Introduction to cosmology

261 Pages·4.109 MB·English

by  Ryden, Barbara

Pearson New International Edition

Introduction to Cosmology

Barbara Ryden
First Edition
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P E A R S O N C U S T O M L I B R AR Y
Table of Contents
Table of Useful Constants
Barbara Ryden 1
1. Introduction
Barbara Ryden 3
2. Fundamental Observations
Barbara Ryden 9
3. Newton Versus Einstein
Barbara Ryden 31
4. Cosmic Dynamics
Barbara Ryden 49
5. Single-Component Universes
Barbara Ryden 69
6. Multiple-Component Universes
Barbara Ryden 89
7. Measuring Cosmological Parameters
Barbara Ryden 111
8. The Cosmic Microwave Background
Barbara Ryden 137
9. Dark Matter
Barbara Ryden 161
10. Nucleosynthesis and the Early Universe
Barbara Ryden 183
11. Inflation and the Very Early Universe
Barbara Ryden 203
12. The Formation of Structure
Barbara Ryden 221
I
222445571
13. Epilogue
Barbara Ryden 245
Annotated Bibliography
Barbara Ryden 247
Index 251
II
Table of Useful Constants
FundamentalConstants
gravitationalconstant G =6.673×10−11m3kg−1s−2
speedoflight c=2.998×108ms−1
reducedPlanckconstant (cid:1)=1.055×10−34Js=6.582×10−16eVs
Boltzmannconstant k =1.381×10−23JK−1 =8.617×10−5eVK−1
electronrestenergy m c2 =0.5110MeV
e
protonrestenergy m c2 =938.272MeV
p
neutronrestenergy m c2 =939.566MeV
n
PlanckUnits
Plancklength l =(G(cid:1)/c3)1/2 =1.616×10−35m
P
Planckmass M =((cid:1)c/G)1/2 =2.177×10−8 kg
P
Plancktime t =(G(cid:1)/c5)1/2 =5.391×10−44s
P
Planckenergy E =((cid:1)c5/G)1/2 =1.956×109J=1.221×1028eV
P
Plancktemperature T = E /k =1.417×1032K
P P
ConversionofUnits
astronomicalunit 1AU=1.496×1011m
megaparsec 1Mpc=3.086×1022m
solarmass 1M(cid:3) =1.989×1030kg
solarluminosity 1L(cid:3) =3.846×1026Js−1
gigayear 1Gyr=3.156×1016s
electronvolt 1eV=1.602×10−19J
CosmologicalParameters
Hubbleconstant H =70±7kms−1Mpc−1
0
Hubbletime H−1 =(4.4±0.4)×1017s=14.0±1.4Gyr
0
Hubbledistance c/H =(1.32±0.13)×1026m=4300±400Mpc
0
criticalenergydensity εc,0 =5200±1000MeVm−3
criticalmassdensity ρc,0 =εc,0/c2 =(9.2±1.8)×10−27kgm−3
From Introduction to Cosmology, First Edition, Barbara Ryden. Copyright © 2003 by Pearson
Education, Inc. Published by Pearson Addison Wesley. All rights reserved.
1
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Introduction
Cosmologyisthestudyoftheuniverse,orcosmos,regardedasawhole.Attempt-
ing to cover the study of the entire universe in a single volume may seem like
a megalomaniac’s dream. The universe, after all, is richly textured, with struc-
turesonavastrangeofscales;planetsorbitstars,starsarecollectedintogalaxies,
galaxiesaregravitationallyboundintoclusters,andevenclustersofgalaxiesare
foundwithinlargersuperclusters.Giventhecomplexityoftheuniverse,theonly
waytocondenseitshistoryintoasingle text is by a process of ruthless simpli-
fication.Formuch ofthistext,therefore,we willbe consideringthe properties
ofanidealized,perfectlysmooth,modeluniverse.It is amusing to note in this con-
text thatthewordscosmologyandcosmetologycomefromthesameGreekroot:the
wordkosmos,meaningharmonyororder.Justascosmetologiststrytomakeahu-
manfacemoreharmoniousbysmoothingoversmall blemishessuchaspimples
andwrinkles,cosmologistssometimesmustsmoothoversmall“blemishes”such
asgalaxies.
A science that regards entire galaxies as being small objects might seem, at
firstglance,veryremotefromtheconcernsofhumanity.Nevertheless,cosmology
dealswithquestionsthatarefundamentaltothehumancondition.Thequestions
thatvexhumanityaregiveninthetitleofapaintingbyPaulGauguin(Figure1):
“Where do we come from? What are we? Where are we going?” Cosmology
grappleswiththesequestionsbydescribingthepast,explainingthepresent,and
predictingthefutureoftheuniverse.Cosmologistsaskquestionssuchas“What
is the universe made of? Is it finite or infinite in spatial extent? Did it have a
beginningsometimeinthepast?Willitcometoanendsometimeinthefuture?”
Cosmologydealswithdistancesthatareverylarge,objectsthatareverybig,
andtimescalesthatareverylong.Cosmologistsfrequentlyfindthatthestandard
SIunitsarenotconvenientfortheirpurposes:themeter(m)isawkwardlyshort,
thekilogram(kg)isawkwardlytiny,andthesecond(s)isawkwardlybrief.For-
tunately, we can adopt the units that have been developed by astronomers for
dealingwithlargedistances,masses,andtimes.
One distance unit used by astronomers is the astronomical unit (AU), equal
tothemeandistancebetweentheEarthandSun;inmetricunits,1AU = 1.5×
1011m. Although the astronomical unit is a useful length scale within the solar
From Chapter 1 of Introduction to Cosmology, First Edition, Barbara Ryden. Copyright © 2003
by Pearson Education, Inc. Published by Pearson Addison Wesley. All rights reserved.
3
Introduction
FIGURE1 WhereDoWeComeFrom?WhatAreWe?WhereAreWeGoing?PaulGauguin,1897.
[MuseumofFineArts,Boston]
system,itissmallcomparedtothedistancesbetweenstars.Tomeasureinterstel-
lar distances, it is useful to use the parsec (pc), equal to the distance at which
1AUsubtendsanangleof1arcsecond;inmetricunits,1pc=3.1×1016m.For
example,weareatadistanceof1.3pcfromProximaCentauri(theSun’snearest
neighbor among the stars) and 8500pc from the center of our galaxy. Although
the parsecisa usefullengthscale withinourgalaxy,itissmall comparedtothe
distancesbetweengalaxies.Tomeasureintergalacticdistances,weusethemega-
parsec(Mpc),equalto106pc,or3.1×1022m.Forexample,weareatadistance
of 0.7Mpc fromM31 (otherwiseknownas the Andromedagalaxy) and 15Mpc
fromtheVirgocluster(thenearestbigclusterofgalaxies).
The standard unit of mass used by astronomers is the solar mass (M(cid:3)); in
metric units, the Sun’s mass is 1M(cid:3) = 2.0 × 1030kg. The total mass of our
galaxy is not known as accurately as the mass of the Sun; in round numbers,
though, it is Mgal ≈ 1012M(cid:3). The Sun, incidentally,also providesthe standard
unitofpowerusedinastronomy.TheSun’sluminosity(thatis,therateatwhich
itradiatesawayenergyintheformoflight)is1L(cid:3) =3.8×1026watts.Thetotal
luminosityofourgalaxyis Lgal =3.6×1010L(cid:3).
Fortimesmuchlongerthanasecond,astronomersusetheyear(yr),definedas
thetimeittakestheEarthtogooncearoundtheSun.Oneyearisapproximately
equalto3.2×107s.Inacosmologicalcontext,ayearisfrequentlyaninconve-
nientlyshortperiodoftime,socosmologistsoftenusegigayears(Gyr),equalto
109yr, or 3.2×1016s. For example, the age of the Earth is more conveniently
writtenas4.6Gyrthanas1.5×1017s.
Inadditiontodealingwithverylargethings,cosmologyalsodealswithvery
small things. Early in its history, as we shall see, the universe was very hot and
dense,andsomeinterestingparticlephysicsphenomenawereoccurring.Conse-
quently, particle physicists have plunged into cosmology, introducing some ter-
minologyandunitsoftheirown.Forinstance,particlephysiciststendtomeasure
energyunitsinelectronvolts(eV)insteadofjoules(J).Theconversionfactorbe-
tween electron volts and joules is 1eV = 1.6×10−19J. The rest energy of an
4
Introduction
electron,forinstance,ism c2 = 511,000eV = 0.511MeV,andtherestenergy
e
ofaprotonism c2 =938.3MeV.
p
Whenyoustoptothinkofit,yourealizethattheunitsofmeters,megaparsecs,
kilograms, solar masses, seconds, and gigayears could only be devised by ten-
fingeredEarthlingsobsessed withthepropertiesofwater.Aneighteen-tentacled
silicon-based lifeform from a planet orbiting Betelgeuse would probably devise
a different set of units. A more universal, less culturally biased system of units
is the Planck system, based on the universal constants G, c, and (cid:1). Combining
the Newtonian gravitational constant, G = 6.7×10−11m3kg−1s−2, the speed
oflight,c = 3.0×108ms−1, andthe reducedPlanckconstant,(cid:1) = h/(2π) =
1.1×10−34Js = 6.6×10−16eVs, yields a unique length scale, known as the
Plancklength:
(cid:1) (cid:2)
G(cid:1) 1/2
(cid:7) ≡ =1.6×10−35m. (1)
P c3
ThesameconstantscanbecombinedtoyieldthePlanckmass,1
(cid:1) (cid:2)
(cid:1)c 1/2
M ≡ =2.2×10−8kg, (2)
P
G
andthePlancktime,
(cid:1) (cid:2)
G(cid:1) 1/2
t ≡ =5.4×10−44s. (3)
P c5
UsingEinstein’srelationbetweenmassandenergy,wecanalsodefinethePlanck
energy,
E = M c2 =2.0×109J=1.2×1028eV. (4)
P P
BybringingtheBoltzmannconstant,k =8.6×10−5eVK−1,intotheact,wecan
alsodefinethePlancktemperature,
T = E /k =1.4×1032K. (5)
P P
When distance, mass, time, and temperature are measured in the appropriate
Planck units, then c = k = (cid:1) = G = 1. This is convenient for individuals
who have difficulty in remembering the numerical values of physical constants.
However,using Planckunitscanhave potentiallyconfusingside effects.Forin-
stance,manycosmologytexts,afternotingthatc=k =(cid:1)=G =1whenPlanck
unitsareused,thenproceedtoomitc,k,(cid:1),and/orG fromallequations.Forin-
stance, Einstein’s celebrated equation, E = mc2, becomes E = m. The blatant
dimensionalincorrectnessofsuchanequationisjarring,butitsimplymeansthat
1ThePlanckmassisroughlyequaltothemassofagrainofsandaquarterofamillimeteracross.
5