Table Of ContentCosmologyandParticleAstrophysics
Lars Bergstro¨m Ariel Goobar
Cosmology and Particle
Astrophysics
Second Edition
Published in associationwith
PPrraaxxiiss PPuubblliisshhiinngg
Chichester, UK
Professor Lars Bergstro¨m and Dr Ariel Goobar
DepartmentofPhysics
StockholmUniversity
Stockholm
Sweden
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Preface to the Second Edition
Astroparticle physics is an arena where things are rapidly evolving. When
we, four years after the first edition, were editing the text we found many
places where the first edition was already obsolete. This is in particular true
in Chapter 4 which treats cosmological models. Since the first edition, the
presence of ‘dark energy’ has become much more established, so we include
a new section on that topic in the new edition. In Chapter 4 we have also
included a section on the distance scale of the Universe.
Wehavealsorearrangedthesectionsslightly,movingthechapteronphase
transitions (Chapter 10) to become Chapter 7. In that way, we assemble the
particlephysicsmaterialtogetherinChapters6and7.Wehavealsoincluded
a summary page for Chapter 6, which was missing in the previous version.
Wehaveincludedadiscussionofatopicalfield,thatofweakgravitational
lensing, in Chapter 5.
In Chapter 10, we have put together some of the material concerning the
presently accelerating Universe with that of primordial inflation, and have
added a section about dark energy and quintessence models.
Also in the neutrino sector much development has taken place, with two
experiments SNO and KamLAND presenting new results that pin down the
solar neutrino sector quite accurately. We have added some comments about
these experimental results in Chapter 14, and also introduced a section on
the Mikheev-Smirnov-Wolfenstein (MSW) mechanism and defined the MSW
large angle solution as indicated by the results.
The subject where the most activity is taking place at present is that
of the cosmic microwave background radiation (CMBR). During the last few
yearstherehasbeenaflurryofballoon-andground-basedexperimentswhich
havemeasuredtheangulardependenceoftheCMBRanduseditsdependence
on cosmological parameters to limit a large number of such parameters. In
February, 2003 the WMAP satellite released its first set of data. We have
added a section which discusses these new developments in Chapter 11. We
have also included a new Appendix, which deals with the problem of pri-
mordial structure formation in terms of quantum fluctuations of a scalar
field,such aspredicted in theoriesof inflation, and which issupported bythe
WMAP data. We think that this is one of the greatest intellectual triumphs
VI Preface to the Second Edition
of modern cosmology. The less sophisticated reader may, however, prefer to
skip the details.
For the convenience of the reader, we have expanded the index consider-
ably.
Finally, we have tried to correct all printing and other errors that existed
in the book. Of course, new ones will most probably be found, so it is always
wise to check on the book’s homepage www.physto.se/˜lbe/cosm book.html.
For finding the errors so far and for discussions that have improved the
contents of the book we wish to thank R. Amanullah, J. Edsjo¨, D. En-
stro¨m, M. Eriksson, M. G˚alfalk, U. Goerlach, Anne Green, C. Gunnarsson,
M. Gustafsson, P.O. Hulth, L. Liljestad, and E. Mo¨rtsell. We wish to thank
John Mason for a careful reading of the manuscript, suggesting many im-
provements.
Stockholm, October 2003 Lars Bergstro¨m & Ariel Goobar
Preface to the First Edition
The fields of cosmology and particle astrophysics (sometimes collectively
named astroparticle physics) are currently experiencing an era which will
most probably be remembered as ‘the golden age’. The developments during
thelastfewyearshavebeentrulyastonishing,andtheplanningandbuilding
of new detectors, telescopes and other experimental facilities will guarantee
an interesting decade to follow.
Whenattempting toconveytostudentsourenthusiasmfortheseexciting
developments, and when trying to teach some of the material to undergradu-
ateand beginning graduatestudents,wefound that atextbook of theappro-
priate level and scope was simply missing. It is our hope that this book will
be found to successfully fill the gap. In addition, we think the book will also
be very helpful for researchers in these areas and especially for those from
the many related fields of science.
Itistruethatthereexistmanyexcellenttextbooksbothinparticlephysics
andcosmology(manyofthemmentionedattheendofthefirstchapter),but
none which brings the student rapidly to the fields where the most exciting
developments are taking place today. We think this may be especially prob-
lematical for astronomy students, who will hardly have the time and energy
to take advanced field theory courses just to acquire some knowledge, for
instance, about the meaning of the cosmological constant. Neither will he
or she be likely to master the full gauge theory machinery of the Standard
Model of particle physics to be able to compute the cross-section for solar
neutrino scattering. Still, these are two examples of subjects of relevance to
the present-day astronomer and astrophysicist where a university education
should not leave them completely without knowledge.
A major problem we encountered when giving a course of this kind is
the very diverse background of students. To grasp the material in this book
the student should have some knowledge of advanced quantum mechanics
and classical field theory. However, not all students have this – especially
not astronomy students. To solve this without having to load the first chap-
ters with material that would be repetitious for many readers, we decided to
make fairly extended appendices, with summaries at the end, which provide
therequiredbackground.Itiseasilypossibletousethebookforanintroduc-
VIII Preface to the First Edition
tory course in relativistic quantum mechanics by just using Chapter 1 and
appendices B, C and D.
Wehaveaimedatmakingthebookself-contained,whichmeansthatmost
of the phenomena discussed in the later chapters of the book may be under-
stoodfrom‘firstprinciples’.Ofcoursethismeansthatwehavehadtonarrow
down the scope of the book to those areas where we think the recent devel-
opments and future prospects are especially exciting. This includes neutrino
astrophysics,structureformationandthemicrowavebackground,gamma-ray
astronomy, gravitational lensing, determination of cosmological parameters,
and gravitational waves. In addition, more ‘traditional’ topics like Big Bang
cosmology, thermodynamics, nucleosynthesis, dark matter and inflation are
treated. A chapter on phase transitions is also provided, which explains in
elementary terms how ‘exotic’ objects like cosmic strings and textures may
have been produced.
We have tried to be as up to date as possible. Among other things we
treatthetechniquethatusesdistantsupernovaetodeterminetheenergyden-
sity components of the Universe. We also explain the principles behind the
atmospheric neutrino oscillation detection by the Super-Kamiokande collab-
oration, which seems to indicate that neutrinos are not massless. We present
theideasbehindthelargeneutrinotelescopes,perhapsreachingsizesofcubic
kilometres, which are currently being planned.
Of course, the risk we take by including very new material is that the
book may age more rapidly than if we had only included standard material.
On the other hand, if the book becomes successful, the chances are high that
we will update it in the not too distant future. For small changes, additions
andothercomments,pleasecheckourinternethomepageforthebook,atthe
internet web address http://www.physto.se/˜lbe/cosm book.html.
According to our experience, the book can serve as a textbook for a one-
semestercourse.Ifthestudentshavelittlepreviousexperiencewithrelativity,
oneshoulddevoteatleasttwoweekseachtoChapters2and3.Asthematerial
in the later chapters is quite extensive, the lecturer probably has to make
a decision as to which topics to include. The chapter on phase transition
(Chapter 7) is fairly advanced and can be omitted without affecting the
understandingofthelaterchapters.Itgives,however,aflavouroftheexciting
links between cosmology and condensed matter physics which at present are
growing stronger. Chapters 12 – 15 are also quite independent and may be
included or omitted in a course according to preference.
Preface to the First Edition IX
The authors are grateful to several colleagues, including J. Bahcall,
P. Carlson, J. Edsjo¨, T.H. Hansson, P.O. Hulth, E. Mo¨rtsell, H. Rubinstein,
G. Smoot, H. Snellman, M. Tegmark and P. Ullio for many useful comments
and suggestions, and to many students taking our course at Stockholm Uni-
versity,especiallyE.Dalberg,C.Gunnarsson,M.KaufmannandL.Samuels-
son, for a careful reading of the manuscript. Special thanks go to R.A. Mar-
riott for many useful suggestions on the style of presentation.
Stockholm, November 1998 Lars Bergstro¨m & Ariel Goobar
Table of Contents
1 The Observable Universe ................................. 1
1.1 Introduction .......................................... 1
1.2 Baryonic Matter ...................................... 2
1.3 Antimatter ........................................... 3
1.4 The Expansion of the Universe.......................... 4
1.5 Dark Matter.......................................... 6
1.6 The Age of the Universe................................ 9
1.7 The Left-Overs from the Big Bang....................... 10
1.8 New Windows to Cosmology and Particle Physics ......... 10
1.9 Problems............................................. 12
2 Special Relativity......................................... 15
2.1 Introduction .......................................... 15
2.2 Frames, Coordinates and Metric......................... 15
2.2.1 Coordinates.................................... 16
2.2.2 Metric and Transformations...................... 17
2.3 Minkowski Space ...................................... 18
2.3.1 Causal Structure of Space-Time .................. 22
2.3.2 Vectors, Scalars and Tensors ..................... 22
2.4 Relativistic Kinematics................................. 23
2.4.1 Kinematics for 2→2 Processes................... 26
2.4.2 System of Units ................................ 28
2.4.3 Some Relativistic Kinematics for 2→2 Processes ... 28
2.5 Relativistic Optics..................................... 29
2.5.1 Aberration..................................... 29
2.5.2 Doppler Effect.................................. 31
2.6 Electromagnetic Vectors and Tensors .................... 32
2.7 Summary............................................. 34
2.8 Problems............................................. 35
3 General Relativity ........................................ 37
3.1 Introduction .......................................... 37
3.2 The Equivalence Principle .............................. 37
3.3 Gravitational Redshift and Bending of Light .............. 39
3.4 Curved Spaces ........................................ 42
