Foundations of Modern Cosmology

569 Pages·2007·12.46 MB·English

Foundations of Modern Cosmology
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Foundations of Modern Cosmology
Second Edition
JohnF.HawleyandKatherineA.Holcomb
UniversityofVirginia
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To ourparents and other teachers
Preface to the Second Edition
Sincethe publicationofthefirstedition ofthis text, the fieldofcosmol-
ogy has undergone dramatic changes. Einstein’s cosmological constant,
oncerelegatedtothestatusofahistoricalartifact,hasreemergedinthe
formof“darkenergy”asasignificantdynamicalelementinthecosmos.
The long-standing question of the geometry of the universe has appar-
ently been answeredby data fromthe Wilkinson Microwave Anisotropy
Probe: theuniverseisflat. Themattercontentoftheuniverseisaround
30% of the critical value, with the balance supplied by the dark energy.
Only a fraction of the matter is composed of baryons. Although the
nature of this unknown dark matter remains elusive, new experimental
results have ruled out the neutrino, while at the same time establishing
thattheneutrinodoespossessasmallnonzerorestmass. Extensivenew
galaxy redsift surveys are providing new data on large-scale clustering
thatareessentiallyinagreementwiththenewconsensus. Somecosmol-
ogists have even begun to speak of an era of precision cosmology. Even
if we have not yet truly reached a time when cosmological parameters
can be measured to two significant digits, it was not so long ago when
cosmologistsweresatisfied for measurements to agreewithin a factor of
two.
Formanyyearstheinstructionalstyleincosmologywastopresentthe
basic ideas behind the perpetually unanswered cosmological questions.
Now for the first time we are confronted by cosmological answers, and
that can be unsettling to those who are content to catalog and contrast
varieties of speculative cosmological models. In this edition we have
updated the text to reflect the new consensus and to present some of
the exciting new observational results of the last few years. Although
it is undoubtedly the casethat the current concordancemodel will con-
tinue to be refined, we have chosen to take this model seriously as the
current best description of the structure of the universe. This has led
to some de-emphasis of alternative models. The original aim of this
textremainsunchanged,however;namely,topresentthefoundations of
modern cosmology.
Every chapter in the text has been revised and updated, and the il-
lustrations have been improved throughout. The overall sequence is es-
sentially unchanged from the first edition, but some modifications have
been made to accommodate new material and increase the instructor’s
flexibility. Chapters 1 through 3 remain focused on the historical roots
ofcosmology. Chapters4and5containbackgroundphysicsandastron-
omy; most instructors can assign these as supplemental reading. Chap-
ters 6 through 9 present topics in relativity. Of these, Chapter 6 intro-
duces the cosmologicalprinciple and the fundamental idea of relativity,
while Chapters 7 and 8 focus on special and general relativity. These
chapters can be covered quickly if the emphasis is to be primarily on
observationalcosmology. Chapter 9 presents black holes, a topic which,
althoughperhapsoutsidethemainthrustofcosmology,isalwaysamong
the most popular in classes. The next section of the book develops the
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essentialelementsofmoderncosmology. Chapter10introducestheidea
of expanding space. Chapter 11 is the most mathematical, as it deals
directlywiththeFriedmannequationandthederivationsofsomeofthe
important parameters of the universe. Instructors preferring to mini-
mize the mathematical content may wish to tread lightly there. Some
ofthebasicideas fromChapter11that arenecessaryto understandthe
implications of cosmological observations are reiterated in Chapter 13.
We haverewritten Chapters 12 through17 to focus onspecific topics of
moderncosmology;eachchaptermoreorlessstandsalone. Thedetailed
physics of the early universe is concentrated in Chapter 12. Chapter 13
discusses how the parameters of the universe can be measured and in-
cludes some of the latest results and their implications for cosmology.
The cosmic background radiation is now covered in its own chapter,
Chapter 14. The emphasis is on observational results, including those
fromthe recentWMAP mission. The natureof the dark matter and its
implications for cosmic structure are presented in Chapter 15. Inflation
is covered in Chapter 16. Chapter 17 concludes the book with a brief
discussion of quantum cosmology and speculations beyond the limits of
current theory.
Severalnewpedagogicalfeatureshavebeenadded. Eachchapternow
has marginalnotes that highlight key concepts. Chapter summaries are
nowprovidedas well. The key terms are listed at the beginning of each
chapter, with definitions given at the end of the chapter. In addition,
all key terms are defined in a glossary at the back of the book.
We have attempted to correct all the errors and other inadequacies
of the first edition, both those discovered by us and those brought to
our attention by helpful colleagues. It is perhaps inevitable that new
ones will have been introduced in the process of revision, but we hope
thatnonewillbebeyondtheabilityoftheinstructorsorthestudentsto
handle. Anotherconcernisthattherapidpaceofcosmologicaldiscovery
will continue over the coming years, and that this edition will become
outdated even more quickly than the first. We can at least hope that
this will prove to be the case.
December, 2004 John F. Hawley
Charlottesville, Virginia Katherine A. Holcomb
Preface to the First Edition
Recent discoveries in astronomy, especially those made with data col-
lected by satellites such as the Cosmic Background Explorer and the
Hubble Space Telescope, have brought cosmology to the forefront of sci-
ence. New observations hold out the tantalizing possibility that the
solutions to some especially elusive mysteries might be found in the
nearfuture. Despiteanincreaseinpublicinterestinblackholesandthe
origins of the universe, however, the unavoidable lack of context with
whichdiscoveriesarereportedpreventsmostpeoplefromunderstanding
the issues, or appreciating the true significance of the new data. Popu-
lar books oncosmologyabound, but often they presentthe subject as a
series of “just so” stories, since some basic physics is a prerequisite for
comprehending how cosmology fits into modern science. The lay reader
may well have trouble distinguishing knowledge from speculation, and
science from mythology. Furthermore, the popular literature often em-
phasizesthe moreexoticaspects ofthe field, oftenat theexpenseof the
firmly grounded achievements of modern cosmology.
Cosmology holds an intrinsic interest for many college students, who
are granted, as part of their general education, the time and opportu-
nity to learn more about the scientific discoveries they see described in
newspapers and magazines. Most colleges and universities offer a com-
prehensiveintroductoryastronomycourse,withtheprimaryobjectiveof
offering science to as broada population of students as possible. Topics
such as relativity, black holes, and the expanding universe are typically
of particular interest, but they are covered in a cursory fashion in most
introductory courses and texts. In our experience, there is alwaysa siz-
ablenumberofstudentswhofindastronomysufficientlyinterestingthat
they wish to continue their study of the subject at a comparable tech-
nical level, but with greater depth. With little but astronomy-major
or graduate-level courses available, however, such students often have
no such opportunities. These students, who are genuinely interested
in learning more about these topics, deserve the opportunity to further
their learning, and to do so in a serious way.
The course from which this book grew is intended for upper-division
liberal arts students at the University of Virginia. Most of the stu-
dentswhotakeithavesomebasicsciencebackground,suchaswouldbe
provided by a general introductory astronomy course; however, well-
prepared students can and do take the course in lieu of general as-
tronomy. Students from wide-ranging areas of study have taken this
course. Their relative success is not necessarily correlated with their
major. Some exceptionally strong students have come from the ranks
of history and philosophy majors, while occasionally an engineering or
astronomy major has floundered. Extensive experience with math and
science are not prerequisites; interest and willingness to think are.
This text is intended to fill the gap between the many popular-level
books which present cosmology in a superficial manner, or which em-
phasize the esotericat the expense of the basic, and the advanced texts
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intendedforreaderswithstrongbackgroundsinphysicsandmathemat-
ics. The book is self-contained, appropriate for a one-semester course,
anddesignedtobeeasilyaccessibletoanyonewithagraspofelementary
algebra. Ourgoalistopresentsufficientqualitativeandquantitativein-
formationtoleadthestudenttoafirmunderstandingofthefoundations
ofmoderntheories ofcosmologyandrelativity,while learningabout as-
pects of basic physics in the bargain.
The level of mathematical detail is always of concern for instructors
ofundergraduateastronomy. We haveaimedfora middle ground;some
may regret the lack of calculus and accompanying derivations, while
others may recoil from the appearance of any equation. The real dif-
ficulty with a topic like cosmology is not the mathematics per se, but
the challenging concepts and the nonintuitive way of thinking required.
However,withoutsomeunderstandingofthemathematicalbasisforcos-
mology,the student may find it difficult to distinguish from mythology;
without data and quantitative analysis, science becomes just another
narrative. Thus, while we have tried to keep the level of mathematics
consistent with minimum college-level algebra, we have not shied from
includingsomeequationswithinthetext,ratherthanrelegatingthemto
an appendix or omitting them altogether. The resulting level is compa-
rableto someof the morecomprehensiveintroductory astronomytexts.
Ofcourse,moreorlessmathematicaldetailmaybeincludedorrequired
by the instructor, depending upon the backgrounds and wishes of the
students.
The book contains more material than can usually be presented in
onesemester. Theinstructorhasagooddealofflexibilityindesigninga
particularcourse. Dependingonthebackgroundofthestudents,various
sections can be given more or less emphasis.
The text is divided into five major sections. Since many students
areunawareofthehistoricalbackgroundfromwhichmoderncosmology
grew, we begin with an overview of historical cosmology, from ancient
mythstopresentscientifictheories. Thehistoryofcosmologicalthought
demonstratesthattheuniverseisnotonlyknowabletothehumanmind,
but that the modern physical universe, constructed in the light of our
newunderstandingofphysics,isfargranderthantheconstrictedheavens
of the ancients. This section also lays out the important cosmological
questions, and introduces the ideas of natural motion, symmetry, and
therelationofphysicallawtothestructureoftheuniverse. Forstudents
who have just completed a typical introductory astronomy course, the
historicalandreviewsectionscouldbecoveredquickly,withanemphasis
on Newton’s laws.
The second section exists primarily to make the book self-contained;
it quickly reviews points that are likely to have been covered in an in-
troductory astronomy or physics course. We do not assume or require
introductory astronomy as a prerequisite; a motivated reader can find
all the necessary background material here. While this section can be
discussedbriefly, or skipped entirely, eventhose students who havepre-
viouslystudiedastronomymightfinditbeneficialtoreviewthissection.