Title: QUaD: Measuring the Polarisation of the CMB
1Astrophysical Cosmology
Andy Taylor Institute for Astronomy, University
of Edinburgh, Royal Observatory Edinburgh
2Lecture 1
3(No Transcript)
4The largescale distribution of galaxies
5Temperature Variations in the Cosmic Microwave
Background
6Properties of the Universe
 Universe is expanding.
 Components of the Universe are
 Universe is 13.7 Billion years old.
 Expansion is currently accelerating.
71920s The Great Debate
Or distant stellar systems (galaxies)
Are these nearby clouds of gas?
81920s The Great Debate
 In 1924 Edwin Hubble finds Cepheid Variable
stars in M31.  Cepheid intrinsic brightness correlate with
variability (standard candle), so can measure
their distance.  Measured 3 million light years (1Mpc) to M31.
brighter fainter
Eye
near
far
Edwin Hubble
9The Expanding Universe
 Between 1912 and 1920 Vesto Slipher finds most
galaxys spectra are redshifted.
Vesto Slipher
Slipher is first to suggest the Universe is
expanding !
10Hubbles Law
In 1929 Hubble also finds fainter galaxies are
more redshifted. Infers that recession velocities
increase with distance.
11The Expanding Universe
1. Grenade Model
12The Expanding Universe
2. Scaling Model x(t) R(t) x0
13The Expanding Universe
Hubble Time tH1/H H70 km/s/Mpc tH14Gyrs
Now
D
tH
0
t
14Relativistic Cosmologies
In 1915 Albert Einstein showed that the geometry
of spacetime is shaped by the massenergy
distribution.
General Theory of Relativity required
to describe the evolution of spacetime.
Albert Einstein
15Relativistic Cosmologies
 Cosmological Coordinates (t , x)
 How do we lay down a global coordinate system?
 In general we cannot.
 Can we lay down a local coordinate system?
 Yes, can use Special Relativity locally, if we
can  cancel gravity.
 We can cancel gravity by freefalling
 (equivalence principle).
16Relativistic Cosmologies
17Relativistic Cosmologies
18Relativistic Cosmologies
 In freefall, a Fundamental Observer locally
 measures the spacetime of Special Relativity.

 Special Relativity Minkowskispace line element
 So all Fundamental Observers will measure time
 changing at the same rate, dt.
 Universal cosmological time coordinate, t.
19Relativistic Cosmologies
 How can we synchronize this Universal
 cosmological time coordinate, t, everywhere?
 With a Symmetry Principle
 On largescales Universe seems isotropic (same
in all  directions, eg, Hubble expansion, galaxy
distribution, CMB).  Combine with Copernican Principle (were not in
a  special place).
20Relativistic Cosmologies
 Isotropy Copernican Principle homogeneity

(same in all places)
rr1
rr2
rr0
So r2r1r0. So uniform density everywhere
21Relativistic Cosmologies
 Isotropy homogeneity Cosmological Principle

rr1
rr2
rr0
So r2r1r0. So uniform density everywhere
22Relativistic Cosmologies
 With the Cosmological Principle, we have uniform
 density everywhere.
 Density will decrease with expansion, so r r
(t).  So can synchronize all Fundamental Observers
 clocks at preset density, r0, and time, t0

23Relativistic Cosmologies
 What is the line element (metric) of a
relativistic cosmology?  Locally Minkowski line element (Special
Relativity)
Worldline
t
x
24Lecture 2
25Relativistic Cosmologies
 A general line element (Pythagoras on curved
surface)  Minkowski metric
 tensor
 We have Universal Cosmic Time of Special
Relativity, t, so 
26Relativistic Cosmologies
 What is spatial metric, s32?
 From Cosmological Principle
 (homogeneity isotropy)
 spatial curvature must be
 constant everywhere.
 Only 3 possibilities
 Sphere positive curvature
 Saddle negative curvature
 Flat zero curvature.
27Relativistic Cosmologies
 What is form of s32?
 Consider the metric on a 2sphere
 of radius R, s22
R
28Relativistic Cosmologies
 The metric on a 2sphere of radius R
 Now relabel q as r and f as q
 where r (0,p) is a dimensionless distance.
R
29Relativistic Cosmologies
 Can generate other 2 models from the 2sphere
k 1 k  1 k 0
30Relativistic Cosmologies
 General 3metric for 3 curvatures
k 1 k  1 k 0
31Relativistic Cosmologies
 Different properties of triangles on curved
surfaces
k 0 k 1
dq
r
r dq
r
sin r dq
32Relativistic Cosmologies
 Different properties of triangles on curved
surfaces
k 1 k  1 k 0
dq
r
sinh r dq
r
r dq
r
sin r dq
33Relativistic Cosmologies
dq
 Finally add extra compact dimension
 Promote a 2sphere to a 3sphere
 So metric of 3sphere is
df
34Relativistic Cosmologies
 The RobertsonWalker metric generalizes the
 Minkowski line element for symmetric
cosmologies
k 1 k  1 k 0
 The RobertsonWalker Metric
35Relativistic Cosmologies
 Alternative form of the RobertsonWalker metric
k 1 k  1 k 0
36Relativistic Cosmologies
 Alternative form of the RobertsonWalker metric
k 1 k  1 k 0
37Relativistic Cosmologies
 The RobertsonWalker models.
 k 1 positive curvature everywhere,
 spatially closed, finite volume,
 unbounded.
 k  1 negative curvature everywhere,
 spatially open, infinite volume,
 unbounded.
 k 0 flat space, spatially open,
 infinite volume, unbounded.
k 1 k  1 k 0
38Relativistic Cosmologies
 The RobertsonWalker models.
 We have defined the comoving radial distance, r,
 to be dimensionless.
 The current comoving angular distance is
 d R0Sk(r) (Mpc).
 The proper physical angular distance is
 d(t) R(t)Sk(r) (Mpc).
39Lecture 3
40Relativistic Cosmologies
 Superluminal expansion
 The proper radial distance is
The proper recession velocity is
What does this mean? Locally things are not
moving (just Special Relativity). But distance
(geometry) is changing. No superluminal
information exchange.
41Light Propagation
 How does light propagate through the expanding
Universe?  Let a photon travel from the pole
 (r0) along a line of constant
 longitude (dq0,df0).
 The line element for a photon is
 a null geodesic (zero proper time)
42Light Propagation
 Equation of motion of a photon
 The comoving distance light travels.
43Light Propagation
 Lets assume R(t)R0(t/t0)a
44Causal structure
t
l
R
t1
l
For t gtgt t1 , r is constant. This is called an
Event Horizon. As t1 tends to 0, l(t) diverges,
everywhere is causally connected.
45Causal structure
t
t0
l
At early times all points are causally
disconnected. The furthest that light can have
travelled is called the Particle Horizon.
46Cosmological Redshifts
 Consider the emission and observation of light
47Cosmological Redshifts
 Consider the emission and observation of light
A bit later
48Cosmological Redshifts
 But the comoving position of an observers is a
constant
Say the wavelength of light is l cdt
so
49Cosmological Redshifts
 Can also understand as a series of small
Doppler shifts
dcdt
dVHdcHdt
t0
tdt
50Decay of particle momentum
 Every particle has a de Broglie wavelength
 So momentum (seen by FOs) is redshifted too
 Why? (Hubble drag, expansion of space?)
dRr, VHd
t0
tdt
51Lecture 4
52The Dynamics of the Expansion
In 1922 Russian physicist Alexandre Friedmann
predicted the expansion of the Universe
Birkhoffs Theorem
m
Newtonian Derivation
Rr
M4pr(Rr)3/3
53The Dynamics of the Expansion
In 1922 Russian physicist Alexandre Friedmann
predicted the expansion of the Universe
V
Birkhoffs Theorem
m
Friedmann Equation
Rr
M4pr(Rr)3/3
54Geometry Density
 There is a direct connection between density
geometry
 So a lowdensity model will evolve to an empty,
flat  expanding universe.
55Geometry Density
 There is a direct connection between density
geometry
 So with the right balance between H and r,
 we have a flat model.
56Critical density density parameter
 We can define a critical density for flat models
and  hence a density parameter which fixes the
geometry.
k 1 rgtrc W gt1 k
 1 rltrc Wlt1 k 0
rrc W1
57Critical density density parameter
 How does W evolve with time?
W
1
t
58Critical density density parameter
 What is present curvature length?
Define a dimensionless Hubble parameter
59Critical density density parameter
Or 1 small galaxy per cubic Mpc. Or 1 proton per
cubic meter.
60The meaning of the expansion of space
 Consider an expanding empty, spatially flat
universe.  c.f. a relativistic Grenade Model
 Minkowski metric
 Let vHr, H1/t so vr/t.
 Switch to comoving frame
61The meaning of the expansion of space
 Rewrite in terms of t (comoving time)
 Hence in the comoving frame
 but this is a k1 open model with Rct!
 So what is curvature?
 And is space expanding ?
62The matter dominated universe
 Consider a universe with pressureless matter
(dust,  galaxies, or cold dark matter).
 As Universe expands, density of matter
decreases  rr0(R/R0)3.
 Consider a flat model k0, W1.
R
t
63Lecture 5
64The matter dominated universe
 The spatially flat, matterdominated model is
called  the Einsteinde Sitter model.
R
t
65The matter dominated universe
 Consider an open or closed, matterdominated
universe.  Define a conformal time, dhcdt/R(t).
R
t
66The matter dominated universe
 Consider a closed, matterdominated universe.
 Define a conformal time, dhcdt/R(t).
R
t
67The matter dominated universe
 Consider an open or closed, matterdominated
universe.  Define a conformal time, dhcdt/R(t).
R
t
68The matter dominated universe
 So for matterdominated models
geometry/densityfate.
W lt 1
Expand forever
k 1
W 1
k 0
Eventual recollapse
W gt 1
k 1
Big Bang
Big Crunch
69The radiation dominated universe
 As Universe expands, density of matter
decreases  rmr0m(R/R0)3.
 Radiation energy density rrr0r(R/R0)4.
 At early enough times we have
radiationdominated Universe.
Log r
rr
For T(CMB)2.73K, zeq1000.
rm
Log R
70The radiation dominated universe
 At early enough times we also have a flat model
k0
So Particle Horizon!
71The radiation dominated universe
 Timescales
 Matterdominated Rt2/3
 Radiation dominated Rt1/2
72The radiation dominated universe
 Spatial flatness at early times
 Recall
 How close to 1 can this be? At Planck time
(t1043s)?
73Energy density and Pressure
 Thermodynamics and Special Relativity
 So energydensity changes due to expansion.
74Energy density and Pressure
 For pressureless matter (CDM, dust, galaxies)
 Radiation pressure
 Cf. electromagnetism.
75Lecture 6
76Pressure and Acceleration
 Time derivative of Friedmann equation
 Acceleration equation for R
77Vacuum energy and acceleration
 Gravity responds to all energy.
 What about energy of the vacuum?
 Two possibilities
 Einsteins cosmological constant.
 Zeropoint energy of virtual particles.
78Einsteins Cosmological Constant
Einstein introduced constant to make Universe
static.
79Einsteins Cosmological Constant
 Problem goes back to Newton (1670s).
 Einsteins 1917 solution
80Einsteins Cosmological Constant
 But this is not stable to expansion/contraction.
Einstein called this My greatest blunder.
81Zeropoint vacuum energy


 British physicist Paul Dirac predicted
antiparticles.  Werner Heisenbergs Uncertainty Principle
Vacuum is filled with virtual particles.  Observable (Casmir Effect) for electromagnetism.
82The Vacuum Energy Problem
 So Quantum Physics predicts vacuum energy.
 But summation diverges.
 If we cut summation at Planck energy it predicts
an energy 10120 times too big.  Density of Universe 10 atoms/m3
 Density predicted 1 million x
mass of the Universe/m3  Perhaps the most inaccurate prediction in
science? Or is it right?
83Vacuum energy
 Vacuum energy is a constant everywhere rV R0
 Thermodynamics Consider a piston
The equation of state of the vacuum.
84Vacuum energy and acceleration
 Effect of negative pressure on acceleration
 So vacuum energy leads to acceleration.
R
t
 Eddington L is the cause of the expansion.
85General equation of State
 In general should include all contributions to
energydensity.
rr
Log r
rm
rV
Log R
86General equation of State
 In general must solve F.E. numerically.
 Geometry is still governed by total density
1 WV 0 1
FLAT
CLOSED
OPEN
0 1 2
Wm
87General equation of State
 In general must solve F.E. numerically.
 But in general no geometryfate relation
R
t
1 WV 0 1
EXPAND FOREVER
FLAT
CLOSED
OPEN
RECOLLAPSE
0 1 2
Wm
R
t
88General equation of State
R
t
R
t
No singularity
1 WV 0 1
EXPAND FOREVER
FLAT
CLOSED
OPEN
RECOLLAPSE
0 1 2
Wm
R
t
89Age and size of Universe
 Evolution of redshift
 where
 Age of the universe
zinfinity
z0
90Age and size of Universe
 Usually evaluate t0 numerically, but
approximately
1 H0t0 2/3
0
WvWm1
Wv0
0
1 Wm
91Age and size of Universe
 Comoving distanceredshift relation
drcdt/Rcdz/R0H(z).  Wm1

 Wm0
92Lecture 7
93Age and size of Universe
 Comoving distanceredshift relation
drcdt/Rcdz/R0H(z).  Einstein de Sitter Wm1

 de Sitter WV1
Wv1
r(z)
Wm 1
z
94Observational Cosmology
 Size and Volume
 Start from line element
 Angular sizes
 Volumes
95Observational Cosmology
 Angular diameter distance
 Einsteinde Sitter universe de
Sitter universe
dS
DA(z)
r2c/H0
EdS
0 1 z
96Observational Cosmology
 Angular size
 Einsteinde Sitter universe de
Sitter universe
1/z
EdS dS
z
dy(z)
0 1 z
97Observational Cosmology
 Luminosity and flux density
 Euclidean space
 Curved, expanding space
 LE/t(1z)2
 LvdL/dv d/dv0(1z)d/dv
 v(1z)v0
98Observational Cosmology
dW
So the highredshift objects are heavily dimmed
by expansion.
99Observational Cosmology
 Luminosity distance
 Einsteinde Sitter
 de Sitter
100Observational Cosmology
 Magnituderedshift relation
 The Kcorrection redshift shifts frequency
passbands.
Lv
dv v
(1z)dv
101Observational Cosmology
 Galaxy Counts Number of galaxies on sky
as  function of
flux, N(gtS).  Euclidean Model Consider n galaxies per Mpc3
with same  luminosity, L, in
a sphere of radius D.
102Observational Cosmology
 Olbers Paradox
 The Sky brightness
 which
diverges as S goes to zero.  Too many
sources as D increases,  due to
increase in volume.
103Lecture 8
104Observational Cosmology
 Olbers Paradox Why is the night sky
dark?  which
diverges as S goes to zero.  Too many
sources as D increases,  due to
increase in volume.
D
105Observational Cosmology
 Relativistic Galaxy Count Model
 W1, k0 Einsteinde Sitter model
 Flux density Lvva
 Number counts. zltlt1
 zgtgt1


V(z)
Euclidean
EdS
0 1 z
106Observational Cosmology
 Relativistic Galaxy Count Model


zgtgt1 sources
Log N(gtS)
Euclidean
S3/2
S
Counts converge due to finite volume/age
/distance at highz. So solves Olbers paradox.
107Distances and age of the Universe
 Cosmological Distances c/H0 3000h1Mpc.
 Cosmological Time 1/H0 14 Gyrs.
 Recall our solution for age of Universe
 So if we know Wm, WV and H0, we can get t0.
 Or if we know H0 and t0 we can get Wm and WV.
108Distances and age of the Universe
 Estimating the age of the Universe, t0
 Nuclear Cosmochronology
 Natural clock of radioactive decay, t10Gyrs.
 Heavy elements ejected from supernova into ISM
 Thorium (232Th) gt Lead (208Pb) 20 Gyrs
 Uranium (235U) gt Lead (207Pb) 1 Gyr
 Uranium (238U) gt Lead (206Pb) 6.5 Gyrs
109Distances and age of the Universe
 Estimating the age of the Universe
 No new nuclei produced after solar system forms,
just nuclear decay  But dont know D0, so how to measure DD?
P0
DP DD
D0
110Distances and age of the Universe
 Estimating the age of the Universe
 Take ratio with a stable isotope of D, S.
 Plot D/S versus P/S
Slope (et/t1)
D/S
D0/S
P/S
Meterorites tSS 4.57(/0.04) Gyrs
Nuclear theory tMW 9.5 Gyrs
111Age from Stellar evolution tM/L
Distances and age of the Universe
Red Giant Branch
Turnoff
tGC 1317 Gyrs. Recall for EdS t09.3Gyrs!
Main Sequence
112 Local distance
Distances and age of the Universe
 Use Cepheid Variables (cf Hubbles measurement to
M31).  Mass M3 9Msun
 Moving onto Red Giant Branch

 Luminosity(Period)1.3
 L 1/D2
 D1/L1/2
 Need to know DLMC51kpc / 6.
 From parallax, or SN1987a.
Red Giant Branch
Surface Temperature
113 Larger distances
Distances and age of the Universe
 Use supernova Hubble diagram.
 SN Ia, Ib, II.
 SNIa standard candles.
 Nuclear detonation of WD.
 HST Key programme
 H0 72/8kms1.
 (error mainly distance to LMC)
Red Giant
White dwarf
114Distances and age of the Universe
 So now know H0 and t0 so now know H0t00.96.
 What can we infer about Wm and WV?
 This implies that if WV0, Wm0.
 Or WV2.3Wm! Implies vacuum domination
 And if flat (k0) WV0.7, Wm0.3.
115Cosmological Geometry
 Can measure Wm and WV from luminosity distances
 to standard candles the supernova Hubble
diagram.
116Cosmological Geometry
 The supernova Type Ia are fainter than expected
given their redshift velocity.
Accelerating Universe
Faintness  log DL
Decelerating Universe
Type 1a supernova Hubble Law
Redshift
117Cosmological Geometry
 Can measure Wm and WV from luminosity distances
 to standard candles the supernova Hubble
diagram.
118Lecture 9
119The thermal history of the Universe
 Recall that as Universe expands
 rmr0m(R/R0)3 rrr0r(R/R0)4
r rv0 (R/R0)0  At early enough times we have
radiationdominated  Universe.
Log r
rr
For T(CMB) 2.73K today.
rm
rv
Log R
120The thermal history of the Universe
 Also expect a neutrino background, rv0.68rg
(see later).
Log r
rr
For T(CMB) 2.73K today.
rm
rv
Log R
121The thermal history of the Universe
 How far back do we think we can go to in time?
 To the Quantum Gravity Limit
 Quantum Mechanics de Broglie
 General Relativity Schwartzschild
Quantum Classical
mpl
122Thermal backgrounds
 If expansion rate lt interaction rate we have
 thermal equilibrium.
 Shall also assume a we have perfect gas.
 Occupation number for relativistic quantum
states is
fermions bosons
1
f(x)
bosons
1/2
fermions
e(em)/kT Boltzmann
x(em)/kT
123Thermal backgrounds
 The Chemical Potential, m
 A change of energy when change in number of
particles.  As in equilibrium, expect total energy does not
change
124Thermal backgrounds
 The particle number density
 N(p) is the density of discrete quantum states
 in a box of volume V with momentum p
g degeneracy factor (eg spin states)
125Thermal backgrounds
 The number density of relativistic quantum
particles
126Thermal backgrounds
 The ultrarelativistic limit pgtgtmc, kTgtgtmc2
(bosons)  The nonrelativistic limit kTltltmc2 (Boltzmann)
127Thermal backgrounds
 Protonantiproton production and annihilation
 mp 103 MeV so for T gt 1013 K there is a
thermal  background of protons and antiprotons.
 But when Tlt1013K annihilation to photons.
 Should annihilate to zero, but in fact
Dp/p109!  (or else we wouldnt be here.)
 So there must have been a MatterAntimatter
Asymmetry!!
128Thermal backgrounds
 The energy density of relativistic quantum
particles (bosons)
129Thermal backgrounds
 The entropy, S, of relativistic quantum
particles  The entropy is an extensive quantity (like E V)
E1 V1 S1
E2 V2 S2
EE1E2 VV1V2 SS1S2
so
Hence
130Thermal backgrounds
 So in the ultrarelativistic case
 So
 But (entropy is a conserved
quantity).  Usual to quote ratios e.g. baryon density
nB/s109.
131Lecture 10
132Thermal backgrounds
 Given these simple scalings with T for bosons,
what is the  scaling for n, u and s for fermions when kT gtgt
mc2 ?  Formally expand
 So occupation numbers
133Thermal backgrounds
 Given these simple scalings with T for bosons,
what is the  scaling for n, u and s for fermions when kT gtgt
mc2 ?  For kTgtgtmc2
 Number densities
134Thermal backgrounds
 Given these simple scalings with T for bosons,
what is the  scaling for n, u and s for fermions when kT gtgt
mc2 ?  For kTgtgtmc2
 Energy densities
135Thermal backgrounds
 Given these simple scalings with T for bosons,
what is the  scaling for n, u and s for fermions when kT gtgt
mc2 ?  For kTgtgtmc2
 Energy densities
136Thermal backgrounds
 Given these simple scalings with T for bosons,
what is the  scaling for n, u and s for fermions when kT gtgt
mc2 ?  Define an effective number of relativistic
particles  So energy of all relativistic particles is
137Thermal backgrounds
 The effective number of relativistic particles
will change  with time as kTltmc2 and particles become
nonrelativistic.
 For highT g100. If supersymmetric, g200.
138Time and Temperature
 At early times radiation and matter are strongly
coupled  and thermalized to temperature, T, of
radiation.  Recall in a
radiationdominated universe,  and
 Hence
 Note also that T2.73K(1z), so zT/(1 K).
139A Thermal History of the Universe
 With time now related to temperature, and hence
 energy, we can map out the thermal history of
 the Universe.
140e e annihilation
1010K 1013K 1015K 1028K
1032K
Protonantiproton annihilation
Dark Matter formed?
Inflation?
141Freezeout and Relic Particles
 Electrons  Positrons annihilation
 For first 3 seconds we have
 Then T drops and energy in g becomes too low, so
 electrons and positrons annihilate.
 Stops when annihilation rate drops below
expansion rate.
142Freezeout and Relic Particles
 Need the Boltzmann Equation to describe
reactions
Rate of change
Loss due to annhilation tint1/(ltsvgtn)R3
Dilution by expansion texp1/HR2
log t
texp gt tint thermal equilibrium
texp lt tint Particle Freezeout/ Decoupling
log R
143Freezeout and Relic Particles
 Creation, annihilation and freezeout of
particle relics
T3
Log n
Pair production
Freezeout
Pair annihilation
log kT
T3
144Freezeout and Relic Particles
 ElectronsPositrons annihilation and
 neutrino decoupling
 What happens to the energy released by
?  At early times only have photons, neutrinos and
ee pairs  in equilibrium.
 At T 5x109K (3 seconds) ee pairs annihilate.
As weak force decoupled at T1010K.
145Freezeout and Relic Particles
 So radiation is boosted above neutrino
temperature  by neutrino decay.
 Before nvng , after nv lt ng and Tv lt Tg.
 But recall entropy is conserved
 where
146Lecture 11
147Freezeout and Relic Particles
 How much is photon temperature boosted ?
 Entropy
 ge2
 gg2
 Neutrino Temperature
148Freezeout and Relic Particles
 How much is radiation energy boosted ?
 Neutrino energy
 Enhances rr by factor of 1.68 for 3 neutrino
species
Neutrinos annihilate
log r
rg
rv
log R
149Relic massive neutrinos
 Can we put cosmological constraints on
 the mass of neutrinos ?
 1960s Particle physics models with mv 0.
 1970s Particle physics models with massive
neutrinos.  1990s Nonzero mass detected (Superkamiokande,
 and Sudbury Neutrino Observatory
(SNO)  confirms Solar model).
150Relic massive neutrinos
 Can we put cosmological constraints on
 the mass of neutrinos ?
 Numberdensity of cosmological neutrinos
 Massdensity
151Relic massive neutrinos
 Can we put cosmological constraints on
 the mass of neutrinos ?
 Densityparameter of cosmological neutrinos
 Rearrange
 Compare with lab mvelt15eV, mvmlt0.17MeV,
mvtlt24MeV. 
Dm2mi2mj27x103 eV2.
152BigBang Nucleosynthesis (BBN)
 As R tends to zero and T increases,
 eventually reach nuclear burning temperatures.
 1940s George Gamow suggests nuclear reactions
in early  Universe led to Helium.
 Prediction of a radiation background (CMB)
 Predicted 25 helium by mass, as found in stars.
 1960s Details worked out by Hoyle, Burbidge
and  Fowler.
 First need free protons and neutrons to form.
153BigBang Nucleosynthesis (BBN)
 So first need proton neutron freezeout.
 Recall
 Below Tlt1013K (MpMn 103 MeV)
 Annihilation leaves a residual Dp/pDn/n109.
 Protons and neutrons undergo Weak Interactions
154BigBang Nucleosynthesis (BBN)
 Assume equilibrium and low energy (kTltltmc2)
limit  Ratio of neutrons to protons at temp T
 (Dmmnmp1.3MeV)
155BigBang Nucleosynthesis (BBN)
 Annihilations stop when p n freezeout occurs
 Reaction expansion
 time gt time
 tint1/svn texp1/H
 So ratio is frozen in at Tfreezeout
156BigBang Nucleosynthesis (BBN)
 What is the observed neutronproton ratio?
 Most He is in the form of 4He
 He fraction by mass is
 Observe Y0.25 for stars.
 So np/nn2/Y17, or
157BigBang Nucleosynthesis (BBN)
 At what time, then, does neutron freezeout
happen?  Need to know weak interation rates ltsvgtweak
 This was calculated by Enrico Fermi in 1930s.
 Find
 So expected neutronproton ratio is
158BigBang Nucleosynthesis (BBN)
 Expect nn/np0.34.
 But we said from observed
stellar abundances.  Close, but a bit big.
 But 1. We have assumed kTfreezeoutgtgtmec2
 but really kTfreezeoutmec2
 2. Neutrons decay. tn887 / 2
seconds for  free neutrons. Need to be locked away
 in a few seconds
159BigBang Nucleosynthesis (BBN)
 The onset of Nuclear Reactions.
 At the same time nuclear reactions become
important.  Neutrons get locked up in Deuteron via the strong
interaction  Happens at deuteron binding energy kT2.2MeV
 Dominant when T(D formation)8x108K, or at a
time  t3 minutes.
n p
D g
D
n
p
160BigBang Nucleosynthesis (BBN)
 The formation of Helium.
 4He is preferred over H or D on thermodynamic
grounds.  Binding energies E(He) 7 MeV
 E(D) 1.1 MeV
 After Deuteron forms

 Then
T gets too low and reactions stop at Li
Be. BBN starts at 1010K, t1s. Ends at 109K,
t3mins.
161Lecture 12
162BigBang Nucleosynthesis (BBN)
 Summary of BBN
 T1013K, t0.1s Neutron proton annihilation
(Dp/pDn/n109).  T1010K, t1s Neutron freezeout
(nn/np0.34.)  Neutrons decay
(nn/np0.14.)  Nuclear reactions
start.  T109K, t3mins
 Formation of Helium.
 Peak of D formation.
 End of nuclear reactions
 H, D, 3He, 4He, 7Li, 7Be
163BigBang Nucleosynthesis (BBN)
 The number of neutrino generations
 The ratio of neutrons to protons is
 Depends weakly on rB higher baryon density
means closer  packed, so n locked up in nucleons (D) faster.
 Depends on Nv More neutrinos, more rr (g), so
Hubble  rate increases, neutron freezeout happens
sooner, so more n.  Cosmological constraint that Nvlt4.
 In 1990s LEP at CERN sets Nv3.
164BigBang Nucleosynthesis (BBN)
 Testing BBN
 The abundance of elements is
 sensitive to density of baryons
 h is number density of baryons
 per unit entropy.
 This gives us the matterantimatter difference
of Dp/p109  Agreement between BBN theory and observation
is a  spectacular confirmation of the BigBang
model !
1011 1010 109 h
165BigBang Nucleosynthesis (BBN)
 Using BBN to weigh the baryons
 The abundance of elements is sensitive to the
density of baryons.  The photon density scales as T3, so
 This yields
 But
 So most of the matter in the Universe
 cannot be made of Baryons !
166Recombination of the Universe
 Energydensity of the Universe
Log r
rr
T103K zrec103
Bound atoms (H) and free photons
zeq104
rm
Log R
Plasma Era g, p, e in a plasma Thomson
scattering (ge)
Recombination (a misnomer)
167Recombination of the Universe
 Ionization of a plasma
 Assume thermal equilibrium.
 Use Saha equation for ionization fraction, x
c13.6 eV H binding energy.
168Recombination of the Universe
 Ionization of a plasma
 But equilibrium rapidly ceases to be valid.
Interactions  are too fast, and photons cannot escape.
 Escape bottleneck with 2photon emission
 This means the ionization fraction is higher
than predicted  by the Saha equation.
0
2s 1s
Ehw lt c
g g
H
169Recombination of the Universe
 The surface of last scattering
 In plasma photons random walk (Thomson
scattering  off electrons).
 After recombination photons travel freely and
atoms form.  The last scattering surface forms a photosphere
(like sun),  The Cosmic Microwave Background.
Dz80
Ionized Plasma
g
z1100
z
170The Cosmic Microwave Background
 The CMB spectrum
 The CMB was discovered by
 accident in 1965 by Arno Penzias
 and Bob Wilson, two researchers
 at Bell Labs, New Jersey.

 This confirmed the BigBang
 model, and ruled out the competing
 SteadyState model of Hoyle.
 They received the 1978 Nobel
 Prize for Physics.
171The Cosmic Microwave Background
 The CMB spectrum
 The Big Bang model predicts a thermal blackbody
spectrum  (thermalized early on and adiabatic
expansion).  The observed CMB is an almost perfect BB
spectrum
 Accuracy limited by
 reference BB source.
 CMB contributes to 1
 of TV noise.
172The Cosmic Microwave Background
 The CMB dipole
 The CMB dipole is due to our motion through
universe.  Doppler Shift vDv0, D1v.r/rc 
dipole.  Same as temperature shift T(1v.r/rc)T0
173The Cosmic Microwave Background
 The CMB dipole
 This gives us the absolute motion of the
 Earth (measured by George Smoot in 1977)
 VEarth 371/ 1 km/s,
 (l,b) (264o,48o)
 assuming no intrinsic dipole.
 What is its origin?
 Not due to rotation of sun around galaxy (wrong
direction).  v300km/s, (l,b)(90o,0o).
 Motion of the Local Group?
 Implies VLG600km/s (l,b)(270o,30o).
174Lecture 13
175The Cosmic Microwave Background
 The CMB dipole
 What is its origin of the dipole?
 Motion of the Local Group.
 VLG600km/s (l,b)(270o,30o).
 Motion due to gravitational attraction of
 largescale structure
 LG is falling into the Virgo Supercluster
 (10Mpcs away)
 Which is being pulled by the Hercules
 Supercluster (the Great Attractor,
 150Mpc away).
176Dark Matter
 Recall from globular cluster ages, supernova
 and BBN
 So we infer most of the matter in the Universe
is  nonbaryonic.
 How secure is the density parameter measurement?
 If its wrong and lower, could all just be
baryons.
177Dark Matter
 Masstolight ratio of galaxies
 We can expect M/LF(M)
 Comets
 LowMass stars
 Galaxy stars
luminosity density from galaxy surveys
M/L
M 3
M
178Dark Matter
 In blue starlight
 So we find
 This is way above the M/L10 we see in stars.
 So not enough luminous baryons in stars.
 In fact not enough baryons in stars to make
 WB0.04, so there must be baryonic dark matter
too.
179Dark Matter
 Dark Matter in Galaxy Halos
 In 1970s Vera Rubin found galaxies rotate
 like solid spheres, not Keplerian.
 For Vconst, need M(ltr)r, so
 Density profile of Isothermal Sphere.
 Yields dark matter 5 x stellar mass
180Dark Matter in Galaxy Clusters
 In 1933 Fritz Zwicky found the Doppler motion of
galaxies in the Coma cluster were moving too fast
to be gravitationally bound.  First detection of dark matter.
 Assume hydrostatic equilibrium
 So need 10 100 x stellar mass.
Zwicky (18981974)
Coma
Velocity dispersion
181Dark Matter in Galaxy Clusters
 Xray emission from galaxy clusters.
 Hot gas emits Xrays.
 Assume hydrostatic equilibrium.
 Equate gravitational and thermal potentials
 Get both total mass, and baryonic (gas) mass.
 So MDM10MB
Coma
182Dark Matter in Galaxy Clusters
 Gravitational lensing by clusters of galaxies.
 Use giant arcs around clusters
 to measure projected mass.
 Strongest distortion at the
 Einstein radius
 Independent of state of cluster (equilibrium).
 Find again MTot 10 100 Mstars
Abell 2218
183Dark Matter and Wm
 So independent methods show in galaxy clusters
 MDM 10 Mgas 100 Mstars
 Can estimate massdensity of Universe from
clusters
184Largescale structure in the Universe
 The distribution of matter in the Universe is
not uniform.  There exists galaxies, stars, planets, complex
life etc.  Where does all this structure come from?
 Is there a fossil remnant from when it was
formed?  How do we reconcile this structure with the
 Cosmological Principle Friedmann model ?
185The largescale distribution of galaxies
The 2degree Field Galaxy Redshift Survey (2dFGRS)
186The largescale distribution of galaxies
The 2degree Field Galaxy Redshift Survey (2dFGRS)
187Largescale structure in the Universe
 The matter density perturbation
 Fourier decomposition
d(r)
L
kxnp/L, n1,2
188Largescale structure in the Universe
 The statistical properties
 The Ergodic Theorem
 Volume averages are equal to ensemble
averages.  Moments of the density field
 Define the power spectrum
189Largescale structure in the Universe
 The statistical properties
 The correlation function
 So correlation function is the Fourier transform
of the power spectrum, P(k).  For point processes, correlation function is the
excess probability of finding a point at 2 given
a point at 1
2
r
1
190Lecture 14
191Largescale structure in the Universe
 The Matter Power Spectrum
 So 2point statistics can be found from P(k).
 What is the form of P(k)?
 For simplicity lets assume for now its a
powerlaw  where A is an amplitude and n is the spectral
index.
log D2(k)
log k
192Largescale structure in the Universe
 The Potential Power Spectrum
 Can we put limits on spectral index, n?
 Consider the potential field, F.
 So far we have assumed Fltlt1 (so metric is
Freidmann).  Poisson equation
 So
193Largescale structure in the Universe
 The Potential Power Spectrum
 Can we put limits on spectral index, n?
 To keep homogeneity, need n less than or equal to
1.  To avoid black holes, need n greater or equal to
1.  So must have n1, with D2Fconst1010 (from
CMB).  n1 is scale invariant (fractal) in the potential
field.
ngt1
log D2F(k)
n1
log k
nlt1
194Structure in the Universe
 Where did this structure come from ?
 In 1946 Russian physicist Evgenii Lifshitz
 suggested small variations in density in the
 Early Universe grow due to gravitational
 instability.
density
position
195Dynamics of structure formation
 Consider the gravitational collapse of a sphere
 Assume Einsteinde Sitter (Wm1, pm0).
 Behaves like a miniuniverse, so
r
rgtr0
r0
t
196Dynamics of structure formation
 Linear theory growth
 0th order

 expansion of universe.  1st order
r0
197Dynamics of structure formation
 Linear growth of overdensities
 Density 1/Vol
 Linear growth in EdS
r0
r
position
198Dynamics of structure formation
 Nonlinear growth of overdensities
 Linear growth
 Turnaround
 Collapse
 Virialization
virialization
199Formation of a galaxy cluster
200Dark Matter and the Power Spectrum
 Since d a on all linear scales, the matter
power spectrum  preserves its shape in the linear regime.
 Linear regime, dltlt1, valid at early times and on
large scales.  If ngt3 initial shape will be preserved on large
scales.  Power spectra is shaped by dark matter, so
leaves imprint.
r
r
log D2(k)
log k
201Dark Matter and the Power Spectrum
 Have already seen we need nonbaryonic dark
matter  (WB0.04 lt Wm0.3, from BBN and clusters, SN,
ages).  But what can the dark matter be?
 Massive Neutrinos?
 Now know to have mass, so possibly.
 Black holes?
 Also now know to exist at centre of all
galaxies. But  if too large, disrupt galactic disk lens
stars in LMC and galactic bugle (MACHO and OGLE
surveys). Too small and will  overproduce Hawking radiation
emission.  A frozenout particle relic from the early
universe  Weakly Interacting Massive Particles (WIMPS).
202What is Dark Matter ?
 Must be weakly interacting to avoid detection so
far.  A promising idea in particle physics is
Supersymmetry  The lightest supersymmetric particle (the
neutralino gravitinophotinozino) could be
detected in 2007 at Europes CERN Large Hadron
Collider (LHC).
Matter Particles (fermions) Force Particles
(boson)
electron
photon
selectron
photino
203Dark Matter and the Power Spectrum
 It is convenient to divide dark matter
candidates into 3 types  1. Hot Dark Matter (HDM)
 Relativistic at freezeout (e.g. neutrinos),
kTgtgtmc2.  2. Warm Dark Matter (WDM)
 Some momentum at freezeout, kTmc2.
 3. Cold Dark Matter (CDM)
 No momentum at freezeout,
 kTltltmc2.

HDM CDM
WDMh2
m
2eV 10GeV
204Dark Matter and the Power Spectrum
 The matter Transfer Functions
 Dark matter affects the matter power spectrum
of density perturbations.  HDM Freestreaming and damping HDM freezesout
 relativistically.
n1
log Dk2
a2
kH1/Ldamp, LdampDamping scale
log k
HDM trapped
HDM escapes
lltltct
lgtgtct
205Lecture 15
206Dark Matter and the Power Spectrum
 HDM Freestreaming and damping
 HDM freezesout relativistically, vc, so can
freestream out of  density perturbations in matterdominated
regime.  So if HDM, expect no structure (galaxies) on
smallscales today!.  This rules out an HDMdominated universe.
log Dk2
a2
log k
207Dark Matter and the Power Spectrum
 Baryons photons Baryon Oscillations and Silk
damping.  tlttrec Baryonphoton plasma
n1
log Dk2
a2
kH1/DH, DHHorizon scale
log k
Photons baryons trapped
Photons baryons trapped in plasma  No collapse
lltltct
lgtgtct
208Dark Matter and the Power Spectrum
 Baryons photons Baryon Oscillations and Silk
damping.  tgttrec Baryon and photons free. Baryons
oscillate.
n1
log Dk2
a2
kH1/DH, DHHorizon scale
log k
Photons freestream carrying baryons (Silk
damping). Baryons oscillate.
Photons baryons trapped
lltltct
lgtgtct
209Dark Matter and the Power Spectrum
 CDM photons The Meszaros Effect.
 Recall at early times rggtgtrm
n1
log Dk2
No growth
a4
kH1/DH, DHHorizon scale
log k
Radiation trapped
Radiation escapes
lltltct
lgtgtct
210Dark Matter and the Power Spectrum
 CDM photons The Meszaros Effect.
 After matterradiation equality, all scales grow
the same.  Produces a break in the matter power spectrum at
comoving  horizon scale at zeq23,900Wmh2.
 Predicts hierarchical sequence of structure
formation (smallest first).
a2
log Dk2
a2
n3
kH1/DH, DHHorizon scale
log k
211Dark Matter and the Power Spectrum
 Transfer Functions
 Can quantify all this with the transfer
function, T(k)
log Tk2
CDM
log k
HDM
Baryonic
212Observations 2dFGRS PowerSpectrum
 No large oscillations or damping.
 Rules out a pure baryonic or pure HDM universe.
 Smooth power expected for CDMdominated
universe.  Detection of baryon oscillations trace baryons.
213Cosmological Parameters from 2dFGRS
Likelihood contours from the shape of the power
spectrum Break scale Matter density
Wmh 0.19 0.02 Baryon oscillations Baryon
fraction 0.18 0.06 (if n 1) So Wm0.27
(h/0.7) 1 WB0.04 (h/0.7) 1
214Observations 2dFGRS PowerSpectrum
 Information about the amplitude of the power
spectrum is confused, as we are looking a
galaxies, not matter.  We usually assume a linear relation between
matter and density perturbations
bbias parameter
galaxies
matter
r
So amplitude of galaxy clustering mixes
primordial power and process of galaxy formation.
215Structure Formation in a CDM Universe
216Cosmological Inflation
 Standard Model of Cosmology explains a lot
(expansion, BBN, CMB, evolution of structure) but
does not explain  Origin of the Expansion
 Why is the Universe expanding
 at t0?
 Flatness Problem
 Why is W1?
217Cosmological Inflation
 Standard Model of Cosmology explains a lot
(expansion, BBN, CMB, evolution of structure) but
does not explain  Horizon Problem
 Why is the CMB so uniform
 over large angles, when the causal
 horizon is 1 degree?
 Structure Problem
 What is the origin of the structure?
218Cosmological Inflation
 Lets tackle the horizon problem first.
 Recall for Rt1/2 we have a particle horizon
 But if Rta, agt1, can causally connect universe
 More generally
 This happens when
 which we get from Vacuum Energy,
219Cosmological Inflation
 In 1980 Alan Guth proposed that the Early
Universe had undergone acceleration, driven by
vacuum energy.  He called this Cosmological Inflation.
 Inflates a small, uniform causal
 patch to the size of observable Universe.
 Explains why Universe ( CMB) looks so uniform.
220Cosmological Inflation
 Expansion Problem
 Vacuum energy leads to acceleration of the Early
Universe  This powers the expansion (recall Eddington).
R
Inflation BigBang
(radiationdominated)
t
 Need Inflation to end to start BB phase.
221Cosmological Inflation
 The Flatness Problem Recall that if we expand a
model  with
curvature, it looks locally flat
 So Inflation predict WWmWv1 to high accuracy.
 Compare with SN galaxy clustering results.
222Cosmological Inflation
 How much Inflation do we need?
 Usually assume Inflation happens at GUT era,
EGUT1015GeV.  So how large is the current horizon at the GUT
era?  But causal horizon at GUT era is just
dGUTctGUT3x1027m.  So need to stretch GUT horizon by factor
aInfl1029 e60
223Lecture 16
Lecture Notes, PowerPoint notes, Tutorial
Problems and Solutions are now available at
http//www.roe.ac.uk/ant/Teaching/Astro20Cosmo/
index.html
224Dynamics of Inflation
 We need a dynamical process to switch off
inflation.  Simplest models are based on scalar fields
(spin0), j, the inflaton (e.g. pmesons, H