Introduction to cosmology

287 Pages·2003·2.125 MB·English

by  Matts Roos

Introduction
to Cosmology
Third Edition
Matts Roos
Introduction
to Cosmology
Third Edition
Introduction
to Cosmology
Third Edition
Matts Roos
Copyright©2003 JohnWiley&Sons,Ltd,TheAtrium,SouthernGate,Chichester,
WestSussexPO198SQ,England
Telephone [phone]
Email(forordersandcustomerserviceenquiries):[email protected]
VisitourHomePageonwww.wileyeurope.comorwww.wiley.com
AllRightsReserved.Nopartofthispublicationmaybereproduced,storedinaretrieval
systemortransmittedinanyformorbyanymeans,electronic,mechanical,photocopy-
ing,recording,scanningorotherwise,exceptunderthetermsoftheCopyright,Designs
andPatentsAct1988orunderthetermsofalicenceissuedbytheCopyrightLicensing
AgencyLtd,90TottenhamCourtRoad,LondonW1T4LP,UK,withoutthepermissionin
writingofthePublisher.RequeststothePublishershouldbeaddressedtothePermissions
Department,JohnWiley&SonsLtd,TheAtrium,SouthernGate,Chichester,WestSussex
PO198SQ,England,[email protected],orfaxedto([phone].
Thispublicationisdesignedtoprovideaccurateandauthoritativeinformationinregard
to the subject matter covered. It is sold on the understanding that the Publisher is not
engagedinrenderingprofessionalservices.Ifprofessionaladviceorotherexpertassis-
tanceisrequired,theservicesofacompetentprofessionalshouldbesought.
OtherWileyEditorialOffices
JohnWiley&SonsInc.,111RiverStreet,Hoboken,NJ07030,USA
Jossey-Bass,989MarketStreet,SanFrancisco,CA94103-1741,USA
Wiley-VCHVerlagGmbH,Boschstr.12,D-69469Weinheim,Germany
JohnWiley&SonsAustraliaLtd,33ParkRoad,Milton,Queensland4064,Australia
JohnWiley&Sons(Asia)PteLtd,2ClementiLoop#02-01,JinXingDistripark,Singapore
129809
JohnWiley&SonsCanadaLtd,22WorcesterRoad,Etobicoke,Ontario,CanadaM9W1L1
Wileyalsopublishesitsbooksinavarietyofelectronicformats.Somecontentthatappears
inprintmaynotbeavailableinelectronicbooks.
LibraryofCongressCataloging-in-PublicationData
Roos,Matts.
Introductiontocosmology/MattRoos.–3rded.
p.cm.
Includesbibliographicalreferencesandindex.
ISBN0-470-84909-6(acid-freepaper)–ISBN0-470-84910-X(pbk.:acid-freepaper)
1.Cosmology. I.Title.
QB981.R6532003
523.1—dc22
2003020688
BritishLibraryCataloguinginPublicationData
AcataloguerecordforthisbookisavailablefromtheBritishLibrary
ISBN0470849096(hardback)
047084910X(paperback)
Typesetin9.5/12.5ptLucidaBrightbyT&TProductionsLtd,London.
PrintedandboundinGreatBritainbyAntonyRoweLtd.,Chippenham,Wilts.
Thisbookisprintedonacid-freepaperresponsiblymanufacturedfromsustainable
forestryinwhichatleasttwotreesareplantedforeachoneusedforpaperproduction.
To my dear grandchildren
Francis Alexandre Wei Ming (1986)
Christian Philippe Wei Sing (1990)
Cornelia (1989)
Erik (1991)
Adrian (1994)
Emile Johannes (2000)
Alaia Ingrid Markuntytär (2002)
Contents
PrefacetoFirstEdition ix
PrefacetoSecondEdition xi
PrefacetoThirdEdition xiii
1 From Newton to Hubble 1
1.1 HistoricalCosmology 2
1.2 InertialFramesandtheCosmologicalPrinciple 7
1.3 Olbers’Paradox 9
1.4 Hubble’sLaw 12
1.5 TheAgeoftheUniverse 17
1.6 ExpansioninaNewtonianWorld 19
2 Relativity 25
2.1 LorentzTransformationsandSpecialRelativity 25
2.2 MetricsofCurvedSpace-time 30
2.3 RelativisticDistanceMeasures 37
2.4 GeneralRelativityandthePrincipleofCovariance 45
2.5 ThePrincipleofEquivalence 49
2.6 Einstein’sTheoryofGravitation 54
3 Gravitational Phenomena 61
3.1 ClassicalTestsofGeneralRelativity 62
3.2 TheBinaryPulsar 63
3.3 GravitationalLensing 64
3.4 BlackHoles 71
3.5 GravitationalWaves 80
4 Cosmological Models 87
4.1 Friedmann–LemaîtreCosmologies 87
4.2 deSitterCosmology 99
4.3 DarkEnergy 101
4.4 ModelTestingandParameterEstimation.I 106
IntroductiontoCosmologyThirdEdition byMattsRoos
©2003JohnWiley&Sons,Ltd ISBN0470849096(cased) ISBN047084910X(pbk)
viii Contents
5 Thermal History of the Universe 113
5.1 Photons 114
5.2 AdiabaticExpansion 117
5.3 ElectroweakInteractions 122
5.4 TheEarlyRadiationEra 128
5.5 PhotonandLeptonDecoupling 132
5.6 BigBangNucleosynthesis 139
6 Particles and Symmetries 149
6.1 SpinSpace 150
6.2 SU(2)Symmetries 156
6.3 HadronsandQuarks 159
6.4 TheDiscreteSymmetriesC,P,T 163
6.5 SpontaneousSymmetryBreaking 166
6.6 PrimevalPhaseTransitionsandSymmetries 171
6.7 BaryosynthesisandAntimatterGeneration 178
7 Cosmic Inflation 185
7.1 ParadoxesoftheExpansion 186
7.2 ‘Old’and‘New’Inflation 192
7.3 ChaoticInflation 196
7.4 TheInflatonasQuintessence 202
7.5 CyclicModels 205
8 Cosmic Microwave Background 211
8.1 TheCMBTemperature 212
8.2 TemperatureAnisotropies 216
8.3 PolarizationAnisotropies 222
8.4 ModelTestingandParameterEstimation.II 225
9 Cosmic Structures and Dark Matter 231
9.1 DensityFluctuations 232
9.2 StructureFormation 237
9.3 TheEvidenceforDarkMatter 241
9.4 DarkMatterCandidates 248
9.5 TheColdDarkMatterParadigm 252
10 Epilogue 259
10.1 Singularities 259
10.2 OpenQuestions 262
Tables 267
Index 271
Preface to First Edition
A few decades ago, astronomy and particle physics started to merge in the com-
mon field of cosmology. The general public had always been more interested in
thevisibleobjectsofastronomythanininvisibleatoms,andprobablymetcosmol-
ogyfirstinStevenWeinberg’sfamousbookTheFirstThreeMinutes.Morerecently
StephenHawking’sABriefHistoryofTimehascausedanavalancheofinterestin
thissubject.
Although there are now many popular monographs on cosmology, there are
so far no introductory textbooks at university undergraduate level. Chapters on
cosmology can be found in introductory books on relativity or astronomy, but
theycoveronlypartofthesubject.Onereasonmaybethatcosmologyisexplicitly
cross-disciplinary,andthereforeitdoesnotoccupyaprominentpositionineither
physicsorastronomycurricula.
At the University of Helsinki I decided to try to take advantage of the great
interestincosmologyamongtheyoungerstudents,offeringthemaone-semester
courseaboutoneyearbeforetheirspecializationstarted.HenceIcouldnotcount
onmuchfamiliaritywithquantummechanics,generalrelativity,particlephysics,
astrophysics or statistical mechanics. At this level, there are courses with the
generic name of Structure of Matter dealing with Lorentz transformations and
thebasicconceptsofquantummechanics.Mycourseaimedatthesamelevel.Its
main constraint was that it had to be taught as a one-semester course, so that it
wouldbeacceptedinphysicsandastronomycurricula.Thepresentbookisbased
onthatcourse,giventhreetimestophysicsandastronomystudentsinHelsinki.
Ofcoursetherealreadyexistgoodbooksoncosmology.Thereaderwillinfact
find many references to such books, which have been an invaluable source of
informationtome.Theproblemisonlythattheyaddressapostgraduateaudience
that intends to specialize in cosmology research. My readers will have to turn to
these books later when they have mastered all the professional skills of physics
andmathematics.
In this book I am not attempting to teach basic physics to astronomers. They
willneedmuchmore.Iamtryingtoteachjustenoughphysicstobeabletoexplain
themainideasincosmologywithouttoomuchhand-waving.Ihavetriedtoavoid
theotherextreme,practisedbysomeofmyparticlephysicscolleagues,ofwriting
booksoncosmologywiththeobviousintentofmakingparticlephysicistsoutof
everytheoreticalastronomer.
IntroductiontoCosmologyThirdEdition byMattsRoos
©2003JohnWiley&Sons,Ltd ISBN0470849096(cased) ISBN047084910X(pbk)
x PrefacetoFirstEdition
I also do not attempt to teach basic astronomy to physicists. In contrast to
astronomy scholars, I think the main ideas in cosmology do not require very
detailed knowledge of astrophysics or observational techniques. Whole books
havebeenwrittenondistancemeasurementsandthevalueoftheHubbleparam-
eter,whichstillremainsimprecisetoafactoroftwo.Physicistsonlyneedtoknow
thatquantitiesenteringformulaearemeasurable—albeitincorporatingfactorsh
tosomepower—sothatthelawscanbediscussedmeaningfully.Atundergraduate
level,itisnotevenusualtogivetheerrorsonmeasuredvalues.
In most chapters there are subjects demanding such a mastery of theoretical
physicsorastrophysicsthattheexplanationshavetobequalitativeandthederiva-
tionsmeagre,forinstanceingeneralrelativity,spontaneoussymmetrybreaking,
inflation and galaxy formation. This is unavoidable because it just reflects the
level of undergraduates. My intention is to go just a few steps further in these
mattersthandothepopularmonographs.
Iamindebtedinparticulartotwocolleaguesandfriendswhoofferedconstruc-
tive criticism and made useful suggestions. The particle physicist Professor Kari
Enqvist of NORDITA, Copenhagen, my former student, has gone to the trouble
ofreadingthewholemanuscript.ThespaceastronomerProfessorStuartBowyer
oftheUniversityofCalifornia,Berkeley,haspassedseveralearlymorningsofjet
lag in Lapland going through the astronomy-related sections. Anyway, he could
notgooutskiingthenbecauseitwaseitherasnowstormor−30 ◦C!Finally,the
publisherprovidedmewithaveryknowledgeableandthoroughreferee,anastro-
physicist no doubt, whose criticism of the chapter on galaxy formation was very
valuabletome.ForallremainingmistakesItakefullresponsibility.Theymaywell
havebeenintroducedbymeafterwards.
Thanks are also due to friends among the local experts: particle physicist Pro-
fessorMasudChaichianandastronomerProfessorKaleviMattilahavehelpedme
with details and have answered my questions on several occasions. I am also
indebted to several people who helped me to assemble the pictorial material:
DrsSubirSarkarinOxford,RockyKolbintheFermilab,CarlosFrenkinDurham,
WernerKienzleatCERNandmembersoftheCOBEteam.
Finally, I must thank my wife Jacqueline for putting up with almost two years
ofnearabsenceandfullabsent-mindednesswhilewritingthisbook.
MattsRoos