Cosmology

Advances in science have greatly changed our ideas on the nature of the universe. Cosmology:The Science of the Universe is a broad and elementary introduction to cosmology that includesaspects of its history, theology, and philosophy. The book explores the realm of recedinggalaxies, the fascinating properties of space and time, the bizarre world of black holes, the

astonishing expansion of the universe, the elegant simplicity of cosmic redshifts, and themomentous issues of ination. Its subjects cover modern views on the origin of atoms,galaxies, life, and the universe itself; they range from the subatomic to the extragalactic,

from the beginning to the end of time, and from terrestrial to extraterrestrial life. Oldproblems (e.g., the cosmic-edge) are revived and new perplexities (e.g., the containmentriddle) are reviewed. In this unique book, Professor Harrison shows how in every age societies

devise universes that make sense of the human experience. He explores the cosmic sceneryof the Babylonian, Pythagorean, Aristotelian, Stoic, Epicurean, Medieval, Cartesian, andNewtonian world systems and shows how these and other systems laid the foundations ofthe modern physical universe.

The rst edition of this best-selling book received world-wide acclaim for its far rangingtreatment and clarity of explanation. This eagerly awaited second edition updates and extendsthe rst edition. The additional chapters discuss Early Scientic Cosmology, Cartesian and

Newtonian World Systems, Cosmology After Newton and Before Einstein, ObservationalCosmology, Ination, and Creation of the Universe.

EDWARD HARRISON, distinguished university professor emeritus of physics and astronomy atthe University of Massachusetts, was born in London at the end of World War I. He studied

at London University and served for several years in action with the British Army in WorldWar II. He was a scientist at the Atomic Energy Research Establishment and the RutherfordHigh Energy Laboratory in England until 1966 when he became a Five College professor at

the University of Massachusetts and taught at Amherst, Hampshire, Mount Holyoke, andSmith Colleges. Professor Harrison is author of The Masks of the Universe (which gainedthe Melcher Award), Darkness at Night: A Riddle of the Universe, and numerous scienticarticles that have contributed to the advance of modern cosmology. He has also written

many articles on the history and philosophy of early cosmology. He is married to Photeni,has two children, John-Peter and June Zoe, and is now adjunct professor at the StewardObservatory, University of Arizona.

CosmologyT H E S C I E N C E O F T H E UN I V E R S E

S E C O N D E D I T I O N

E D W A R D H A R R I S O NFive College Astronomy Department, University of Massachusetts

Steward Observatory, University of Arizona

# Cambridge University Press 1981, 2000

This book is in copyright. Subject to statutory exception

and to the provisions of relevant collective licensing agreements,

no reproduction of any part may take place without

the written permission of Cambridge University Press.

First published 1981

Reprinted 1985, 1986, 1988, 1989, 1991

Second edition 2000

Printed at MPG Books Group, UK

A catalogue record for this book is available from the British Library

Library of Congress Cataloguing in Publication data

Harrison, Edward Robert.

Cosmology: the science of the universe / Edward R. Harrison.

2nd ed.

p. cm.

Includes bibliographical references and index.

ISBN 0 521 66148 X

1. Cosmology. I. Title. II. Title: Cosmology, the science of the universe.

QB981.H276 1999

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CONTENTS

Preface ixIntroduction 1

PART I

1 What is cosmology? 13The Universe 13Cosmology 15The magic universe 17The mythic universe 17The anthropometric universe 19Cosmology and society 20Reections 21Projects 25Further reading 26Sources 26

2 Early scientic cosmology 28The beginning of western science 28Platos universe 29Three cosmic systems of the

ancient world 29The Aristotelian universe 30The Epicurean universe 33The Stoic universe 34The mystery religions 34The medieval universe 35The heliocentric universe 37The innite universe 38Reections 42Projects 45Further reading 46Sources 46

3 Cartesian and Newtonian worldsystems 49

The decline of Aristotelian science 49The Cartesian world system 51The Newtonian world system 54Newton and the innite universe 60The atomic theory 61Reections 61Projects 63Further reading 64Sources 64

4 Cosmology after Newton andbefore Einstein 66

Hierarchical universes 66The nebula hypothesis 70Cosmical islands 70The new astronomy 73The Victorian universe 77The age problem 78Fall of the Victorian universe 80Reections 81Projects 83Further reading 83Sources 84

5 Stars 87The distant stars 87A forest of stars 89Inside the stars 93Nuclear energy 95Birth of stars 100The star is dead! Long live the star! 103Reections 105Projects 110

v

Further reading 111Sources 112

6 Galaxies 113Our Galaxy 113The distant galaxies 119Birth of galaxies 123Radio galaxies and quasars 126Reections 129Projects 131Further reading 132Sources 132

7 Location and the cosmic center 134The location principle 134The isotropic universe 137The cosmological principle 138Perfect cosmological principle 140Reections 141Projects 145Further reading 145Sources 145

8 Containment and the cosmic edge 147The containment principle 147The cosmic edge 149Containment of space and time 153Design argument 155Many physical universes 156Theistic and anthropic principles 157Whither the laws of nature? 159Containment riddle 161Reections 162Projects 166Further reading 167Sources 167

9 Space and time 169Space 169Space and time 171Time 172The now 176Time travel 178Atomic time 179Reections 180Projects 184Further reading 185Sources 185

PART II

10 Curved space 189Euclidean geometry 189Non-Euclidean geometry 190Measuring the curvature of space 194The outstanding theorem 196Riemannian spaces 198Reections 199Projects 203Further reading 204Sources 204

11 Special relativity 206New ideas for old 206The strangeness of spacetime 207Travels in space and time 210Reections 214Projects 218Further reading 218Sources 219

12 General relativity 220Principle of equivalence 220A closer look 222Geometry and gravity 224Tidal forces 225Theory of general relativity 228Tests of general relativity 233Machs principle 236Reections 239Projects 243Further reading 244Sources 245

13 Black holes 246Gravitational collapse 246Curved spacetime of black holes 248Rotating black holes 253Superholes 257Miniholes 258Black-hole magic 259Hawking radiation 260Black holes are heat engines 263Reections 264Projects 267Further reading 268Sources 268

14 Expansion of the universe 270The great discovery 270

vi C O N T E N T S

The expanding space paradigm 275The expanding rubber sheet universe 275Measuring the expansion of the

universe 285The velocitydistance law 287Accelerating and decelerating universes 289Classifying universes 290Reections 292Projects 299Further reading 300Sources 300

15 Redshifts 302Cosmic redshifts 302The three redshifts 306Two basic laws 307Distances and recession velocities 309Cosmological pitfalls 309Redshift curiosities 311Reections 314Projects 320Sources 321

16 Newtonian cosmology 323Static Newtonian universe 323Expanding cosmic sphere 326Cosmological constant 331Why does Newtonian cosmology

give the same answer? 332Reections 333Projects 336Further reading 337Sources 337

17 The cosmic box 339The universe in a nutshell 339Particles and waves 341Thermodynamics and cosmology 344Where has all the energy gone? 348Reections 350Projects 353Sources 353

18 The many universes 355Static universes 355De Sitter universe 358Friedmann universes 359Oscillating universes 362FriedmannLematre universes 363Classication of universes 365

Universes in compression 368Universes in tension 369Worlds in convulsion 371Kinematic relativity 373Continuous creation 374Scalartensor theory 376Reections 379Projects 383Further reading 384Sources 384

19 Observational cosmology 387Introduction 387Cosmography 387Local observations 388Intermediate-distance observations 397Large-distance observations 400Is the universe open or closed? 403Reections 404Projects 407Further reading 408Sources 408

PART III

20 The early universe 413The primeval atom 413The last fteen billion years 415The rst million years 416The rst second 419The rst hundred microseconds 422Grand unied era 427Reections 428Projects 435Further reading 436Sources 436

21 Horizons in the universe 438What are cosmological horizons? 438Horizons in static universes 439The horizon riddle 441The horizon problem 442Hubble spheres 443Reception and emission distances 444The photon horizon in cosmology 446The particle horizon 447Conformal diagrams 449Event horizons 451Reections 454

vii

C O N T E N T S vii

Projects 457Sources 457

22 Ination 458Perfect symmetry 458The monopole problem 458Discovery of ination 459Cosmic tension 459Ination 460Ination solves the monopole problem 463Ination solves the atness problem 463Ination solves the horizon problem 465Nonluminous matter 467The origin of galaxies 468Reections 470Projects 472Further reading 472Sources 473

23 The cosmic numbers 474Constants of nature 474The cosmic connection 479Magic numbers 480Solving the cosmic connection 483Reections 486Projects 490Further reading 490Sources 490

24 Darkness at night 491The great riddle 491Two interpretations 493Halleys shells 494Bright-sky universes 497The paradox resolved 499The golden walls of the universe 502The celebrated hypothesis 503Expansion and darkness 503

Reections 506Projects 513Further reading 513

25 Creation of the universe 515Cosmogenesis I 515Creation myths 515Genesis 518Cosmogenesis II 519Cosmogenesis III 520Fitness of the universe 522Fitness and creation 523Theistic theories 523Anthropic theories 524Spontaneous creation theories 524Natural selection theories 525Eschatology 526Reections 528Projects 532Further reading 532Sources 533

26 Life in the universe 535Origin of life on Earth 535The exuberant Earth 537The evolution of life 538Natural selection 540Intelligent life 542What is life? 542Life beyond the Earth 543Epilogue 547Reections 547Projects 551Further reading 552Sources 553

Appendix Fundamental quantities 555Index 557

viii C O N T E N T S

PRE FACE

This second edition of Cosmology: TheScience of the Universe revises and extendsthe rst edition published in 1981. Muchhas happened since the rst edition;many developments have occurred, andcosmology has become a wider eld ofresearch.

As before, the treatment is elementaryyet broad in scope, and the aim is to presentan outline that appeals to the thoughtfulperson at a level not requiring an advancedknowledge in the natural sciences. Cosmol-ogy has many faces, scientic and nonscien-tic; in this work the primary emphasis is oncosmology as a science, but the importanthistorical, philosophical, and theologicalaspects are not ignored. Mathematics isavoided except in a few places, mostly atthe end of chapters, and the treatment isvaried enough to meet the needs of boththose who enjoy and do not enjoy mathe-matics.

At the end of each chapter are twosections entitled Reections and Projects.The Reections section presents topics forreection and discussion. The Projectssection raises questions and issues that achallenged reader might care to tackle.Cosmology impels us to ask deep questions,read widely, and think deeply. It is not thesort of subject that lends itself readily tosimple yes and no answers. On most issuesthere are conicting arguments to be inves-tigated, weighed, rejected, accepted, ormodied according to ones personal tastesand beliefs. Cosmology challenges the

mind, shapes our way of thinking aboutthe world in which we live, and leavesimpressions and ideas that last a lifetime.

Many texts on cosmology and generalrelativity tend to be too technical for collegestudents and nonspecialists. Numerous less-technical treatments now exist that are oftentoo brief and of insucient scope and depthfor a course of study. At the end of eachchapter are suggestions for further readingto help the reader explore alternative treat-ments (sometimes in greater depth anddetail) of the subjects discussed in thechapter. Also provided is a list of sourcescontaining references that are usually read-able and not too technical; the few that aremore technical are included for their histor-ical interest.

The rst edition of this book evolvedfrom class notes used for teaching elemen-tary cosmology in the Five College Astron-omy Department of Amherst College,Hampshire College, Mount HolyokeCollege, Smith College, and the Universityof Massachusetts. At that time the methodof grading consisted of brief weekly papers,mostly on topics (germane to the lectures)of each students choice. It was evidentthat a text of broad scope was needed thatmight hold the attention of students of dif-ferent backgrounds and interests, and pro-vide the information needed for discussionsand the preparation of papers. After thepublication of the rst edition, the methodof grading changed and consisted of fourequally spaced take-home examinations

ix

followed by an end-of-semester examina-tion. Many questions included in the exam-inations did not require mathematicalskills. Both methods of grading have theiradvantages and disadvantages. There mustbe a better way!

I am indebted to many persons for theircomments and helpful suggestions, par-ticularly Thomas Arny (University ofMassachusetts, Amherst), Gregory Benford(University of California, Irvine), RobertBrandenberger (Brown University), MarioBunge (McGill University), ThomasDennis (Mount Holyoke College), JamesEllern (University of Southern California,Los Angeles), George Ellis (University ofCapetown), Stephen Gottesman (Universityof Florida, Gainsville), George Greenstein(Amherst College), Gary Hinshaw(NASA/Goddard Space Flight Center),Paul Hodge (University of Washington),Duane Howells (Hughs Research Labora-tories), John Huchra (HarvardSmith-sonian Center for Astrophysics), John

Lathrop, Charles Leert, William McCrea(University of Sussex), A. J. Meadows(Loughborough University of Technology),Heinz Pagels (University of California,Santa Cruz), Joel Primack (University ofCalifornia, Santa Cruz), Martin Rees (Cam-bridge University), Joe Rosen (University ofCentral Arkansas), Rick Shafer (NASA/Goddard Space Flight Center), StephenSchneider (University of Massachusetts,Amherst), Joseph Snider (Oberlin College),Joseph Tenn (Sonoma State University),Virginia Trimble (University of California,Irvine), David Van Blerkom (University ofMassachusetts, Amherst), Gerard deVaucouleurs (University of Texas, Austin),and Robert Wilson (Smithsonian Astro-physical Observatory).

I am particularly grateful to Fred Steven-son (University of Leeds) for his helpfulcomments and corrections.

EDWARD HARRISON

Mesilla, New Mexico, May 1998

x P R E F A C E

INTRODUCTION

With equal passion I have sought knowledge. I have wished to understand the hearts of

men, I have wished to know why the stars shine. And I have tried to apprehend the

Pythagorean power by which number holds sway above the ux. A little of this, but not

much, I have achieved.

Bertrand Russell (18721970), Autobiography, Prologue

PROLOGUE

Cosmology, the science of the universe,attracts and fascinates us all. In one sense,it is the science of the large-scale structureof the universe: of the realm of extragalacticnebulae, of distant and receding horizons,and of the dynamic curvature of cosmicspace and time. In another sense, it seeksto assemble all knowledge into a unifyingcosmic picture. Most sciences tear thingsapart into smaller and smaller constituentsin order to examine the world in evergreater detail, whereas cosmology is theone science that puts the pieces togetherinto a mighty frame. In yet anothersense, it is the history of mankinds searchfor understanding of the universe, a questthat began long ago at the dawn of thehuman race. We cannot study cosmologyin the broadest sense without heeding themany cosmic pictures of the past that haveshaped human history. We trace the rise ofthe scientic method and how it hasincreased our understanding of the physicaluniverse. Which brings us to the major aimof this book: gaining an elementary under-standing of the physical universe of moderntimes.

Cosmology compels us, willy-nilly, toexamine our deepest and sometimes mostcherished beliefs. It awakens an awarenessof ancient vestigial paradigms that controlour lives and direct the destiny of societies.A person who migrates to a new land, joinsa revolution, goes to war, seeks politicalpower, gains or loses a fortune, gets married,

or does any momentous thing is inuencedby cosmic beliefs.

A brief summary of the contents of thisbook serves as an introduction to the scopeof cosmology as amodern science. In outlineonly, chapter by chapter, the subjectscovered are as follows.

CHAPTER 1

WHAT IS COSMOLOGY?

The history of cosmology shows that inevery age in all societies people believe thatthey have at last discovered the true natureof the Universe. But in each case they havedevised a mask tted on the face of theunknown Universe. In this book we useuniverse to denote a model of theUniverse and avoid making claims to trueand nal knowledge of the Universe.Where there is a society of rational indivi-duals, there we nd a universe, and wherethere is a universe, there we nd a societyof rational individuals. Proud of theirknowledge and condent of its nal truth,the members of a society pity the ignoranceof their ancestors and fail to foresee thattheir descendants will also pity them fortheir ignorance.

Cosmology is the study of universes, howthey originate, how they evolve. Plausibly,hundreds of thousands of years ago, in anAge of Magic, the world was explained bythe activity of ambient spirits. In an Age ofMyths, tens of thousand years ago, lastinguntil recent times, the world was explainedby the capricious acts of nature spirits and

1

the will of remote gods and goddesses. In anAge of Science, we have abandoned muchof our anthropocentric heritage, and havedevised a series of mechanistic universes.The old historic universes (Sumerian,Egyptian, Judaic, Zoroastrian, Confucian,Taoist, Jainic, Buddhist, Aristotelian,Platonic, Stoic, Epicurean, Neoplatonic,Medieval, . . .) dealt with cosmic themesthat gave meaning to human life, themesthat now fail to t naturally into thecurrent physical universe. This causesconcern and prompts us all to think deeply.The last section in this chapter considershow cosmology relates to society andaects our everyday thoughts, actions, andbeliefs.

CHAPTER 2

EARLY SCIENTIFIC COSMOLOGY

This chapter briey reviews known earlyscientic cosmology with comments on theBabylonian, Pythagorean, and Platonicsystems. Emphasis is placed on the threeimportant and enduring Hellenistic worldsystems: Aristotelianism, Epicureanism,and Stoicism. The Aristotelian universe,nite in size, consisted of planetary spheresbounded by an outer sphere of stars; theEpicurean universe, innite in extent, con-sisted of endless worlds composed ofatoms; and the Stoic universe, nite in size,consisted of a cosmos of planets and starssurrounded by empty innite space. Theseworld systems have shaped the history ofsubsequent cosmology.

The Medieval universe, with Aristotelianfoundations, reached its peak in the HighMiddle Ages. Because of the Condemna-tions by the bishop of Paris of Aristoteliancosmology in 1277, the Medieval universeevolved into a Stoic-like system, able toaccommodate an omnipotent God ofunlimited extent. The Copernican revolu-tion overthrew geocentric astronomy infavor of heliocentric astronomy, whichin turn was soon overthrown by the riseof the Cartesian and Newtonian worldsystems.

CHAPTER 3

CARTESIAN AND NEWTONIAN

WORLD SYSTEMS

In the seventeenth century, the revolution-ary Cartesian andNewtonian systems math-ematized andmechanized the natural world.From medieval mathematics and dynamics,Rene Descartes fashioned a mechanizedatomless Epicurean-like world of matterand motion operating in strict obedience tonatural laws. The repercussions scientic,philosophical, and theological were, andstill are, profound. The bodymind (orbodysoul) duality became more sharplyetched than ever before and haunts us tothis day.

Isaac Newton reacted strongly againstCartesian materialism and at rst believedin a nite Stoic cosmos surrounded by aninnite mysterious space. What Descarteshad denied the existence of atoms, thevacuum, and forces acting at a distance Newton armed. Newtons laws of motionand the theory of universal gravity trans-formed astronomy. The atomic theory lostits atheistic associations and began tomake sense of the properties of matter.Where there is no matter, declared Newton,space still exists by virtue of the presence ofspirit. Bodies act upon one another acrossempty space bymeans of long-range gravity.The implications of universal gravity causedNewton later to change his mind and believein an innite Epicurean-like universe, end-lessly populated with uniformly distributedstars.

CHAPTER 4

COSMOLOGY AFTER NEWTON AND

BEFORE EINSTEIN

But even the naked eye sees that stars do notcover the sky uniformly. Thomas Wright inthe eighteenth century proposed that theMilky Way is an enormous assembly ofstars, and that possibly other milky waysexist far away. Immanuel Kant expandedon this idea and devised a hierarchical uni-verse. The renowned astronomer WilliamHerschel explored the heavens, surveyed theGalaxy, and formed the opinion that many

2 C O SMO L O G Y

of the small fuzzy patches of light (nebulae)not only are clusters of unresolved stars butalso some are distant milky ways (galaxies)similar to our own Milky Way (Galaxy).The nebula hypothesis, the idea that theSun and planets formed from a rotating andcontracting cloud of interstellar gas, wassuggested by Kant and later considered inmore detail by Pierre Simon de Laplace.Thus began the riddle of the nebulae: arethe nebulae distant milky ways in a many-island universe or are they solar systems inthe process of formation in a one-island uni-verse? Herschel later in life changed his mindand favored the one-island universe. In thenineteenth century, the spectroscopic analy-sis of starlight by William Huggins andother astronomers and the development ofphotography established the new astron-omy that later became known as astro-physics. At last human beings knew thestars consist of chemical elements exactlythe same as on Earth. And astronomersknew that many nebulae consist only of gas(tipping the balance in favor of the KantLaplace nebula hypothesis and against theWrightKant milky way hypothesis).Astronomers succeeded in measuring theradial velocities of stars by the FizeauDoppler displacement in spectral lines. TheVictorian universe of the nineteenth centurywas a one-island universe. The Solar Systemoccupied the center of the Galaxy, whichexisted in a void of innite, mysteriousspace. TheDarwinian theory of natural selec-tion exacerbated the age-of-the-universeproblem and brought fundamental cosmolo-gical issues into every home. The old conictbetween the Stoic and Epicurean systemsclimaxed in the early years of the twentiethcentury and the many-island universeemerged triumphant. We now know thatsome of the fuzzy patches of light are un-resolved star clusters, some are swirling gasclouds, and others are distant galaxies.

CHAPTERS 5 AND 6

STARS AND GALAXIES

These two chapters discuss stars and galaxiesand their treatment is oriented toward

cosmology.Readers familiarwith elementaryastronomy may wish to skip these twochapters and proceed immediately to thenext two chapters that discuss the importantsubjects of location and containment.

CHAPTER 7

LOCATION AND THE COSMIC

CENTER

Generally, the subject of location (Chapter7) deals with the cosmic center, and the sub-ject of containment (Chapter 8) deals withthe cosmic edge. The location and contain-ment principles, which seem deceptivelysimple, serve to guide us among the pitfallsthat trapped earlier cosmologists and stilltrap students.

This chapter deals with the rise and fall ofthe geocentric and heliocentric universes,and the rise of the centerless universes. Welive in an isotropic universe in which alldirections in space are alike. The locationprinciple states that probably we do notoccupy a cosmic center. The observedisotropy of the universe, coupled with thelocation principle, leads us to the conclusionthat the universe is probably homogeneous.

The homogeneity of the universe, mean-ing that all places in space are alike at acommon instant in time, is the essence ofthe cosmological principle. The perfectcosmological principle, which states thatall places in both space and time are alike,applies not only to theCartesian andNewto-nian world systems, but also to the morerecent expanding steady-state universe.

CHAPTER 8

CONTAINMENT AND THE COSMIC

EDGE

Containment deals with the edge andcontents of the physical universe. The con-tainment principle states: the physical uni-verse contains only physical things. Inmodern physics, both space and time in theform of spacetime are physically real andtherefore part of the physical universe. Ascosmophysicists we deal with the physicaluniverse. But the Universe contains alsononphysical things and this aspect of

I N T R O D U C T I O N 3

containment has implications in the socialand life sciences. Various topics are consid-ered, such as cosmic design and the nelytuned fundamental physical constants, thetheistic and anthropic principles, and thelaws of nature.

A word of warning comes not amiss whileon the subject of containment. Cosmology isincomplete in the fundamental sense that wedo not know how to put ourselves, ascosmologists, into our world systems. TheUniverse is self-aware it contains us whoare conscious beings but the physical uni-verse is not self-aware and does not containus as self-aware beings. We can put ourphysical bodies and biochemical brainsinto a physical universe, which is a modelof the Universe, but we cannot put ourminds (whatever that means) into a universeconceived and studied by our minds. Whenwe try, we fall into an innite regression:the cosmologist studies a universe, whichcontains the cosmologist studying that uni-verse, which contains the cosmologist, . . .and so on, indenitely. For the same reason,painters in the act of painting landscapesleave themselves out of the landscapesthey paint. Otherwise they would have toinclude themselves painting a picture thatincludes themselves painting a picturethat includes . . . . This subject is referred toas the containment riddle: Where in auniverse is the cosmologist studying thatuniverse? The solution to the riddlerequires that we distinguish between theinconceivable Universe (of which we aretotally a part) and our conceived uni-verses (of which we are not totally a part)that we create to make sense of ourexperiences.

CHAPTER 9

SPACE AND TIME

In more depth than usual in an elementarywork, we consider the fascinating nature ofspace and time in pre-Newtonian and post-Newtonian universes. Some topics discussedare the arrow of time, the now, timetravel, Zenos paradoxes, Parmenideanstates of being, Heraclitean acts of becoming,

and conjugate time in the Islamic Kalamuniverse.

Our everyday understanding of time is apatchwork of primitive and sophisticatedconcepts. The time that is used in specialrelativity is not the same as that used inmost other sciences, which is not the sameas that in everyday speech, which in turn isnot the same as the time we actually experi-ence. Conict and contrast abound when-ever we discuss the nature of time. Withnot much hope of success, we try to clarifysome of the issues involved in this perplexingsubject; any fundamental change in ourunderstanding of timewill undoubtedly pro-foundly aect cosmology.

CHAPTER 10

CURVED SPACE

The development of non-Euclidean geome-try in the nineteenth century forms anengrossing subject in the history of scienceand mathematics. Understanding curvedspace is not easy, even for people who livein curved spaces. Much of our attention inthis chapter focuses on the three homoge-neous and isotropic spaces that are of basicimportance in modern cosmology.

CHAPTER 11

SPECIAL RELATIVITY

Special relativity, contrary to studentsexpectations, is easy to understand, and atrue grasp of the essential ideas does notrequire mathematics. The secret lies inspacetime pictures and the realization thatin spacetime the shortest distance is not astraight line. Space travel close to the speedof light provides interesting applications ofrelativity theory. The twin paradox ispuzzling only when the most elementaryaspects of the theory are not understood.

CHAPTER 12

GENERAL RELATIVITY

Special relativity and curved space lead us togeneral relativity and the labors of AlbertEinstein. The rst stepping-stone is theprinciple of equivalence. This is establishedby means of experiments in imaginary

4 C O SMO L O G Y

laboratories that move freely in space near toand far from stars. The second stepping-stoneis the realization that this dynamic state ofaairs is analogous in many respects to thegeometric properties of curved space. In aight of inspiration we are catapulted to thetheory of general relativity and the Einsteinmaster equation. Many ingenious tests ofgeneral relativity have been performed, suc-cessfully verifying the validity of the theoryon astronomical (not cosmic) scales.

We consider the bootstrap ideas em-bodied in Machs principle, a principle so-named by Einstein who found Machsideas inspiring. The old bootstrap theory,periodically revived, asserts that all thingsare immanent within one another, and thenature of any one thing is determined bythe universe as a whole. So far, science hasfailed to make sense of the bootstrap theory.Machs principle, a bootstrap theory, claimsthat the inertia of a body is determined by allthe matter distributed in the universe. Manypersons dislike an undressed space thatexists in its own right, and with the ancients,Bishop Berkeley, and Ernst Mach, thinkthat space cannot exist in a real sense unlessdecently dressed in a distribution of matter.Berkeleys ideas, revamped byMach, playeda historic role in the formulation of generalrelativity. But the idea: the materializationof space, championed at rst by Einstein,was dropped when Einstein performed theconverse: the geometrization of matter.

CHAPTER 13

BLACK HOLES

Although black holes were anticipated inthe eighteenth century on the basis of New-tonian theory, the proper theory for theirstudy is general relativity. Of sphericalbodies of similar mass, black holes havethe highest density and the strongest gravita-tional force at their surface. They arewrapped in their own curved spacetime. Ablack hole exists in a frozen state of perma-nent free-fall collapse. Owing to the extremedistortion of spacetime, an external observersees the black hole in a frozen state, fromwhich nothing (according to the classical

theory), not even light, can escape. Weconsider several topics of interest, such asnonrotating and rotating black holes, theenergy liberated by accretion of matter,miniholes and superholes, the temperatureof black holes, Hawking radiation, andviolation of certain cherished laws of con-servation.

CHAPTER 14

EXPANSION OF THE UNIVERSE

The expansion of the physical universe ranksas one of the greatest discoveries in thehistory of the human race. We invoke theexpanding space paradigm and performimaginary experiments with ERSU Expanding Rubber Sheet Universe. To aidus in our investigations we use the two dier-ent observers introduced in Chapter 7: theordinary stay-at-home observer wholooks out at distant things in the same waythat we do, and the imaginary gadaboutexplorer who rushes around at innitespeed and traverses the universe in zero cos-mic time. The explorer in these experimentsis really us looking down on ERSU as exter-nal observers. Our experiments shed light onmany topics, such as homogeneous expan-sion, cosmic time, recession of the galaxies,the velocitydistance law of expansion, andthe Hubble redshiftdistance law. Theexperiments stress that the galaxies are nothurling away through space but are actuallyat rest in space that is expanding. This is whydistant galaxies can recede from us fasterthan the speed of light. Recession velocityis unlike the ordinary velocity with whichwe are familiar. Measuring the expansionrequires the introduction of comoving coor-dinates, coordinate distances, the scalingfactor, the Hubble term, and the decelera-tion term, and we show how universes areclassied according to the way the scalingfactor changes in time.

CHAPTER 15

REDSHIFTS

Light rays from distant galaxies are red-shifted because of the expansion of theuniverse. This cosmological redshift, which

I N T R O D U C T I O N 5

is distinct from the Doppler and gravita-tional redshifts, is produced by the stretch-ing of wavelengths as radiation propagatesthrough expanding space. Space expands,wavelengths are stretched, and the cosmicredshift is as simple as that. There are afew redshift curiosities. The oddest curiosityof all is the unwise practice in popular litera-ture of failing to distinguish between cosmicand Doppler redshifts. The Doppler eectimplies that galaxies are rushing awaythrough space and that special relativityexplains the universe. This is a dangerousinterpretation and leads to endless confu-sion for those trying to understand moderncosmology. It restores the cosmic edge atwhich recession reaches the speed of light.Our treatment stresses two concepts: rst,recession is the result of the expansion ofspace (and galaxies are more or less station-ary in expanding space); and second, cosmicredshifts are the result of the stretching ofwavelengths as light and other forms ofradiation travel through expanding space.It is now clear why we have previouslyinsisted that space and time are physicallyreal (this is the essence of general relativity)and are contained in the universe; the uni-verse is not expanding in space, but consistsof expanding space.

CHAPTER 16

NEWTONIAN COSMOLOGY

Isaac Newton resolved the gravity paradox(or war of cosmic forces) by assuming thatthe universe is perfectly homogeneous.Under certain limiting conditions Newto-nian theory gives the same results as generalrelativity. The dynamics of the universeshowing how gravity and the lambda forcedetermine expansion are discussed with theaid of Newtonian ideas. We try to explainwhy Newtonian theory under certain condi-tions yields the same results in cosmology asgeneral relativity.

CHAPTER 17

THE COSMIC BOX

The principle that all places in the universeare alike at each moment in cosmic time has

far-reaching consequences. Distant regionsare in the same state as local regions whencompared at the same time, and we can dis-cover much about the universe by studyingthe history of only a sample region. This isthe basic idea of the universe in a nutshell.We suppose that a part of the universe isenclosed in an imaginary cosmic box thathas perfectly reecting walls and expandswith the universe. What happens inside isexactly the same as what happens outside.The cosmic box is small on the cosmic scale,hence we assume Euclidean space and theordinary laws of physics, as used in thelaboratory, to study the various forms ofcosmic phenomena. The enclosed cosmicbox serves as a useful tool for tackling sub-jects that otherwise would be dicult, suchas the entropy of the universe and the non-conservation of energy on the cosmic scale.

CHAPTER 18

THE MANY UNIVERSES

In the past, many cosmological theories,now mostly of historical interest, have beenproposed. We look at various mightyframes, or cosmic models, such as theEinstein, de Sitter, Friedmann, and Fried-mannLematre universes. These modelsmay be classied as static, bang, whimper,or oscillating. Other methods of classica-tions are given. In this great gallery of uni-verses, the lambda force, popularized byEinstein, adds much to the variety. Fromthis cosmological supermarket we selectand examine Milnes kinematic universe,steady-state universes, and universes in com-pression, tension, and convulsion. We con-sider also ination, chaos, and antichaos.The dream machine of the scalartensortheory is discussed; by adjusting its controlknobs the cosmologist converts a universeinto any one of an innite number of dier-ent universes.

CHAPTER 19

OBSERVATIONAL COSMOLOGY

We consider rst local observations, thenobservations at intermediate distances, andnally observations at cosmically large

6 C O SMO L O G Y

distances. The local observations are con-ned to the Solar System, Galaxy, andLocal Group of galaxies and extend nofarther than a few million light years. Theydetermine the rst steps in a distance ladder,the distribution and density of matter, theages of stars and the age of the Galaxy (set-ting lower limits on the age of the universe),the abundance of the chemical elements, thecosmic background radiation that origi-nated in the early universe (and reveals thepeculiar motion of the Galaxy), and givecosmological information on topics such asthe baryon density and properties of thecosmic background radiation.

Observations at intermediate distancesare conned mainly to the Local (or Virgo)Supercluster and extend a few hundred mil-lion light years. They explore only the sub-Hubble sphere and do not extend into thefull Hubble ow. They determine the struc-ture, distribution, and motions of galaxies,extended distance scales, redshiftdistanceand velocitydistance laws in approximateform, and give information on topics suchas the age of the universe, baryon density,the density parameters, and the approximatevalue of the Hubble term.

Observations at cosmically large distancesextend deep into the Hubble ow where theredshiftdistance relation ceases to be linear.We piece together evolutionary histories bycomparing nearby and distant astronomicalsystems. What is seen in the world picture(on the observers backward lightcone)must be projected forward onto the worldmap (in which the linear velocitydistancelaw holds). This mapping procedure greatlycomplicates the determination of the cosmo-logical parameters and we are still far from asecure knowledge of the values of the Hubbleterm, the density parameters, the decelera-tion term, the cosmological term, and thecurvature constant.

CHAPTER 20

THE EARLY UNIVERSE

The cosmic background radiation, discov-ered in 1965, provides unambiguous evi-dence of a big bang in the early history of

the universe. We explore the big bang, notby traveling in space, but by remainingwhere we are and traveling far back intime. The big bang was everywhere. If theuniverse extends innitely in space, then soalso did the big bang. As we journey backin time, the cosmic density and temperaturerise steadily and the universe at age a fewhundred thousand years is lled with brilli-ant light. We stand at the threshold of theradiation era. From this epoch descendsdirectly the cosmic background radiation,cooled by expansion, that we nowadaysobserve. When the universe is one secondold, and the temperature is 10 billion kelvinand the density is one million times that ofwater, we quit the radiation era and enterthe bizarre world of the lepton era. Hordesof electrons and muons, and their antiparti-cles, struggle to survive and from the leptonbattleelds ee hosts of ghostly neutrinoscondemned forever to wander unseenthrough the universe. We continue ourjourney back in time, traveling through thehadron era and its warring matter and anti-matter ruled by the strong, electromagnetic,and weak forces. Eventually we enter thequark era ruled by the strong and electro-weak forces. Finally phase transitions passus through an ination era into a worldruled by the hyperweak force in whichmatter and antimatter are indistinguishable.Our journey back in time ultimately comesto a halt at the impenetrable Planck barrier.At the Planck epoch the age of the universe isone billion-trillionth of a jiy (a jiy is onebillion-trillionth of a second) and the densityof the universe is 1 followed by 93 zerostimes the density of water. Quantum uctua-tions of space and time are now of cosmicmagnitude and spacetime forms a foam oftangled discontinuities.

We return from the early universe andwith our time machine turned to the futurewe journey to the end of time. We nd thatperhaps the universe ceases to expand, thencollapses and terminates in a new big bang,or perhaps it expands forever and dies in along drawn-out whimper. In the rst possibi-lity, during the collapse of the universe,

I N T R O D U C T I O N 7

galaxies are crushed together, and in thedevastation that follows, dissolving stars zipthrough space at speeds close to that oflight. The brilliance of the radiation erareturns and the universe reverts to its originalprimordial state. In the second possibility, thegalaxies continue to recede from one anotherand after hundreds of billions of years aredead and lifeless. In the enormous stretchesof time that follow, star systems and galaxiescontract to form black holes, and particlesslowly decay and convert into radiation.After eons of time all black holes evaporate,mostly into low-temperature radiation, andthe universe then contains almost no matter,only feeble radiation forever growing feebler.

CHAPTER 21

HORIZONS IN THE UNIVERSE

How far can we see in the universe? Theanswer depends on the things that we see,whether they are events or world lines.Event and particle (or world line) horizonsare discussed, rst in the static Newtonianuniverse to illustrate their nature, and thenmore generally in nonstatic universes. Thehorizon riddle, the horizon problem, theHubble sphere, and other topics are dis-cussed. Also discussed is the photon hori-zon, beyond which photons emitted in ourdirection actually recede.

CHAPTER 22

INFLATION

Possibly, the universe begins in a state ofutmost symmetry, and progresses througha series of phase transitions to states oflower symmetry and richer diversity.Among the rst-born in the very early uni-verse are the magnetic monopole particles.These massive monopoles cannot decayand should still exist and be as abundant asthe photons of the cosmic backgroundradiation. An era of ination explains whythey have not been observed. During thegrand-unied phase transition, in whichthe hyperweak force split into the electro-weak and strong forces, the universe isthrown into a state of extreme tension. Inthis state, the universe expands (or inates)

enormously at constant density. This ina-tion solves not only the monopole problembut also the atness and horizon problems.But ination exacts a price: it creates theproblem of missing nonbaryonic matter.

CHAPTER 23

THE COSMIC NUMBERS

Cosmic numbers connect the subatomic andcosmic properties of the universe. Thesedimensionless numbers have intriguingcoincidences. Discussed are the clusterhypothesis and Diracs large-numberhypothesis, and their connection with theanthropic principle. The art of cosmo-numerology began long ago in the ancientworld when Archimedes calculated in theSand Reckoner the number of grains ofsand needed to ll the universe.

CHAPTER 24

DARKNESS AT NIGHT

The dark night-sky riddle, known as Olbersparadox, originated during the Copernicanrevolution in the sixteenth century. Why thesky at night is dark, and not ablaze withlight from countless stars has puzzled manyscientists, and played a conspicuous role inthe history of cosmology. Many writers inrecent times have said the night sky is darkbecause of the expansion of the universe.But this cannot be true because calculationshows that if our universe were static thesky at night would still be dark. The universedoes not contain enough energy to create abright-sky universe. The correct solutionwas anticipated by the poet Edgar AllanPoe and investigated in depth by Lord Kel-vin. The sky at night is dark because thestars shine for too short a time to ll the uni-verse with radiation in equilibriumwith stars;equivalently, stars shine for too short a timefor the universe to contain sucient visiblestars to cover the sky.

CHAPTER 25

CREATION OF THE UNIVERSE

We consider miscellaneous topics in cosmo-geny, beginning with the creation myths ofearlier societies. The Mosaic chronology

8 C O SMO L O G Y

that xes the date of creation of the universeto ve or six thousand years before thepresent has been the cause of considerableconict between science and religion. Crea-tion and tness of the universe are distin-guished as separate subjects and examinedin current theistic, anthropic, spontaneous,and natural selection theories. Eschato-logical myths and end-of-the-world theoriesare also briey reviewed.

CHAPTER 26

LIFE IN THE UNIVERSE

In this last chapter we consider past and

present theories of the origin of life anddiscuss aspects of evolution and naturalselection. Understanding the nature of intel-ligence is vitally important in cosmology,and we consider how human beings mighthave acquired their large brains. As cosmol-ogists, in our nely tuned universe, we feelimpelled to believe that intelligent life mustexist elsewhere in the multitudes of galaxies.But what is life? What is intelligence? Doesintelligent life, technologically advanced,exist elsewhere in our Galaxy? Avenues ofinquiry open up in pursuit of answers tothis and other questions.

I N T R O D U C T I O N 9

Part I

WHAT IS COSMOLOGY?

He has ventured far beyond the aming ramparts of the world

and in mind and spirit traversed the boundless universe.

Lucretius (9955 BC), The Nature of the Universe

THE UNIVERSE

From the outset we must decide whether touseUniverse or universe. This is not so triviala matter as it might seem. We know of onlyone planet called Earth; similarly, we knowof only one Universe. Surely then the properword is Universe?

The Universe is everything and includesus thinking about what to call it. But whatis the Universe? Do we truly know? It hasmany faces and means many dierent thingsto dierent people. To religious people it is atheistically created world ruled by super-natural forces; to artists it is an exquisiteworld revealed by sensitive perceptions; toprofessional philosophers it is a logicalworld of analytic and synthetic structures;and to scientists it is a world of controlledobservations elucidated by natural forces.Or it may be all these things at dierenttimes. Even more diverse are the worlds orcosmic pictures held by people of dierentsocieties, such as the Australian aboriginals,Chinese, Eskimos, Hindus, Hopi, Maoris,Navajo, Polynesians, Zulus. Cosmic pic-tures evolve because cultures inuence oneanother, and because knowledge advances.Thus in Europe the medieval picture, inu-enced by the rise of Islam, evolved into theCartesian, then Newtonian, Victorian, andnally Einsteinian pictures. The standardWestern world picture of the late nineteenthcentury the Victorian picture was totallyunlike the standard picture the Einsteinianpicture of a hundred years later. Eachsociety in each age constructs a dierent

cosmic picture that is like a mask tted onthe face of the unknown Universe.

If the word Universe is used we mustdistinguish between the various modelsof the Universe. Each model, religious,artistic, philosophical, or scientic, is oneof many representations; and similarlywith the models of dierent societies. Thusin the history of science we distinguishbetween the Pythagorean model, theAtomist model, the Aristotelian model,and so on. More precisely, we should say,the Pythagorean model of the Universe,the Atomist model of the Universe, theAristotelian model of the Universe, and soon. Inevitably, the models receive the abbre-viated titles: the Pythagorean Universe, theAtomist Universe, the Aristotelian Uni-verse, . . . , and we confuse ourselves byusing the word Universe to mean a modelof the Universe.

The grandiose word Universe has afurther major disadvantage. When usedalone, without specication of the modelwe have in mind, it conveys the impressionthat we know the true nature of the Uni-verse. We nd ourselves, in the company ofmultitudes of others in the past, speakingof theUniverse as if it were at last discoveredand revealed. By referring to the contempor-arymodel of theUniverse as the Universe,we forget that our contemporary model willundoubtedly suer the same fate as itspredecessors. Always, we mistake the maskfor the face, the model universe for theactual Universe. Our ancestors made this

1

13

mistake continually and most likely our des-cendants will look back and see us repeatingthe same mistake.

Because we cannot guess even in ourwildest imaginings the true nature of theUniverse, we may avoid referring to itdirectly by using the more modest worduniverse. A universe is simply a model ofthe Universe (see Figure 1.3). Hence we may

speak of the Pythagorean universe, theAtomist universe, Aristotelian universe,and so on, and each universe is a mask, acosmic picture, a model that is invented,modied as knowledge advances, and nallydiscarded.

The word universe, which we shall use,has the further advantage that it may be usedfreely and loosely without any need to

Figure 1.1. The universe according to Hildegaard of Bingen in Germany in the

twelfth century. In her lifetime we see in her writings how the medieval picture

evolved toward its climax in Dantes Divine Comedy (Figure 8.4). (Reproduced

from the Wiesbaden Codex B as gure 2 in Charles Singers The scientic views

and visions of Saint Hildegaard.)

14 C O SMO L O G Y

remind ourselves constantly that the Uni-verse is still mysterious and unknown.When the word universe is used alone,as in such phrases as the vastness of theuniverse, it denotes our present universeas disclosed by modern science.

COSMOLOGY

We search the sky, the Earth, and withinourselves, and forever wonder about themystery of the universe: What is it allabout? Why did it all begin? How will it allend? And are these questions meaningful?Always we ask the burning question: Whatis the meaning of life? Each of us echoesthe words of Erwin Schrodinger I knownot whence I came nor whither I go norwho I am, and seeks the answer. The searchis doomed to go astray from the beginningunless we familiarize ourselves with the

universes of the past and particularly withthe modern universe.

Cosmology is the study of universes. Inthe broadest sense it is a joint enterprise byscience, philosophy, theology, and the artsthat seeks to gain understanding of whatunies and is fundamental. As a science,which is the main concern in this book, it isthe study of the large and small structuresof the universe; it draws on knowledgefrom other sciences, such as physics andastronomy, and assembles a physically all-inclusive cosmic picture.

In our everyday life we deal with ordinarythings, such as plants and owerpots, and tounderstand these things of sensible size weexplore the small-scale and large-scalerealms of the universe. We delve deeplyinto the microscopic realms of cells, mol-ecules, atoms, and subatomic particles, andreach far out into the macroscopic realmsof planets, stars, galaxies, and the universe.We nd that the very small and the verylarge are intimately related in cosmology.

Since the seventeenth century, knowledgehas advanced rapidly and the number ofsciences has grown enormously. Eachscience focuses on a domain of the universeand tends in the course of time to fragmentinto closely related new sciences of greaterspecialization. Originally, the characteristics

Figure 1.2. The Universe, one and all-inclusive, by

Filippo Picinelli, 1694. In The Cosmographical

Glass: Renaissance Diagrams of the Universe

(1977), S. K. Heninger writes, We might

conjecture that the artist, not bound by the

constraint of cosmological dogma, felt free to

engage in cosmological speculations of his own

sort. He assumed a license to create his own

universe. The worlds of Hieronymus Bosch, of Leon

Battista Alberti, and of John Milton, to name a few

examples, are the result. (Courtesy of the Henry E.

Huntingdon Library, San Marino, California.)

Figure 1.3. The Universe contains us who

construct the many universes. Each universe is a

model of the Universe. An intriguing thought is that

each universe is the Universe attempting to

understand itself.

WHA T I S C O SMO L O G Y ? 15

of living and nonliving things dened thedierences between the broad domains ofbiology and physics. Each of these basicsciences, as it advanced, branched into newsciences, which in turn branched into morespecialized sciences. Physics once knownas natural philosophy has grown andbranched into high-energy subatomic parti-cle physics, low-energy nuclear physics,atomic physics, chemical physics, con-densed-matter physics, biophysics, geophy-sics, astrophysics, and so on, and each hasits own theoreticians, experimenters, andtechnicians. Biology once the subject ofnaturalists of broad interests with asso-ciated sciences such as botany, zoology,entomology, ecology, and paleontology,and so on, has grown and branched intomolecular biology, biochemistry, genetics,and so on. And astronomy once thesubject in which everybody had equalknowledge (but not computing skill) hasbranched into planetary sciences, the studyof stellar structure and atmospheres, inter-stellar media, galactic astronomy, extra-galactic astronomy, and the separate eldsof radio, infrared, optical, ultraviolet, x-ray, and gamma-ray astronomy.

It is evident that the sciences divide theuniverse in order that each can construct indetail a domain of special knowledge.Science tears things apart into constituentsof greater and greater specialization ofteninto smaller and smaller pieces and devotescloser and closer attention to detail. A per-son studying in depth a branch of sciencebecomes a specialist, engrossed in a mazeof detailed knowledge, who knows muchabout a small domain of the universe andis comparatively ignorant of all the rest.

Cosmology is the one science in whichspecialization is rather dicult. Its mainaim is to assemble the cosmic jigsaw puzzle,not to study in detail any particular jigsawpiece. While other scientists are pulling theuniverse apart into progressively moredetailed pieces, the cosmologists are endeav-oring to put the pieces together to see thepicture on the jigsaw puzzle. Unlike allother scientists, the cosmologists take a

broad view; like the impressionist paintersthey stand well back from their canvases soas not to see too much distracting detail.

Introductory cosmology is not a branchof astronomy. It is a cosmopedia, morethan an inventory of the contents of theuniverse, and is not a whole-universe cata-logue of descriptive astronomical data.Cosmology is the study of the primarycosmic constituents, such as the origin andhistory of the chemical elements, and ofspace and time that form the frame of theexpanding universe. The primary things ofimportance are scattered over large regionsof space and endure over long periods oftime. The origin and evolution of stars andgalaxies, even the origin of life and intelli-gence, are important cosmic subjects. Sub-atomic particles, the role they play duringthe earliest moments of the universe, theirsubsequent combination into atoms andmolecules that form the complexity of theliving cell and our surrounding world, areall of cosmic interest.

At each turn, the issues of cosmologycause us to pause and reect. Many subjectsof vital importance are still obscure and notunderstood: how human beings acquiredspeech and large brains; and how they devel-oped the ability to create abstract mentalstructures and think quantitatively. Whatdetermines the way that human beingsthink also determines the design they per-ceive in their universes. Human beingsform a vital part of cosmology and representthe Universe perceiving and thinking aboutitself.

Who are the cosmologists? Professionalcosmologists are relatively few; they arewell-versed in mathematics, physics, andastronomy, and they study the evolutionand large-scale structure of the physical uni-verse. In general, however, whenever aperson seeks to understand the Universe,that person becomes a cosmologist. Whenwe stand back from the study of a specializedarea of knowledge, or just step aside fromoureveryday aairs, and reect on things ingeneral, and try to see the forest and notjust the trees, the whole painting and not

16 C O SMO L O G Y

just the dabs of paint, the whole tapestry andnot just the threads, we become cosmologists.

THE MAGIC UNIVERSE

Cosmology is as old asHomo sapiens. It goesback to a time when human beings, living inprimitive social groups, developed languageand made their rst attempts to understandthe world around them. Probably, hundredsof thousands of years ago, human beingsexplained their world by means of spirits.Spirits of all kinds, motivated by humanlikeimpulses and passions, activated everything.The early people projected their own innerthoughts and feelings into an outer animisticworld, a world in which everything wasalive. With supplications, prayers, sacrices,and gifts to the spirits, human beings gainedcontrol of the phenomena of their world.

It was the Age of Magic, of benign anddemonic spirits incarnate in plant, animal,and human form. Everything that happenedwas explained readily and easily by thepassions, motives, and actions of ambientand indwelling spirits. It was an anthropo-morphic world, of the living earth, water,wind, and re, into which men and womenprojected their own emotions and motivesas the guiding forces; the kind of worldthat children read about in fairy tales.From this golden age comes our primevalfear of the menace of darkness and the rageof storms, and our enchantment with thewizardry of sunrises, sunsets, and rainbows.For reasons not yet fully understood, humanbeings everywhere remained one species,and cultures (languages, social codes, beliefsystems, laws, technologies) interdiused.Possibly, our moral codes of today, whichregulate behavior in the family and societyand determine in general what is ethicallyright and wrong, were naturally selectedover long periods of time in primitive socie-ties. Societies decient in codes of mutualcare and support among individuals hadlittle chance of surviving.

THE MYTHIC UNIVERSE

At the dawn of history, ten or more thou-sand years ago, the early city-states attained

more abstract concepts of the Universe. Themagic universe evolved into the mythicuniverse. The long age of magic gave wayto what might be called the Age of Theism.The spirits that had been everywhere, acti-vating everything, amalgamated, retreatedinto remote mythic realms, and becamepowerful gods who personied abstractionsof thought and language. James Frazer, inThe Golden Bough, speculated on howmagic among primitive people evolved intotheism, and how the magic universe trans-formed into a variety of mythic universe:

But with the growth of knowledge man learns to

realize more clearly the vastness of nature and his

own littleness and feebleness in the presence of it.

The recognition of his helplessness does not,

however, carry with it a corresponding belief in

the impotence of those supernatural beings with

which his imagination peoples the universe. On

the contrary, it enhances his conception of their

power. . . . If then he feels himself to be so frail and

slight, how vast and powerful must he deem the

beings who control the gigantic machinery of

nature! . . . Thus in the acuter minds magic is

gradually superseded by religion, which explains

the succession of natural phenomena as regulated

by will, passion, or caprice of the spiritual beings

like man in kind, though vastly superior to him in

power.

Much of mythology consists of primitivecosmic imagery (Figure 1.4). The Sumerian,Assyro-Babylonian, Minoan, Greek, Chi-nese, Norse, Celtic, and Mayan mytholo-gies, to name only a few, are of historicalinterest because they illustrate mankindsearlier views of the universe. The creationmyths, often dicult to interpret, are ofparticular interest (see Chapter 25).

Human beings at the cosmic centerNo matter how powerful and remote theybecame, the mythic gods continued to serveand protect human beings, and men andwomen everywhere remained secure and ofcentral importance in an anthropocentricuniverse. The universe was assembled abouta center and human beings were located pro-minently at the center.

Anthropocentricity formed the basis ofthe Greek cosmology of an Earth-centered

WHA T I S C O SMO L O G Y ? 17

universe. The universe of Aristotle in thefourth century BC was geocentric (or Earthcentered); the spherical Earth rested at thecenter of the universe and the Moon, Sun,planets, and stars, xed to translucent celes-tial spheres, revolved about the Earth. Theinnermost region of heaven the sublunarsphere between the Earth and the Moon contained earthly and tangible things in an

ever-changing state, and the outer regionsof heaven the celestial spheres containedethereal and intangible things in a never-changing state. The subsequent elaborationsof this system, bringing it into closer agree-ment with astronomical observations, cul-minated in the Ptolemaic system of AD 140.

The Middle Ages (fth to fteenth centu-ries) were not so terribly dark as was once

Figure 1.4. The Ancient of Days by William Blake (17571827). When he sets a

compass upon the face of the depths (Proverbs 8:27).

18 C O SMO L O G Y

supposed. The medieval universe from thethirteenth century to the sixteenth centurywas perhaps the most satisfying form ofcosmology known in history. Christians,Jews, andMoslems were blessed with a niteuniverse in which they had utmost impor-tance. By the Arab and European standardsof those times it was a rational and well-organized universe that everybody couldunderstand; it gave location and prominencetomankinds place in the scheme of things, itprovided a secure foundation for religionand gave meaning and purpose to humanlife on Earth. Never before or since hascosmology served in so vivid a manner theeveryday needs of ordinary people; it wassimultaneously their religion, philosophy,and science.

The Copernican RevolutionThe transition from the nite geocentric uni-verse to the innite and centerless universe isknown as the Copernican Revolution. In thesixteenth century, Nicolaus Copernicuscrystallized trends in astronomical thoughtthat had originated in Greek science almost2000 years before and proposed the helio-centric (or Sun-centered) universe. TheCopernican heliocentric universe was soontransformed into the innite and centerlessCartesian universe, which in turn wasfollowed by the Newtonian universe. Thisrevolution in outlook occupied the sixteenthand seventeenth centuries. The CopernicanRevolution opened the way for moderncosmology.

But the spiritual universe, thought to bevastly more important than the physicaluniverse, remained rmly anthropocentric.The spiritual universe was the great chainof being, a chain of countless links that des-cended from human beings through all thelower forms of life to inanimate matter,and ascended from human beings throughhierarchies of angelic beings to the throneof God. Mankind was the central link con-necting the angelic and brute worlds. Evenin an innitely large physical universe,deprived rst of the Earth and then of theSun as its natural center, it was still possible

to cling to old ideas that portrayed humanbeings as having central importance in thecosmic drama. The gods were ever myster-ious and after the Copernican Revolutionthey became more mysterious than before.

The Darwinian revolutionIn the middle of the nineteenth century camethe most dreadful of all revolutions: theDarwinian Revolution. Human beings,hitherto the central gures in the cosmicdrama, became akin to the beasts of theeld. The gods who had attended and pro-tected mankind for so long were cast out ofthe physical universe.

The anthropomorphic (magic) andanthropocentric (mythic) universes werewrong in almost every detail. The medievaluniverse has gone and with it has gone thegreat chain of being. Science at last is thevictor, putting to ight the myths and super-stitions of the past. We applaud the Renais-sance (fteenth to sixteenth centuries) withits revival of art and learning, we applaudthe rise of the Cartesian and Newtonianworld-systems in the seventeenth century,we applaud the Age of Reason (the Enlight-enment of the eighteenth century) with itsconviction in the power of human reason,and we applaud the Age of Science (seven-teenth to twentieth centuries), and tooeasily forget the growing dismay of ordinarymen and women in a universe that centuryby century progressively became moremeaningless and senseless. With thedecline and death of the old universes anthropomorphic and anthropocentric mankind was cast aimlessly adrift in analien universe.

THE ANTHROPOMETRIC UNIVERSE

Man is the measure of all things.

Protagoras (fth century BC)

We believe that the universe is not anthro-pomorphic and not made in the image ofhuman beings; it is not a magic realm alivewith humanlike spirits. Also we believethat the universe is not anthropocentricwith human beings occupying its center; we

WHA T I S C O SMO L O G Y ? 19

are not the central gures; and the world isnot controlled by gods and goddesses.

Instead, as Protagoras said, we are themeasure of the universe, and this meansthat the universe is anthropometric. Let ustry to understand what this means.

We have minds, or as some would say, wehave brains. For our purpose it is not neces-sary to inquire into the nature of the mindbrain and attempt to probe its mysteries.It does not matter if we think the mind is anonphysical entity of psychic activity or isa physical brain throbbing with bioelectro-chemical activity. We have mindbrainsinto which information pours via the sen-sory pathways and from this informationwe devise in our mindbrains the Aristote-lian, Stoic, Epicurean, Zoroastrian, Neopla-tonic, Medieval, Cartesian, Newtonian, andall the other universes that have dominatedhuman thought in dierent ages.We observeplants and owerpots and other things anddevise grand theories that relate and explainthem, and these theories reside not in thethings themselves but in our mindbrains.At each step in the history of cosmology, dif-ferent universes prevail, and every universein every society is a grand mental edicethat makes sense of the human experience.Each universe is anthropometric because itconsists of ideas devised by human beingsseeking to understand the things theyobserve and experience.

For those lost in the vast and apparentlymeaningless modern universe there is com-fort in the realization that all universes areanthropometric. The Medieval universewas made and measured by men andwomen, although the medievalists them-selves would have hotly denied the thought.The modern universe with its bioelectro-chemical brains pondering over it is alsohuman-made. Like the Medieval universeit will inevitably fade away in time and bereplaced by other universes. The universesof the future will almost certainly dierfrom our modern version; nevertheless,they will all be anthropometric becauseman is the measure of all things enter-tained by man. The Universe itself, of

course, is not human-made, but we haveno true conception of what it actually is.All we know is that it contains us thedreamers of universes.

COSMOLOGY AND SOCIETY

Cosmology and society are intimatelyrelated. Where there is a society, there is auniverse, and where there is a universe,there is a society of thinking individuals.Each universe shapes the history and directsthe destiny of its society.

This intimate relationship is mostobvious in primitive cosmology wheremythology and society mirror each otherand the ways of gods and goddesses are theways of men and women. Cruel people cre-ate cruel gods who sanction cruel behavior,and peaceful people create peaceful godswho foster peaceful behavior. The interplaybetween cosmology and society in themodern world is as strong as ever, if notstronger, but often in less easily recognizedforms.

Without doubt the most powerful andinuential ideas in any society are those thatrelate to the universe. They shape histories,inspire civilizations, foment wars, createmonarchies, launch empires, and establishpolitical systems. One such idea was theprinciple of plenitude, which can be tracedback to Plato and has been enormouslyinuential since the fteenth century.

The principle of plenitude originated inthe anthropocentric belief system that theuniverse is created for mankind by an intel-ligible supreme being. In its simplest formit states that a benecent Creator has givento human beings for their own use anEarth of unlimited bounty. Themore formalargument is as follows. The supreme being iswithout limitation because limitationimplies imperfection and imperfection iscontrary to belief. The unlimited potentialof the supreme being is made manifest inthe unlimited actuality of the createdworld. The Earth necessarily displays everyform of reality in inexhaustible abundance.This is the principle of plenitude that satu-rates Western culture.

20 C O SMO L O G Y

In the Late Middle Ages, telescopesdisclosed the richness of the heavens, micro-scopes disclosed a teeming world of micro-organic life, and the worldwide voyages bymariners opened up dazzling vistas of avast and bountiful Earth. An unlimitedabundance of every conceivable thing pro-vided sucient proof of the principle ofplenitude. Europeans developed the princi-ple, were guided by it, and have sinceexported it to the rest of the world.

Political ideologies were shaped by theprinciple of plenitude. The principle guaran-teed endless untapped wealth and free enter-prise ourished as never before. To osetdepletion and escape population growth itwas necessary only to push farther east andwest to the glittering prizes of unravishedlands. The real price of anything is thetoil and trouble of acquiring it said AdamSmith. Go east! the streets are paved ingold. Go west! beyond the sunset lie landsof unharvested wealth. Husbandry of niteresources was not part of plenitude philoso-phy. People condently believed that every-thing existed in unlimited abundance, andwhen anything became exhausted (such asthe elimination of the bison herds, theextinction of the carrier pigeons and thegreat auks), they were taken by surpriseand felt cheated.

The inevitable question followed, and hassince echoed around the world: Why shouldinequality of wealth exist in a world ofunlimited abundance? One answer came inthe message fromKarlMarx: in theCommu-nist Manifesto we are told the less wealthyhave nothing to lose but their chains.They have a world to win. The principleof plenitude, which now lies buried deep inour cultural heritage and has been dissemi-nated in various forms throughout theworld, is unfortunately nothing but acosmological myth.

Old ideas of cosmological breadth stilldominate our everyday thoughts and manyof these ideas are totally unsuitable in themodern world. We are, it seems, lockedinto the misguiding logic of obsolete uni-verses that threaten to destroy us. We live

in an age of crises unchecked populationgrowth, rapid depletion of resources, envir-onmental and atmospheric pollution andare mesmerized by prophecies of doom.

In 1776 the engineering rm of Boultonand Watt began to sell steam engines that,unlike previous steam devices, were power-ful, quick-acting, and easily adapted fordriving machinery of various kinds. Thisevent more than any other ushered in theIndustrial Revolution that has transformedour way of life. Many persons say that theills of today are the direct consequence ofthe Industrial Revolution. But it is notthe technologies that are to blame, but theideas the belief systems that govern theuse of the technology.

To make the point clear, let us imaginethat space travelers encounter a planetthat has been devastated by unbridledtechnology and become lifeless. In theirinvestigations the space travelers cannotautomatically assume that technology wasthe cause of the devastation. They mustsearch for evidence indicating the nature ofthe beliefs of the vanished inhabitants.What inner mental world resulted in theouter ruined world? In their reports theywill probably draw the conclusion that theruined world is the result of an ancient cos-mology, a cosmology founded on principlesthat in their saner moments the inhabitantshad rejected and yet had driven them totheir doom.

REFLECTIONS

1 I dont pretend to understand theUniverse its a great deal bigger than Iam. Attributed to William Allingham(18281889).. The word Universe can be thought of ascombining Unity and the diverse. The wordcosmos means the harmonious whole of allreality. But what are the full meanings ofunity, diversity, harmony, and reality?2 In cosmology, there are two distinctlanguages: the rst refers to universes andthe second refers to cosmologies. In therst, cosmology is the study of many uni-verses, and each universe is a model of the

WHA T I S C O SMO L O G Y ? 21

Universe. (Naturally in any age cosmologytends to be the study of the contemporary uni-verse.) In the second, the Universe is studiedby many cosmologies, and each cosmology ispeculiar to a particular society. We haveeither a single cosmology studying many uni-verses or a single Universe studied by manycosmologies. The rst refers repeatedly touniverses and the second refers repeatedly tothe Universe. In this book we adopt the rstmethod because it avoids using the word Uni-verse, except occasionally to make a pointclear, and does not foster the illusion thatthe Universe is a known or even knowablething.3 Homo sapiens has existed for about onemillion years. How did the early human beingsview the world around them? I shall invite myreaders to step outside the closed study of thetheorist into the open air of the anthropo-logical eld, wrote Bransilaw Malinowskiin his book on the Tobriand Islanders ofMelanesia. Through his observations andthose of many other anthropologists studyingdierent societies we nd not primitive butsophisticated cultures and intricate languagesexisting everywhere. Truly primitive humanbeings, oering us insight into how our remoteancestors thought and lived, most probablyexist nowhere in the world today.

The world of primitive people was pos-sessed, pervaded, and crowded with spiritualbeings, according to the Victorian anthro-pologist Edward Tylor in his book PrimitiveCulture. He advanced the theory of animism.The early human beings projected their ownemotions and motives into the surroundingworld, and the world, thus animated, wasable to explain almost everything that neededexplaining. In the course of time, with thegrowth in language and abstract thought,the ambient spirits amalgamated into power-ful nature spirits, godlings, gods, and god-desses.

The conception of gods as superhumanbeings endowed with the powers to whichman possesses nothing comparable in degreeand hardly in kind has been slowly evolved inthe course of history, wrote James Frazerin The Golden Bough. Frazer discussed the

evolution of animism into theism, and of howthe management of the gigantic machineryof nature was handed over to the gods. Heassumed as a basic premise that religion wasborn with the rise of the gods.4 Religion in general is not easily dened. Itseems to comprise emotions and ideas. Thereligious emotions experienced by individualsare much the same in all societies, whereas thereligious ideas that evoke those emotions arepeculiar to each society. Religious emotionsare probably an integral part of human natureand essential in the survival of humansocieties. Theology is the study of religiousideas, and faith is the conviction in the abso-lute truth of those ideas. Invariably, theideas have cosmological signicance (seeChapters 2, 3, 4, 7, 8, 25, and 26). We notethat everywhere in every age people in dier-ent societies have similar religious emotions,but have totally dierent religious ideas inwhose absolute truth they have complete faith.

Recognition of the universality of religiousemotions and the diversity of religious ideassuggests that Frazer was wrong when hetraced the roots of religion back to the birthof gods. Possibly religion is as old as Homosapiens. The error of confusing religiousemotions with religious ideas seems quitecommon. When members of religious institu-tions insist on keeping their mythic beliefs,they unwittingly make the mistake of con-fusing theory with emotional experience andthink that without primitive cosmology theycannot have religion. They fail to realizethat scientic rejection of mythic cosmologydoes not bring science into conict withreligious experience. The modern theory oflight as quanta of energy, for example, hasnot robbed us of the sensation of color andthe emotional experience that accompaniescolor.

Mythology is the study of myths. Mythsapparently are ideas and stories that providehistorical insights into the belief systems ofother and often earlier cultures. Althoughcredible in the belief systems in which theyrst originated, myths become incrediblewhen transplanted into the belief systems ofother cultures.

22 C O SMO L O G Y

5 Cosmological concepts have great inu-ence for good and evil. Consider: Thoushalt not suer a witch to live. It is estimatedthat in the witch universe of the late MiddleAges (known as the Renaissance) and of theAge of Reason (known as the Enlightenment)about half a million men, women, and childrenconfessed heresy and witchcraft under tortureand were burned to death. It was said thatheretics would burn forever in hell and thetemporary anguish of re on Earth wasjustied if they were saved from eternal reof hell. Here is an instance of the maxim:cruel people create cruel gods who sanctioncruel behavior.. And the awful fact was that whenever youfound one witch and used the just and properinstruments of inquiry, you inevitably foundmany others. Their numbers multiplied andseemed without limit. Male and femalewitches and their evilly spawned childrenwere consumed by re in mounting numbers,and still they multiplied (E. Harrison,Masks of the Universe).

All Christianity, it seems, is at the mercyof these horrifying creatures. Countries inwhich they had previously been unknown arenow suddenly found to be swarming withthem, and the closer we look, the more ofthem we nd. All contemporary observersagree that they are multiplying at an incred-ible rate. They have acquired powers hithertounknown, a complex international organiza-tion and social habits of indecent sophistica-tion. Some of the most powerful minds of thetime turn from human sciences to explorethis newly discovered continent, this Americaof the spiritual world (Trevor-Roper, TheEuropean Witch Craze).

The details they discovered are constantlyand amply conrmed by other researchworkers experimenters in confessional andtorture chamber, theorists in library andcloister leaving the facts still more securelyestablished and the prospect even more alarm-ing than before. Instead of being stamped out,the witches increased at a frightening rate,until the whole of Christendom seemedabout to be overwhelmed by the marshaledforces of triumphant evil. To protest in any

way against witch hunting as inhuman in atime of emergency was sheer lunacy, con-demned by the popes as bewitchment and theresult of consorting with devils (E.Harrison,Masks of the Universe).6 Edward Milne in his last book ModernCosmology and the Christian Idea of God,published posthumously in 1952, wrote:There is a remarkable dierence betweenphysics and philosophy. On the one hand,physicists agree with one another in generalat any one time, yet the physical theories ofany one decade dier profoundly from thoseof each succeeding decade at any rate inthe twentieth century. On the other hand,philosophers disagree with one another atany one time, yet the grand problems of philo-sophy remain the same from age to age. . . .The man of science should be essentially arebel, a prophet rather than a priest, onewho should not be ashamed of nding himselfin opposition to the hierarchy. . . . The hard-baked or hardboiled scientist usually holdsthat science and religion, whilst on noddingterms, have no immediate bearing on oneanother. On the contrary, one cannot studycosmology without having a religious attitudeto the universe. Cosmology assumes therationality of the universe, but can give noreason for it short of a creator of the laws ofnature being a rational creator.7 Whereas philosophers and theologiansappear to possess an emotional attachmentto their theories and ideas that requires themto believe in them, scientists tend to regardtheir ideas dierently. They are interested informulating many logically consistent possi-bilities, leaving any judgment regarding theirtruth to observation. Scientists feel no qualmsabout suggesting dierent but mutually exclu-sive explanations for the same phenomenon(John Barrow and Frank Tipler, TheAnthropic Cosmological Principle, 1986).8 The emergence of science, says HerbertButtereld in The Origins of ModernScience, outshines everything since the riseof Christianity and reduces the Renaissanceand Reformation to the rank of mere epi-sodes, and looms so large as the real originboth of the modern world and the modern

WHA T I S C O SMO L O G Y ? 23

mentality that our customary periodisation ofEuropean history has become an anachronismand an encumbrance. Buttereld argues thatscience saved Europe from the mad witchuniverse. Not the humanities, not religion,but the sciences ended the witch craze of theRenaissance. Science was reaching out to anew universe more capable of distinguishingbetween the supernatural and the naturaland of dening the limits of human controlover nature.9 Possibly the world of external facts ismuch more fertile and plastic than we haveventured to suppose: it may be that all thesecosmologies and many more analyses andclassications are genuine ways of arrangingwhat nature oers to our understanding, andthat the main condition determining ourselection between them is something in usrather than something in the external world(Edwin Burtt, The Metaphysical Founda-tions of Modern Physical Science, 1932).. Natural science does not simply describeand explain nature; it is part of the interplaybetween nature and ourselves; it describesnature as exposed to our method of question-ing (Werner Heisenberg, Physics andPhilosophy, 1958).. In The Discarded Image (1967), C. S.Lewis writes: The great masters do nottake any Model quite so seriously as the restof us. They know that it is, after all, only amodel, possibly replaceable. Later he con-tinues: It is not impossible that our ownModel will die a violent death, ruthlesslysmashed by an unprovoked assault of newfacts unprovoked as the nova of 1572. ButI think it is more likely to change when, andbecause, far-reaching changes in the mentaltemper of our descendants demand that itshould. The newModel will not be set up with-out evidence, but the evidence will turn upwhen the inner need for it becomes sucientlygreat. It will be true evidence. But nature givesmost of her evidence in answer to the questionswe ask her.10 In The Great Chain of Being (1936) byArthur Lovejoy, we read: Next to the wordnature, the Great Chain of Being wasthe sacred phrase of the eighteenth century,

playing a part somewhat analogous to thatof the blessed word evolution in the late nine-teenth. The great chain inspired the notion ofmissing links long before Darwin. Thegreat chain of being, according to Lovejoy,was intimately associated with the principleof plenitude. Not so very long ago theworld seemed almost innite in its ability toprovide for mans needs and limitless as areceptacle for mans waste products. Thosewith an inclination to escape from worn-outfarms or the clutter of urban life could alwaysmove out into a fresh, unspoiled environment.There were virgin forests, rich lodes waiting tobe discovered, frontiers to push back, andlarge blank regions marked unexplored onthe map. . . . It has, so far as I know, neverbeen distinguished by an appropriate name;and for want of this, its identity in varyingcontexts and in dierent phrasings seemsoften to have escaped recognition by histor-ians. I shall call it the principle of plenitude.. Garrett Hardin in The tragedy of thecommons (1968) discusses how old mythsand cosmological beliefs aect the way welive. Individuals strive to maximize theirshare of a common resource in the beliefthat ownership is a natural and even divineright. When herdsmen graze their beasts oncommon land, each strives to increase thesize of his herd. Disease and tribal warfaremaintain a state of equilibrium by limitingthe numbers of persons and beasts below thecapacity of the land. Then comes a moreorderly and civilized way of life that, withdiminished war and disease, places anincreased burden on the commons. A herds-man now thinks, If I increase my herd, theloss owing to overgrazing will be shared byall, and my gain will exceed my loss. Allherdsmen think this way and therein lies thetragedy. Each person, states Hardin, islocked into a system that compels him toincrease his herd without limit in a worldthat is limited. . . . Ruin is the destination towhich all men rush. Unfortunately, mostproblems created by outdated cosmic myths(such as the Great Chain of Being, the princi-ple of plenitude, and the freedom to reproducewithout limit) do not have technical solutions.

24 C O SMO L O G Y

A technical solution may be dened as onethat requires a change only in the techniquesof the natural sciences, demanding little ornothing in the way of change in human valuesor ideas of morality. The concern here iswith that important concept of a class ofhuman problems which can be called no tech-nical solution problems. . . . My thesis is thatthe population problem, as conventionallyconceived, is a member of this class. . . . It isfair to say that most people who anguishover the population problem . . . think thatfarming the seas or developing new strains ofwheat will solve the problem technically.

PROJECTS

1 Consider the old English prayer: Godhelp me in my search for truth, and protectme from those who believe they havefound it.. Consider also: In theMemoirs of Zeus byMaurice Druon, the goddess Mnemosyndeclares we would be better mirrors of theUniverse if we were less concerned aboutour own image.2 In the ancient world and in the MiddleAges astrology was the science of planetsand stars, astrolatry was the worship ofstars, and astromancy was the practiceof soothsaying and divination by means ofcelestial congurations. We use the wordbiology for the science of living things andproperly speaking we should use the wordastrology for the science of stars. Butastrology became corrupted and took theplace of astrolatry and astromancy.Astrology now is the mythological beliefthat the aairs of human beings are inu-enced by the heavenly bodies.

Millions of people in America read theastrology