbrust. I owe special thanks to Dr. KlausAffholderbach and Dipl.Phys. Olaf Krasel who created the computer layout of thewhole book in the LaTeX style. I am especially indebted to Dipl.Phys. Tilo Stroh forhis constant help, not only as far as physics questions are concerned, but also inparticular for applying the final touch to the manuscript with his inimitable, mas-terful eye for finding the remaining flaws in the text and the figures. Finally, I owemany thanks to the Vieweg editors, Ms. Christine Haite and Dipl.Math. WolfgangSchwarz.

Geneva, July 2000 Claus Grupen

xii Preface to the German Edition

Contents

1 Historical Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Early Indications of Celestial Phenomena in the Sky . . . . . . . . 21.2 Discoveries in the 20th Century . . . . . . . . . . . . . . . . . . . . . . . 41.3 Discoveries of New Elementary Particles in Cosmic Rays . . . . 101.4 Start of the Satellite Era . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141.5 Contributions of Accelerators to Cosmic Rays . . . . . . . . . . . . 201.6 Renaissance of Cosmic Rays . . . . . . . . . . . . . . . . . . . . . . . . . 211.7 Open Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2 The Standard Model of Elementary Particles . . . . . . . . . . . . . . . . . 292.1 Examples of Interaction Processes . . . . . . . . . . . . . . . . . . . . . 362.2 Quantum Numbers and Symmetries . . . . . . . . . . . . . . . . . . . . 402.3 Unified Theory of Interactions . . . . . . . . . . . . . . . . . . . . . . . . 432.4 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

3 Kinematics and Cross Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493.1 Threshold Energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513.2 Examples for the Determination of Center-of-Mass

Energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523.3 Four-Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543.4 Examples for the Treatment of Decays . . . . . . . . . . . . . . . . . . 60

3.4.1 Two-Body Decays . . . . . . . . . . . . . . . . . . . . . . . . . . 603.4.2 Three-Body Decays . . . . . . . . . . . . . . . . . . . . . . . . . 62

3.5 Lorentz Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 653.6 Determination of Cross Sections . . . . . . . . . . . . . . . . . . . . . . 663.7 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

4 Physics of Particle and Radiation Detection . . . . . . . . . . . . . . . . . . 714.1 Interactions of Astroparticles . . . . . . . . . . . . . . . . . . . . . . . . . 724.2 Interaction Processes Used for Particle Detection . . . . . . . . . . 74

xiii

4.3 Particle Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 794.4 Principles of the Atmospheric Air Cherenkov Technique . . . . . 804.5 Special Aspects of Photon Detection . . . . . . . . . . . . . . . . . . . 834.6 Cryogenic Detection Techniques . . . . . . . . . . . . . . . . . . . . . . 864.7 Propagation and Interactions of Astroparticles in

Galactic and Extragalactic Space . . . . . . . . . . . . . . . . . . . . . . 924.8 Characteristic Features of Detectors . . . . . . . . . . . . . . . . . . . . 954.9 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

5 Acceleration Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 995.1 Cyclotron Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1005.2 Acceleration by Sunspots . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1015.3 Shock Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1025.4 Fermi Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1075.5 Pulsars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1095.6 Binaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1125.7 Energy Spectra for Primary Particles . . . . . . . . . . . . . . . . . . . 1165.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

6 Primary Cosmic Rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1216.1 Charged Component of Primary Cosmic Rays . . . . . . . . . . . . 1226.2 Nature and Origin of the Highest-Energy Cosmic Rays . . . . . . 1366.3 Neutrino Astronomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

6.3.1 Atmospheric Neutrinos . . . . . . . . . . . . . . . . . . . . . . . 1426.3.2 Solar Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1496.3.3 Supernova Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . 1596.3.4 High-Energy Galactic and Extragalactic Neutrinos . . . 1656.3.5 Geoneutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

6.4 Gamma Astronomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1786.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1786.4.2 Production Mechanisms for c Rays . . . . . . . . . . . . . . 1806.4.3 Detection of c Rays . . . . . . . . . . . . . . . . . . . . . . . . . 1856.4.4 Observation of c-Ray Point Sources . . . . . . . . . . . . . . 1936.4.5 c-Ray Bursters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

6.5 X-Ray Astronomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2036.5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2036.5.2 Production Mechanisms for X Rays . . . . . . . . . . . . . . 2046.5.3 Detection of X Rays . . . . . . . . . . . . . . . . . . . . . . . . . 2076.5.4 Observation of X-Ray Sources . . . . . . . . . . . . . . . . . 210

6.6 Gravitational-Wave Astronomy . . . . . . . . . . . . . . . . . . . . . . . 2196.7 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229

xiv Contents

7 Secondary Cosmic Rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2357.1 Propagation in the Atmosphere . . . . . . . . . . . . . . . . . . . . . . . 2367.2 Cosmic Rays at Sea Level . . . . . . . . . . . . . . . . . . . . . . . . . . . 2457.3 Cosmic Rays Underground . . . . . . . . . . . . . . . . . . . . . . . . . . 2527.4 Extensive Air Showers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2627.5 Radio Measurement of Air Showers . . . . . . . . . . . . . . . . . . . . 2757.6 Acoustic Detection of Air Showers . . . . . . . . . . . . . . . . . . . . 2817.7 Some Thoughts on the Highest Energies . . . . . . . . . . . . . . . . 2837.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2887.9 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289

8 Cosmology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2938.1 The Hubble Expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2948.2 The Isotropic and Homogeneous Universe . . . . . . . . . . . . . . . 2998.3 The Friedmann Equation from Newtonian Gravity . . . . . . . . . 3008.4 The Fluid Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3058.5 The Acceleration Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . 3068.6 Solution of the Friedmann Equation Without Vacuum

Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3068.7 Experimental Evidence for the Vacuum Energy . . . . . . . . . . . 3098.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3138.9 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313

9 The Early Universe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3159.1 The Planck Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3159.2 Thermodynamics of the Early Universe . . . . . . . . . . . . . . . . . 3179.3 Equation of State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3219.4 Refining the Solution of the Friedmann Equation . . . . . . . . . . 3229.5 Thermal History of the First Ten Microseconds . . . . . . . . . . . 3259.6 The Baryon Asymmetry of the Universe . . . . . . . . . . . . . . . . . 327

9.6.1 Experimental Evidence for the Baryon Asymmetry . . . 3279.6.2 Size of the Baryon Asymmetry . . . . . . . . . . . . . . . . . 3329.6.3 The Sakharov Conditions . . . . . . . . . . . . . . . . . . . . . 333

9.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3369.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336

10 Big Bang Nucleosynthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33910.1 Some Ingredients for the Big Bang Nucleosynthesis . . . . . . . . 34010.2 Start of the BBQ Era . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34110.3 The Neutron-to-Proton Ratio . . . . . . . . . . . . . . . . . . . . . . . . . 34210.4 Synthesis of Light Elements . . . . . . . . . . . . . . . . . . . . . . . . . 34410.5 Detailed Big Bang Nucleosynthesis . . . . . . . . . . . . . . . . . . . . 346

Contents xv

10.6 Determination of the Number of Neutrino Families . . . . . . . . . 35010.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35410.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354

11 The Cosmic Microwave Background . . . . . . . . . . . . . . . . . . . . . . . 35711.1 Prelude: Transition to a Matter-Dominated Universe . . . . . . . . 35811.2 Discovery and Basic Properties of the CMB . . . . . . . . . . . . . . 35911.3 Formation of the CMB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36111.4 CMB Anisotropies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36311.5 The Monopole and Dipole Terms . . . . . . . . . . . . . . . . . . . . . . 36411.6 Small-Angle Anisotropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36511.7 Determination of Cosmological Parameters . . . . . . . . . . . . . . . 36711.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37211.9 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372

12 Inflation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37512.1 The Horizon Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37612.2 The Flatness Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37712.3 The Monopole Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38012.4 How Inflation Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38312.5 Mechanisms for Inflation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38512.6 Solution to the Flatness Problem . . . . . . . . . . . . . . . . . . . . . . 39012.7 Solution to the Horizon Problem . . . . . . . . . . . . . . . . . . . . . . 39212.8 Solution of the Monopole Problem . . . . . . . . . . . . . . . . . . . . . 39212.9 Inflation and Growth of Structure . . . . . . . . . . . . . . . . . . . . . . 39412.10 Outlook on Inflation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39612.11 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39812.12 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399

13 Dark Energy and Dark Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40113.1 Large-Scale Structure of the Universe . . . . . . . . . . . . . . . . . . 40213.2 Dark Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40313.3 Dark Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407

13.3.1 Dark Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41113.3.2 Neutrinos as Dark Matter . . . . . . . . . . . . . . . . . . . . . 41813.3.3 Weakly Interacting Massive Particles (WIMPs) . . . . . 42113.3.4 Axions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42513.3.5 The Role of Dark Matter and the Vacuum

Energy Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42713.3.6 Galaxy Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . 42813.3.7 Resume on Dark Matter and Dark Energy . . . . . . . . . 429

13.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43213.5 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433

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14 Astrobiology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43514.1 Extrasolar Planets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43514.2 Extremophiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43914.3 Finely Tuned Parameters of Life . . . . . . . . . . . . . . . . . . . . . . 44014.4 Multiverses and the Anthropic Principle . . . . . . . . . . . . . . . . . 44414.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44514.6 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446

15 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44915.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45315.2 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454

Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 457

Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513

Photo Credits and References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555

Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 571

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575

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