07/22/2004
An Introduction to Cosmology
Daniel J. H. Chung (UW – Madison)
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2 Daniel Chung
UNITS 1
c
The most natural units to use: Consequence: mass= energy= GeV
8
1,
M pl
dimensionless.
c
If
length=time=1/GeV Sometimes normal units wil be used in the talk.
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Basic Intro to cosmology and its problems
Inflation
Lecture 1 (Basics)
Baryogenesis/Leptogenesis
Electroweak Baryogenesis
Lecture 2 (Connecting High Energy and Cosmo) Dark Matter
Plan
Outlook and Conclusions
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The Very Basic
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Large scale > 10 kpc (= 30,000 lyr ; galaxy size).
Study of the origin and large scale structure of the universe Largest scale observed (around 10,000 Mpc).
Traditionally: gravitational and thermal history
What is cosmology?
Far away galaxies seem to receding away from us with a velocity proportional to its distance. (universe is not static or stationary -- history) There is a thermal background radiation at 2.7 degrees Kelvin. (thermal history)
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Hubble Expansion (redshift of galaxies, quasar, supernovae, etc. as a function of brightness)
Homogeneous and isotropic T=2.72°K background γ
Light element abundances (absorption/emssion spectra)
Galaxy surveys (distribution of visible matter)
Lensing (distribution of invisible clumped matter)
Temperature fluctuations (primordial, SZ effect, etc.)
Diffuse gamma ray, X-ray, etc.
Observational foundations
Cosmic rays (neutrino, positron, antiproton, ultra-high energy, etc.)
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8 T
g LM
Put in known fields (more later . . .)
R
Boltzmann Equations
C f
p
f x ,p
p p
x
p
d4x
R
1 g 2
gR
16
d4x
1
S
Einstein equations (Equivalence principle)
Theory
Collision term; Approximation
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“on the average” Homogeneity and isotropy 2
2
d
2
r sin
2
2
r d
2
dt
dr 2 a t 1 kr 2
2
ds
2
Homogeneity and Isotropy
characterizes the curvature of space at a fixed time $
'
10
44
(
0.01 H 2
&
%
6 k a2
GeV
2
T 11 a 2 P
Open Problem: Is the naïve averaging of the background density correct?
$
)
e.g. T 00
$
P t g
#
P t u u
#
t
"
T
R
Stress Tensor: Perfect fluid !
3
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9
Background
4
3P
ordinary matter: decelerate perfect fluid energy conservation and adiabatic flow
1 , w 4 a
1 3
7
5
a t
2 3
9
0
7
2
9
a t1
6
8
Radiation dominated
6
.
-
1 , w 3 a
6
Matter dominated
6
2
P d a3
equation of state
/
/
expansion rate
5
w
P
GN 8
8
0-
2
3
a3
1
-
+
P
,
1 6
8
Notation and examples :
*
1
a' ' t combine: a t
alternate: d
k 2 a
3H 2
1
2
,
2 H' t
3
1
-
H
,
H
M pl
a' t a t
3
k a2
2
.
Einstein -
*
Daniel Chung
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10 Daniel Chung
;
<
73 % “dark energy” defined by its negative pressure
<
22 % cold dark matter
<
4.4 % in baryons (protons and neutrons)
<
0.6 % neutrinos
<
T00 contains the following fraction of the total
0.005 % in photons
The universe is spatially flat to about 1 %. d ln a t dt
70 km/s/Mpc.
>
a(t) is expanding
with H
=
;
;
;
Basic picture emerging
Energy density was homogeneous and isotropic to 5 1 part in 10 about 15 billion years ago.
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Explicit Stress-Energy Components 2
3
0.044
O
R P b ,c
0
b
a
0.22
R
t0
5
noninteracting particle O
b ,c
a0
c
P
H O P
0.73
VWU
[email protected]
t0
negative pressure I O R
X
a
0.01
0
C
P
1.0
F
JID
c
P
I
G
Pc
G
Pb
G
P
b
H
P
E
P tot
G
tot
D
BHD
E BFD
D
R
G
G
G
G
O
S
X @
t0
[email protected] C
[email protected]
[email protected] C
3
a0
GeV
c
C
@ C
@ b ,c
46
Q
F O P
A @
P
10
C
a0 a
X
energy conservation A
[email protected] C A @
X
3
D
?
Popular Model 4 t0
10
Z K [ L \ M N ] M
3H0
c
tot
4
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12
f E E d3p p2 3 f E d p 3E
_
` g
1
_ exp
E
1
j
d
T
2
can fall exponentially with temperature
30
k
q
o
o lmk n
2T
4
R
30
g* T T4
Entropy (conservation gives T history) o
g* T
g *S T
r
2
z
4
eV
107
w
v
300 GeV
g *S
3.9
g*
3.36
s
g
10
g* T
s
2.34
t
T
y
today (for massless neutrinos):
SM only:
s
T
x
n
s
Early Universe (T>1 MeV)
2
2 g *s T T 3 45
q
k
p
p
u
^
2
m
Photon Temperature = “temperature of universe” 2
^
2
f E
e 3
2
p
h
c
P
2
i
d
2
E
f
3
g
3
f E d p
3
e
g
g
n
a
Equilibrium Thermodynamics cb
^
Temperature of the Universe
Daniel Chung
photons dominate and can be measured!
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}
~
X Z Y and Z in equilib with photon
maintains same temperature particle number does not change
Chemical equilibrium: X Y
}
H
~
}
}
Kinetic equilibrium: X Y
}
|
Z Y and Z in equilib with photon
maintains same temperature particle number changes particle number is determined by temperature
Boltzmann equations govern approach to equilibrium }
Out of equilibrium: }
{ {
Equilibrium conditions: |
{
Equilibrium?
Kinetic: decoupled Chemical: freeze out
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Theorem: Let T be the temperature of particle after decoupling and T be the temperature of the photon after decoupling. Suppose decouples at temperature T D . 1 3 g *S T
g *S T D
H
T
1
T
Decoupled Species Temperature
[Proof] Separate conservation of entropy: 3
s t0 a t0
3
s tD a tD
Total conservation of entropy: s tot t 0 a 3 t 0
s tot t D a 3 t D
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Suppose a dark matter species X decoupled at temperature of 120 MeV. Compute the dark matter temperature today assuming 3 neutrino species are massless. answer:
1 3 4
1.5 10
T
43 4 11 57
TX
Exercise
eV
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Introduction
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What is the composition of CDM? Why more baryons than antibaryons?
What is the composition of dark energy?
Problems of cosmology
If inflation solves the cosmological initial condition problems, what is the inflaton? Classical singularities of general relativity? Why is the observed cosmological constant small when SM says it should be big? Origin of ultra-high energy cosmic rays?
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Inflation
Baryogenesis
Second focus on selected topics.
First, a general introduction to these problems.
Rest of the Lectures
Dark Matter
Collaborative scorecard between problems of physics beyond the standard model and cosmology.
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What is dark energy? 2 pl
¢
¡
1 3
£
P
0
3M
3P
4
a a
Recall that normal gas of matter has positive pressure. 2
3
x
xN
pN
N
2
pN
2
mN
P x
1 3
Field energy can have negative pressure (like inflation). ¤
V
Why is the energy density nearly coincident with the matter density today?
P
2
¤
1 d 2 dt
If a dynamical field explains the coincidence, how can such a small mass scale (cosmological time scale) be protected?
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Definition: dark matter that is nonrelativistic at the time of matter radiation equality.
Microlensing (gravitational deflection of light from compact objects) agrees with this picture.
BBN (chemistry of producing elements heavier than hydrogen) says no.
Can it be all in cold baryons not emitting light?
CDM neutrinos would overclose the universe.
What is cold dark matter?
Physics beyond the standard model necessary!
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21 Daniel Chung
¥
Why more baryons than antibaryons? The absorption spectra measurements, CMB, and BBN agree n B
10
©
¨
10
Naturalness of small dimensionless number? n
18
¨
10
§
According to SM,
nB
at T > 100 GeV.
¥
¦
¥
¥
¦
n
Probability that the small number is from mere thermal fluctuation is very small.
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ª
What is the inflaton? CMB data looks like that expected from inflation i.e. 1. “no” spatial curvature
ª
2. scale invariant spectra on “superhorizon” scales
Similar in negative pressure characterization as dark energy; no known particle can produce this
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Hawking-Penrose-Geroch theorem: As long as there is nonzero spacetime curvature somewhere and energy is positive, Einstein's theory will develop a singularity. (a classical self-destruction) Evidence for black holes exist. Is there a singularity behind the apparent horizon? Big bang singularity naively exists: i.e. a2 t
1 t2
²±
°
k
¯
a' t a t
®
R
a' ' t 6 a t
®
2
¬
«
«
«
Singularities of GR
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24 Daniel Chung
Due to SM quantum fluctuations M4
¹
Planck scale 1018 GeV
¹
M
GUT scale 1016 GeV
¹
Possible values of
See-saw scale 1013 GeV
On the other hand we observe 10
12
¸
¶
·
µ
³
³
¶
·
µ´
³
A small cosmological constant?
GeV
4
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25 Daniel Chung
There is a GZK cutoff
at 10
19.8
eV due to efficient
º
»
p
½¼
º
Ultra-high energy cosmic rays
p
Proton cannot ravel more
than 40 Mpc. º
Events above 10
º
No energetic extragalactic sources within 40 Mpc.
º
19.8
eV measured (possibly).
Primary? Source & acceleration mechanism?
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26 Daniel Chung
Inflation Motivation: Mostly initial condition problems. 1. Flatness Problem
at nucleosynthesis
H e2 a e2
time dependent
2
10
4
10
6 2
10
18
Ã
ar
10
¾
H 20 a 20 a 0
2
Ã
ae
Ã
ar
k
2
Ã
1 10
Ã
k
0
1
Â
¾ ÁÀ¿ À¿
H a k H 20 a 20
2
Â
early universe:
2
¾
today:
k
¾
Friedmann:
Why small?
Initial spatial curvature had to be finely tuned for universe to be this old and flat. Why?
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27 Daniel Chung
More Motivation 2. Horizon/causality problem: Why homogeneous and isotropic on “acausal scales?
“singularity” “outside horizon”
real singularity naïve horizon (with 1
Ë
ÊÉÈ
Ä
t 2
): “inside horizon”
Æ
1 H
3 1 w
Ç
0
dt ' a t'
1 3
Ì
t
Å a t
Ä
dH
w
causal signals travel beyond naïve horizon
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28 Daniel Chung
Unwanted Relics 3. Unobserved relic problem e.g. Suppose the SM is embedded in a larger theory with gauge group G 1
Ñ
Ð
Ò
Ò
unacceptably large!
Ò
3
15
Ó
10
Ò
Ò
10 11
Ò
Ô Í M
T c3
3
M pl
Ð
Ò
I
10 14 19 10
nM s 10 16 GeV
2
Y
H 3 T c6 M 3pl
nM
mM
Gi G j
Ð
Monopoles arise whenever
U 1
L
Ï
c
Î
SU 2
Î
SU 3
Í
...
Í
G2
Í
G1
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29 Daniel Chung
dt 2 a 2 t dx i dx j
Ù
Ö
Ú
Ø
Ø
×
dx dx
ij
Õ
Inflationary solution: Blow up a small flat patch into the entire universe Flat patch becomes the entire universe (solves flatness)
Õ
Lengthen the time it takes to reach the singularity (horizon) 0
0
d 2a 2 dt
0
Þ
xa 1 H
ß
d dt
Þ
a t
Û
dH
dt ' a t'
Ý
t
Ü
Õ
× Ö
ds 2 g
Inflation
causal signals travel beyond naïve horizon
comoving coordinate separation
ê
è
ä
hor
2
10
5
í
k
ê
k
ì
æ
à
ã
2
3
3 2
ë
k
ç
å
éèÚ
âáà
Ú
Dilutes unwanted relics
Prediction: scale invariant density perturbations power: 1 d3k e ik x á
Õ
Õ
î
x
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30 Daniel Chung
Qualitative description of inflaton V
õ ö ÷ ò
ó
1 g 2
ôõ
1 R 2
ô ö ÷
ò
g
ò
d4x
ñ
ð
Action: S
÷
single field inflationary models:
How to choose the potential and initial conditions? eN
ï
Spatial inhomogeneities of must be sufficiently small to be consistent with cosmology (too big = too many black holes, too small = not enough structure). After inflation ends, the universe must reheat to T 10 MeV . After inflation ends, unwanted relics must not be created (e.g. low enough temperature).
ú
÷
ï
Inflation must end.
ï
a ti
efold
ï
for about 60 e-folds.
a tf
ù
0
ø
ï
2
d a 2 dt
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31 Daniel Chung
Horizon problem 4
ÿ
ü
V
H
þ
a e
dt H
d dt
H
slow roll inflation
2
da a dt
V
(just like dark energy)
þ
1 3
2
dt
2
1 d 2 dt
d dt
d2
P
ý
0 P
V
60 efolds desired:
û
3P
2
ý
1 d 2 dt
3M
2 pl
ü
ý
2
d a a 2 dt
þ
û
Magic of negative pressure
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32 Daniel Chung
Quantitative Single Field
2
60
ti
d
0.2
5
$
#
10
"
2
tf
at the minimum of
6
60
24
ti
2
!
indicates source of fine tuning
0 V
60
V 3
1
min
Density perturbation amplitude: P k scale invariance nearly automatic!
H
with V
2
V'
N
1
V'' V
d dt
tf
1
End of inflation: the potential
1 V' 2 V
dH dt H2
Negative Pressure and 60 e-folding 2
3H
Slow Roll approximation
60
never Planckian
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33 Daniel Chung
,
m
2
2
4
2
Li
0 -,
0
/.
Li
1 2
/
L
4
Inflaton field decays: e.g. 3/
%
Standard Reheating
)
1
2
m2 m
tot )
2 tot
*
2
2
2
2
2
30
4
T RH
0.2
200 g*
@
?
R
g* T T
>
5
reheating temperature as a function of time
2
1 4
2
;
<
tot
m
estimate:
)
R
4
:
m
9
2
8
' '
t
4H
2
6 5
R
m
2
'
4
5
2
(
'
& 5
(
&
t
t
=
0
&
1 2
t
* ' +
'(
tot
2
(
)
(
*
'( 6 5 7
use following approx:
m
&
3H
&
2 t
tot
M
pl
07/22/2004
34
a dec
H0
3 2
a
2
2 H0
G
da a0 a
D
C
a0
a0
F
a dec
da H a2
E
a0
a0
D
dx
B
B
a0
a0 X
3
a0
T0
F
a0 1 ln 2
g * S t RH
T0
g *S t 0
T RH
R0
60
ln
T0
M
H
T RH
a RH
T RH
T RH 15
10 GeV
R
ln
ae
O
a0
max
1 3
N
ae
need enough efolds
a0 M
L
N
aI
a0 X
Q
HI
T 2RH
e
1 HI
P
ae a0
X aI
L
O
a0
aI ae
D
aI
J
(also for curvature)
H
1 HI
I
inflation can take place only if homogeneous (small patch of comoving coordinate size > X became the observable universe): sufficiently small
K
A
L
C
Largest scale that we see homogeneous and isotropic: C
A
Why 60 efolds?
Daniel Chung
N
07/22/2004
35 Daniel Chung
Single Scalar Field Computation
i
g
2
i
f
B
ij
r
2
d
2
dx
ts
a
s
0
2
B g
g f
i
f
a
2
2
g
d c
b
g
a
b
a
B
g
0
x h
0
e
[ ^
_
[
\ [ ]
`
perturb :
r
q
dx dx g
N
Z
V
q
U
Z
Y Z X
V
1 g 2
Y WX
1 R 2
g
W
U
d x
U
4
T S
Action: S
i
j
E
o
p
n
'
m
lk
a' a a 0'
a ' a' a y
x
2
x
~
2
y
v
}
|
1 v'2 2
'
a' a f
d3x
a
0
v2
y
f
v u w
constant on constant
x
a' a v a 0'
d
z
S
c
{
v
j
l
gauge degree of freedom: Freedom of slicing the spacetime (splitting perturbed versus unperturbed) infinitesimally gauge invariant (same as longitudinal gauge)
hypersurface (comoving)
Seed formation of galaxies!
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36 Daniel Chung
ei k
x
k'
2
» ° ¼
º
¸
e
2
ik
£
¢
®
°
¬
2
¹ ¸
24
10
V ¶·
3 2 À
k
«
Á
0
k aH
Pk
´ ³ µ
² ¿
«
k
À
1
2
2
i
4p
¯
e
9
±
1 2 2
k
i
ª
¬
«
2
H
1
«
ª
vk
H
2
3 3
¾
p
a' a a 0'
2k
©
boundary condition: v k
0
¨§
vk
¥ ¤ ¦
¨
p
2
2
3
¡
k
vk' '
,y
,x
dk sin k x y P k k x y
k 2
a' a v P a 0'
¥
k
*
vk
3
dagger k
½
dagger
ak , ak '
2
a
ak v k
,x
v
quantize:
3
d k 3 2
Power Spectrum
60
5
vk
2
07/22/2004
37 Daniel Chung
a
Ä
0
a
'
Æ Ç Å
0
'
a' a Ã
vk' '
2
vk
È
a' a a 0' Ã
0
Ä
Ê
É
k aH
Â
On large scales:
Ä
Quantum to “Classical” Transition 0
Ã
¿
growing mode: v k A k a ' a Ï Ñ
Í
*
vk
Î
Õ
Ì
Ì
k
are classical random variables!
d ln k
1
Û
2
ß
2
ß
Ú
24
Þ
16
6
Shape of the potential is given by n S k Ü
d ns
2
ns
Þ
ns
k
ÝÜ
Spectral index: P
Ø
k
Ñ Ù
0
Û
aH
dagger k
0
×
Ò
lim k
Ô
,
Ó
k
k dagger l
Ï
Ï
k
a
are constants Constants on superhorizon scales!
Ð
Ã
a' a
ak v k
Ö
k
'
Ë
0
Ä
a
V'V''' V2
Running of spectral index measurement = measuring potential
07/22/2004
38 Daniel Chung
2 k
k
nT
1
é
h
è
2
ç
k3 h+k 2 8
nT
ò
1
ñ
In multifield inflation (more realistic): r
î
ã
2
í
ì
ê
ê
2 P
ï
ë
2
î
1
2
ã
nT
î
PT
H 2
r
r
ð
å
ä
PT k
0 0 0 h ij æ
ã
T â
g
á
Tensor perturbations:
à
Gravity waves
PT PR
Consistency relation gives evidence for single field inflation.
07/22/2004
39 Daniel Chung
What is this good for? fixes the boundary condition to the Boltzmann equation
0
F
ö
ô
2
b
4
ý
þ
2
ô
2
l
1
'
õ ÷ ö
l
õ
ö
2
ý
1
3 k dk k 2l
...
ClPl
0
õ
2l 1 Cl 4
x, '
ú
ú ÷
ô
x,
÷
0,
jl k
üû÷
÷
õ
ù
ô ø õ
1
ô
2l
0
ô
ti
“acoustic oscillations”
÷
l
Pl k
l
õ
2
k cs 3
R
x
õ
õ
1 R 1 1 31 R
0
ÿ
õ
ó
ö
t
ei k
ô
c 2s
0
R
ô
t
ô
2 t
0
l
ó
ó
ô
T T
ti
07/22/2004
40 Daniel Chung
Transferring power from isocurvature to curvature perturbations.
“Recent” Developments Can be used to generate density perturbations during reheating (Gruzinov and Zaldarriaga 2003) Helps to relax constraints on inflationary models, but loss of predictivity.
Stringy models of inflation: no inherently stringy insights. Uncertainties in the boundary condition determining the inflationary vacuum. quantum gravity giving rise to nonstandard vacuum. Unlikely, arbitrary, and lacks compelling motivation thus far.
07/22/2004
Polarization:
B polarization comes from tensor and lensing (contaminant as far as inflation is concerned). B polarization has no contribution from scalar perturbations. measuring tensor is important for checking consistency condition (to know if it really is inflation!) Unfortunately, typically less than 1% of the scalar spectrum
Theoretical Problems
Daniel Chung
Running of the spectral index will be better known with future experiments such as Planck.
Future Prospects
41
What is the inflaton? Are there truly natural models? Stability of de Sitter space and back reaction. More observables to experimentally ascertain inflation.
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42 Daniel Chung
Baryogenesis
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43 Daniel Chung
In solar system much more baryons than antibaryons
3 10
He
8
n
4
He
?
2
.
Other constraints: distortion of CBR, diffuse
[e.g. Cohen and de Rujula 1997]
+
void
-ray.
!
0
from
pp
bound on
4
Dominance of matter clear on scales < 10 Mpc:
n
p
4
3 10
np np
3p
explained by pp
Observation
-
07/22/2004
44 Daniel Chung
SM contains nonperturbative baryon number violating operators that erase B+L T
Tc
100 GeV
$
These become efficient when
#
"
"
Is there a problem?
"
Otherwise, an aesthetic initial condition problem
"
erases preexisting B+L
Starting from
& %
10
*
10
'
n
6
)
+
nB
initial conditions why
0
,
nb
(
nb
&
nB
18
/
.
-
naively,
10
naive
and not separated.
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45 Daniel Chung
Suppose “X” carrying 0 baryon number can decay only into “a” carrying baryon number b a and “b” carrying baryon number b b . r
X
X
4 5
9
r ba 1 r bb r ba 1 r b b B BX BX
rephasing invariant
:
B violation CP violation
<
>
<
bb
r
=
=
;
=
=
;
;
ba
r
Out of equilibrium: otherwise, the other direction produces bb r
=
=
ba
r
b
X
<=
; 0
X
1
BX BX
r
6
5
5
7
Baryon produced:
8
0
X
1
7
“CP”:
4
1 r
b
6
5
X
X
a
5
“CP”:
6
5
a
4
X
2
r
3
2
Branching ratios:
1
0
0
Illustration of Sakharov Criteria
07/22/2004
46 Daniel Chung
Boltzmann G
g 2
M
n t
N
3
d p C f E
L
@
I
A
K
d pf
C f
@
@
D I
f x ,p
X
R
3
d3 p f
2
b
pb
c
X
Q
Q
pc
T
pa
a
W
fbfc 1 fX 1 fa W
2 b
pX
J
S
O
M
4
U
U
a
c
4
V
Q
W
W
f fa 1 fb 1 fc c X
2
U
d b
R
R
R
d a
d3 pX
gX O
X
d X
R
P 2 X
d
KQ
P
EX
3
C f
U
O
3
2E X
Simplification fb
eq
fb ,
fc
eq
fc
eq eq Kinetic equilibrium of all states: e.g. f X F t f X , f a A t f a
K
K
K
Chemical equilibrium of others:
K
?
e.g.
?
?
p
3
d pX M
d
3
V
H
3H
J
I
3
gX 2
F
A
@
x
d pf
t
p p
B F DEC @
@
p
A
A
?
Phase space evolution (useful B-genesis, dark matter, CMB):
07/22/2004
47 Daniel Chung
CP violation involves a complex parameter in the Lagrangian: _^ 2
1
* 1
* 2
[
i
e
h
ei
_
a
\
`_^ _ 2
1
q
CP violation = interference of transition amplitudes 2
i
2
phys
M 1M 2e
i
s
M2
M 1 M 2e
u
t
2
w
2
2
r
r
M1
M2
b
2
2
b
phys
M1 v
i
s
M 2e
2
u
M1
phys
j
i
s
M 2e
b
2
v
M CP
M1
r
2
j
M
: s
j mlk
i
opl n
In this Lagrangian, there is only one physical phase (phase that cannot be removed by field redefinition). phys
Y
m LR
2
[
a
2
a
a
1
\
i
e
i
[
a
e
[
a
i
\
i
g edc f f
M3 e
2
m e
h
] 1
b
b Y
2
[
2
\
2
[
m
dec f f
L
Z
Y
Interference
phys
07/22/2004
48 Daniel Chung
x
Cutting
Recall in the simple example
B violation CP violation
r
M 1 M 2e
i
phys
|
~
i
r
~
v
M 1 M 2e
bb
{
ba
{
BX
y
}
CP 2
z
y
M
j
2
|
M
BX
v
y
B
phys
x
This is 0 unless the non-CP violating part develops an imaginary part due to virtual states going on shell.
Diagrammatically +
interferes
Since the real part of this should be taken:
07/22/2004
49 Daniel Chung
Generate L as we have been discussing. Convert L into B through the B+L violating sphaleron.
22 N f
4N H
13 N H
B
L
8Nf
B
j
Have only perturbatively significant B-L violating operators.
Thermal Leptogenesis
Theoretical attractiveness: L-violating operators natural in seesaw neutrino masses “uncomfortable” aspect: in gravity mediated SUSY breaking models, gravitino bound strongly constrains it.
07/22/2004
50
...
...
a
j
...
i
eq
j
K1 z
n eq
m
ma
4
64
2
ds
m
s
(same equation is applicable to dark matter.)
ma
2
s
2
ma
m
s
2 s v
v n eq s
T
...
j
i
a
eq
K2 z
scatter
decay
T
v
z
j
...
i
eq j
Y Y ...
m
Y Y ... Y i Y j ... eq eq i
a
eq a
eq
a , i , j , ...
j
eq
Y Y a ...
1 H
z dY Y eq dz
s
ni
Boltzmann Eq.
Yi
Daniel Chung
s
s K1
s T
07/22/2004
51 Daniel Chung
Leptogenesis Estimate
1) Assume temperature of the universe is high enough
right-handed neutrinos are in equilibrium (fixes initial cond.)
Typically, CP conserving reactions control this.
v n
R
T
2
2) Temperature falls:
T M pl
right handed neutrinos go out of equilibrium
M e Tc
M T
c
0.1
g * 100,
mW
100 GeV
10 9 GeV ,
M
¡
10 1 eV ,
m
c
¤
10
¡
10
M T
£
g*v
2
M e Tc
m M
¢
CP
3) When the right handed neutrino abundance falls below L density, the lepton number freezes out.
(out of equilibrium temperature)
07/22/2004
¦
Edward Kolb and Michael Turner, THE EARLY UNIVERSE.
¦
Scott Dodelson, MODERN COSMOLOGY
¦
Mukhanov, Feldman, Brandenberger, Phys. Rept. 215 (1992).
¦
Lidsey, Liddle, Kolb, Copeland Barreiro, and Abney Rev. Mod. Phys 69, 373 (1997).
¦
Lyth and Riotto, hep-ph/9807278.
¦
Inflationary references
Hu and Sugiyama, astro-ph/9411008.
General Baryogenesis Kolb and Wolfram, Nucl. Phys. B 172, 224 (1980).
Cosmology related to supersymmetry ¦
¥
Daniel Chung
General Cosmology
¦
¥
¥
¥
End of Lecture 1
52
Chung, Everett, Kane, King, Lykken, and Wang hep-ph/0312378.
07/22/2004
Wagner, Westphal Weinstock, Worah, Yaffe...
¥
hep-ph/0312378
¥
hep-ph/0208043
¥
de Carlos, Dine, Dolan, Elmfors, Enqvist, Espinosa, Farrar, Gavela, Giudice, Good, Grasso, Hernandez, Huet, Jakiw, Jansen, Joyce, Kane, Kainulainen, Kajantie, Kaplan, Keung, Khlebnikov, Klinkhamer, Kolb, Kuzmin, Laine, Linde, Losada, Moore, Moreno, Multamaki, Murayama, Nelson, Olive, Orloff, Oaknin, Pietroni, Quimbay, Quiros, Pene, Pierce, Prokopec, Rajagopal, Ringwald, Riotto, Rubakov, Rummukainen, Sather, Schmidt, Seco, Servant, Shaposhnikov, Singleton, Thomas, Tkachev, Trodden, Tsypin, Turok, Vilja, Vischer,
hep-ph/0006119
¥
Carena, Chang, Cline, Cohen, Davoudiasl,
hep-ph/9901362
¥
Ambjorn, Arnold, Bodeker, Brhlik,
Daniel Chung
“Randomly” selected “overview” references
hep-ph/9901312
¥
Incomplete list of ewbgenesis people:
§
§
People and References for EW baryogenesis
53
hep-ph/9802240
07/22/2004
54 Daniel Chung
In minimal SM, EW phase transition is inevitable!
¨
Tc
mh
«
T
ª
¨
EW Motivation EW symmetry restoration
An exciting era: probing at LHC and its microphysics Tc
associated with SM measurable
©
Almost no cosmological probe to this era Explaining the baryon asymmetry of the universe
©
¨
Nearly everything at
Establishing thermal equilibrium for WIMPs close
07/22/2004
Neutrino mass suggests such scenario if see saw invoked (lepton num violation & dim 5 operator suppression scale) May depend on near-future-lab-immeasurable phase:
m
diag R R
T
m
®
U MNS
®
®
¯
Computationally simpler: spatially homogeneous
m
dagger
diag U MNS
Squeezed by gravitino bound
EW Baryogenesis is physics at 100 GeV Almost everything about it can be lab probed in principle
¬
Daniel Chung
Leptogenesis
¬
Why worry about electroweak baryogenesis scenario instead of leptogenesis?
55
In SM and MSSM, EW phase transition occurred!
07/22/2004
56
Aspects of MSSM
Daniel Chung
soft susy breaking (definition: does not introduce quadratic divergence) ²
²
1 M 3 g g M 2w w M 1B B 2 c b H d H u H u Q i A u ij U j
±
j
ij
·
2
mH H u
d
·
j
m U2 U ij
c j
ij
D ci * m 2D D cj
E
·
c* i
U
ij
c j
h.c.
²
HdLiAe E
·
*
´ ij
·
2
mH H d
L i m 2L L
·´
´
*
·
´
Q i m Q2 Q
c j
²
²
°
°
´
¶
HdQ iAdD
¶
´ ²³ µ
´
¶
°
L soft
c* i
m 2E E
Li
EL
ij
c j
2
u
supersymmetric Yukawa and mass term
E cL
i
H
i
Hu
H
i
H
u
d
D cL
Hd
i
H
¼
´
¶
H dH
D cL
i
Li
±
Di
c j
°
¶
²
c
UL
¸
c Li
U
´
¶
¸
u
H d L i Y eij E
±
c Li
Ui
¸
E
Li
QL
´
´ °
Q
H d Q i Y dij D cj
²
c j
¶
H u Q i Y uij U
¶
´ ±³
Ei
¸
Qi
¸
W
u
E
i
d
» -
X
M2
2 M W sin
¾
W ++Hu
2 M W sin
¼
+-
¾
+
º
T
X 0
º
0 X
º
-
º
+
º
¹
¸
Lc
1 2
½
Chargino mass matrix
07/22/2004
57
Sakharov conditions
Daniel Chung
recall: 1) B-violation, 2) CP violation, 3) out of equilibrium 1) Baryon number violation: SU(2) sphaleron qL qL qL lL
k
Ä
Å
Ã
unbroken phase:
uL
EW
i
d Ld L
Â
4 W
T
W
e
k
4
W
O 1
4
4
Î
Ì W
Í
8 ×
×
E sph
2 mW
ÕÔÏ
Í
4
exp
g
H
Ò
ÓÒ
1
Ï
7
10
Ð
W
Ï
2.8 10 5 T 4 Ë
ÊÉÈ
broken phase:
Ì
Ñ
10
Ñ
e.g. 1 generation
i
E sph T
T
Ö
i
Ç
i
Æ
i
2
Á
1
Å
C h L h L w 4L
À L
¿
OB
07/22/2004
58
Sakharov conditions
Daniel Chung
recall: 1) B-violation, 2) CP violation, 3) out of equilibrium 2) CP violation: In SM: 12
ã â
*
*
V cs V us V ud V cd
10
4
M2 Û
h dagger hL R
h.c.
Ü
1 M 2 W dagger WL R 2
Ù
Ú
L
Ü
Ù
Ø
Too small. In MSSM, soft SUSY breaking phases: e.g.
2
2
2
ms ms
2
md j
10
22
á
2
md m b
à
2
ß
ß
2
mu m b
ß
2
ß
2
mc mc
ß
2
á
j
2 mW
2
mu mt ä
CP
2
mt
ß
Þ
Ý
gW
07/22/2004
59
Out of equilibrium
Daniel Chung
å
T>100 GeV, symmetry is restored.
å
3) Phase transition: T<100 GeV, symmetry broken. H
2
ETH
3
T
Tc
4
ë
ë
T
4
H
í
2 0
ç
T
ç
D T
æ
V H
2
è
é
H
Tc
ì
T
î
V H
z
w
H
0
z
H
ê
ê
H
(Attractive, because almost no new assumption!)
07/22/2004
60 Daniel Chung
EW B creation step 1 1. Pick up CP/chiral asymmetry q
0
ñ
n bR
0
e.g. 1 generation B
0
ê
uLuR
w
ê
n Lb
ð
ê
ò
n bR
ð
ð
n Lb
L
nb
ð
L
nb nb
ê
0
ï
sphalerons inactive
nb
H
z
ê
H
sphalerons active
07/22/2004
61 Daniel Chung
EW B creation step 2 q 0
ê
H
z
ê
H
L
R
nb
õ
nb
õ
õ
ö
e
R
nb
ù
uLd L
e
1 0
ê
B B
ê
ù
uL
uR d Ld L
nb
ø
e.g. 1 generation u R
L
nb
n Lb
ø
nb
ê
sphalerons inactive
n Lb
0
÷
w
õ
ô
ó
sphalerons active
07/22/2004
62 Daniel Chung
EW B creation step 3 sphalerons active H
z
ú
ê
H
w
sphalerons inactive 0
ý
R
nb
û
L
nb
û
R
nb
ü
L
nb
ê
nb
û
nb
0
ê
q
07/22/2004
63 Daniel Chung
Diffusion equations for (s)quarks and higgs(inos): relatively fast process
þ
Make assumptions about certain processes (Yukawa and strong sphaleron) being in equilibrium due to large interaction rate. Solve for SU(2) charged left handed fermions
þ
þ
þ
Computational Steps
Integrate sphaleron transition sourced by above.
07/22/2004
64 Daniel Chung
z
Y
kQ
kT
kH
scattering
h
kH
nH
SH
source
1
nh
nH
nT
nh
nQ
Dh
2 z
nH
vw
One of massaged diffusion equations
ÿ
Schematically
ÿ
H
Source term = CP violating, Higgs field gradient
f3
EW
vw
exp f 1 z
dz n L z exp c 2 z
vw
0
EW
SQ
0
dx S H x exp
nL z
c1
nB
ÿ
SH
flow of current w/ background force
f 2x
07/22/2004
65 Daniel Chung
300 GeV
z
M2
F2 z
m1
v1 F1 z
z
z
m2
z
mA
v2 v2
v1
2
2 z
M
2 2
Dh
SH
M2
Source uncertainty (off diagonal term)
Uncertainties
Partially addressed by Carena et al in hep-ph/0208043
Some contend the problem persists hep-ph/0312110
Damping rates in the diffusion equations Overall uncertainties in final baryon asymmetry
07/22/2004
66 Daniel Chung
Consider mass matrix
M
m2
m1
"
m1
!
2
z #
4
#
2
4
z
2
m2
2
2
z
z
z
F2 z
m1
#
v1 F1 z
v2 v2
v1
"
2 z
&
"
!
2 2
&
Dh
#
%
SH
M2
m2
0
0
m1
z
1
m2
z
z
z
m1
M z
$
Resonance
z
m2
07/22/2004
67 Daniel Chung
+ *
+
M
L
h.c.
Dispute unsettled
4
1 exp i 2fd
dz f d
(
f d2 U f 2 V dagger
V
+
0 +
10/
f2
(
0
3 +
(
2
fd
+
,
2 z
2 z
.
CKJPSW uses WKB-like approximation
2 '
dagger R
*
z
)
x
-
'
L int
,
CQSW has “interaction” term; never diagonal (
'
Source of source discrepancy
07/22/2004
68 Daniel Chung
mh
At
7
7
0.2 m Q
0.4 m Q
6
115 GeV
strong enough phase transition charge and color breaking minima if m h 114 GeV (suggestive)
tan
4
mQ
1 TeV mQ
, M 1,2 2 T c
=
;
5
=
9
>
?
M 1,2 T c2
6
;
, M 1,2
5
=
5
6
9
5
6
9 8 :
5
9
6
;
5
5
tR
mt
6
;
m
<
120 GeV
;
5
sketch of parameter region
0.05
sufficient diffusion sufficient CP violation sufficient density processed by the sphaleron
07/22/2004
69 Daniel Chung
mh
At
7
7
0.2 m Q
0.4 m Q
6
115 GeV
strong enough phase transition charge and color breaking minima if m h 114 GeV (suggestive)
tan
4
mQ
1 TeV mQ
, M 1,2 2 T c
=
;
5
=
9
>
?
M 1,2 T c2
6
;
, M 1,2
5
=
5
6
9
5
6
9 8 :
5
9
6
;
5
5
tR
mt
6
;
m
<
120 GeV
;
5
sketch of parameter region
0.05
sufficient diffusion sufficient CP violation sufficient density processed by the sphaleron
07/22/2004
70 Daniel Chung
mh
At
7
7
0.2 m Q
0.4 m Q
6
115 GeV
strong enough phase transition charge and color breaking minima if m h 114 GeV (suggestive)
tan
4
mQ
1 TeV mQ
, M 1,2 2 T c
=
;
5
=
9
>
?
M 1,2 T c2
6
;
, M 1,2
5
=
5
6
9
5
6
9 8 :
5
9
6
;
5
5
tR
mt
6
;
m
<
120 GeV
;
5
sketch of parameter region
0.05
sufficient diffusion sufficient CP violation sufficient density processed by the sphaleron
07/22/2004
71 Daniel Chung
mh
At
7
7
0.2 m Q
0.4 m Q
6
115 GeV
strong enough phase transition charge and color breaking minima if m h 114 GeV (suggestive)
tan
4
mQ
1 TeV mQ
, M 1,2 2 T c
A
B
5
=
@
>
?
M 1,2 T c2
6
;
, M 1,2
5
=
5
6
9
5
6
9 8 :
5
@
6
B
5
5
tR
mt
6
;
m
<
120 GeV
;
5
sketch of parameter region
0.05
sufficient diffusion sufficient CP violation sufficient density processed by the sphaleron
07/22/2004
72 Daniel Chung
G
D
m 1
tan
2
m 2H
0.4 m Q
mH
v2
D
mt
[
115 GeV
R
T S N
2
mQ W
mt At
m t2 1
2
3 2 U
tan
m Q2
J
K
X
0.15 M 2Z cos 2
[
K
m U2
[
W
m t2
At X
At
2 t
Z
V
0.15 M cos 2
P
T
2 z
Y
tR
P
Q P
m
2 U
m U2 , m t2
J
2
O
N
T
Tc
1.3
N
F K
F
4
E
E Tc
4
R
JI
H
ET
In the MSSM , m Q2 M
C L
V
V
3
F
To protect the baryon number D
C
Strong enough phase transition
07/22/2004
73
a
L
m1 z
0
0
m2 z
M dagger
R
`
`
a
b
dagger L
a
derivative
M
^
dagger
Daniel Chung
U z M
z V dagger z S LR w , y
SQ
_
]
r 2
M 1,2 ,
b
b
if
r ,z 2
n
Sh
S RR z
m
1 TeV
0 Tr
l
1 lim r 2
j
2 z
k
MQ
i
Dh l
Sh
^
mass suppressed ... MQ
h
z
g
d 4 w S RR x , w w
g
d
S RR x , y
f
The CP violating current is proportional to the CP violating propagator correction. e
\
UMV
c
dagger R
a
z
`
x
_
L
^
Interaction Lagrangian ]
\
Source Term
h.c.
07/22/2004
74 Daniel Chung
Estimate 4 w
CP
e.g.
gs
6
Mw
CP
y
x
10
10
w
v
u
2
4 w
10
10
~
0.1
10
}
}
vW
2
Tc
OB
{
Large top Yukawa coupling
z
p
Importance p
o
|
gs f
f CP
r
t
s
w
qr
k
s
o
Sufficient CP violation
L
h L h L w 4L 1
2
Higgs mediated CP asymmetry
Chargino, Higgs(ino), neutralinos, (s)quark
i
qL qL qL l L i
i
i
i
07/22/2004
75 Daniel Chung
26
10
e cm
[Regan et al 2002] [Lamoreaux et al 2002]
e cm
2.33
10
27
28
e cm
[Romalis et al 2001]
Theoretical constraints complicated & uncertain Arg M 2
e.g. without cancellations,
d Hg
12
10
dn
1.6
de
experimental EDM bounds
EDM
0.05 [Chang et al 2002; Pilaftsis 2002]
07/22/2004
76 Daniel Chung
3 2
Tc
100 GeV
, M 1,2 2 T c
Critical temperature
m T
T
1 exp E
T exp
1
T
sinh
mT 2g 2
1
1 exp E
otherwise
T2 6
g
2
2
m2
2 dE E E m
g
nP
nP
For there to be sufficiently large current
Sufficient density
07/22/2004
77 Daniel Chung
Next generation of colliders can rule out the MSSM electroweak baryogenesis scenario very squeezed parameter space viable ruled out if large Higgs mass or right handed stops more stringent EDM constraints M2
¡
There is a dispute of the strength of the source term when M 2
EW bgenesis Prospects
07/22/2004
78 Daniel Chung
Recent collaborative progress
07/22/2004
79 Daniel Chung
cosmological time
Integrating out degrees of freedom in field theory is most of the time not invertible. Entropy producing events time reversal.
¥
£ ¢ ¢
¤
renormalization group flow flow. £
¢
Cosmology and High Energy Physics
evolution noninvariant under
What are some recent collaborative efforts between high energy physics and cosmology? Any prospects for further success?
07/22/2004
80 Daniel Chung
¦
¦
¦
¦
¦
Problems of the Standard Model (SM) Why is the Higgs field light? What is the origin of electroweak symmetry breaking? Is it simply an accident that the gauge couplings seem to meet? How is gravity incorporated into the SM? Why is the CP violation from QCD small?
07/22/2004
81 Daniel Chung
mH
200 GeV
§
¬
§
Unnatural if
2
m
2 H
Planck scale 1018 GeV GUT scale 1016 GeV See-saw scale 1013 GeV
What generates low
¬
2 ®
¬ «
0 2
mH
ª
m 2H
©
®
®
H
H
Possible values of
¬
Quantum fluctuations §
§
114 GeV
¨
Precision electroweak data & LEP direct search ¨
§
Lightness of Higgs
?
07/22/2004
82 Daniel Chung
The value of the Higgs field H 100 GeV permeating the universe is much smaller than what we might expect from short distance scales. As before, the possible values are
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¯
¯
¯
¦
°
¦
Origin of the electroweak scale
Planck scale 1018 GeV GUT scale 1016 GeV See-saw scale 1013 GeV
Protection from radiative corrections does not mean that the EW scale can be naturally small.
07/22/2004
83 Daniel Chung
¦
¦
Unification of coupling Because of “backreaction” (renormalization) coupling constants depend on energy scale (or length scale). Is this an accident?
07/22/2004
84 Daniel Chung
S SM
d4x
³
Gravity appears in SM.
²
All fields are quantized according to the SM. ©
±
±
Incorporating quantum gravity g L SM
±
undetermined!
Gravity becomes non-predictive!
µ
... c 31 R 3 ... µ
g c 21 R 2 c 22 R a b R ab µ
d4x
³
©
´
S GR
µ
Quantize gravity as well. ²
±
gravity!
07/22/2004
85 Daniel Chung
F
¾
Tr F
½
½ »¼ º
·
g
»¼
¹
4
d x
©
L CP
¾
The strong interactions (responsible for holding the nucleus together) contains ¸
¶
Strong CP problem
gE B À
d4x
¹
¸
¿
¿
which is the analog of the CP violating term
Absence of electric dipole moment of the neutron 9 10 requires .
¶
Á · Â
Ã
¶
in Maxwell theory.
The problem: to explain this small number.
07/22/2004
86 Daniel Chung
Why is the Higgs field light?
What is the dark energy? What is the CDM?
Ä
Ä
Ä
Å
Collaborative score card What is the origin of electroweak symmetry Ä
Why more baryons than antibaryons?
Is it simply an accident that the gauge
Å
Ä
breaking?
How is gravity incorporated into the SM? Why is the CP violation from QCD small? Å
Ä
Å
Å
Å
couplings seem to meet?
with SUSY with PQ
If inflation solves the cosmological initial condition problems, what is the inflaton? Classical singularities of general relativity? Why is the observed cosmological constant small when SM says it should be big? Origin of ultra-high energy cosmic rays?
Many other speculative connections exist. Not very convincing yet, unfortunately. Restricting to particle physics.
07/22/2004
87 Daniel Chung
(N=1 SUSY) a symmetry exchanging bosons and fermions f
b
SM
electron spin 1 2
new particle
selectron spin 0 É
Higgsino spin 1 2 Ê
É
gravitino spin 3 2
Ç
Key feature: “Solves” Ç
Æ
graviton spin 2
Ê
Higgs spin 0
Ê
É
examples:
È
Æ
Supersymmetry (SUSY)
Why is the Higgs field light? (partially) Is gauge coupling unification an accident?
07/22/2004
88 Daniel Chung
Ë
Lightness of Higgs In SM, the trouble was H
With SUSY
Ì
Ï Î
0 2
mH
Í
m 2H
2
H
Ò
H
Ï Î
m 2H
ÑÌ
Ð
Ò
Ë
H
2
Cancellation of the quantum back reaction! The Higgs mass is stabilized!
07/22/2004
89 Daniel Chung
Ó
Unification of coupling “Accident” is more and more looking not like an accident!
07/22/2004
90 Daniel Chung
General theme in physics: Every new solution has a new set of problems. Recall in SM, proton is very stable due to accidental symm.
Ô
0
e+
To ensure such operators do not appear: conserve R-parity (a new quantum number natural in SUSY). Conservation of R-charge forbids an R-charged particle to decay to a non-R-charged final states. Õ
Ô
p
Ø
The MSSM (minimal supersymmetric standard model) obtained by supersymmeterizing the SM contains baryon number violating operator which leads to proton decays Ö×
Ô
Ô
Ô
Ensuring the proton stability
lightest R-charged particle is stable!
07/22/2004
91 Daniel Chung
Ù
Direct detection
Earth's orbit around the sun add
subtract
Ù
annual modulation diurnal modulation can also
be sought with direction sensitive detectors (DRIFT) Ú
theoretical uncertainties: Ú
Ù
Ó
LSP Neutralino dark matter
local density of dark matter: 4-5 nuclear physics of detector: 2-3
07/22/2004
92 Daniel Chung
collect in the sun by elastic scattering can escape effeciently (no muons in the sun)
p
detected
-
n
Ü
+
W W
Ü
-
Þ á Ý
neutrinos produce muons à
Û
Þ
Ý
Þ ß Ý
à
Þ
Ý
Û
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Indirect detection
07/22/2004
93 Daniel Chung
â
â
Optimistically,
ã
Saturation effect:
Ì
â
Neutrino telescope reach A
C tanh 2 t C C A 2
Theoretical uncertainty: similar to direct detection (i.e. 10)
07/22/2004
94 Daniel Chung
Gamma rays, radiowaves, antimatter,... HEAT shows an “excess” of positrons at 10 GeV.
ä
ä
Ù
Ó
Ó
Other cosmic rays
Explanation in terms of LSPs speculative
Greater uncertainty in modelling (as much as 103) Need a better dark matter distribution of the galaxy (perhaps by lensing?)
07/22/2004
95 Daniel Chung
å
é
ç æ
æ
é
é
èçæ
In some region of parameter space (large higgsino component and LSP heavy), the only detection method: æ
å
Summary of LSP
Z
Even if LSP is not the dominant CDM (say 1%), direct detectors and neutrino telescopes can detect CDM.
07/22/2004
96 Daniel Chung
Ù
Ù
Ù
Ù
Ù
Ù
Ù
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More Opinions string theory (we still do not have the standard model) brane world & large extra dimensions (too arbitrary) moduli problem (good guidance to restricting string theory related speculations); above is a subset long distance modifications of gravity (surprisingly difficult) self-interacting dark matter (better simulations) CMB and inflation (no connection to SM yet) Self-tuning cosmological constant (unsuccessful thus far) New aspects of reheating (curvature perturb. not frozen) Transplanckian physics (ill motivated)
07/22/2004
97 Daniel Chung
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Outlook Supersymmetry is probably the best motivated. Dark matter direct and indirect detection experiments look promising and are indispensible for cosmology AND particle physics. Must be combined with collider data to make progress. NEED PROGRESS IN GALACTIC DISTRIBUTION OF DARK MATTER. MSSM EW baryogenesis almost ruled out. A good example of how collider data affects cosmology. Neutrinos and leptogenesis look promising. (Still plagued by gravitino progblem within SUSY.) As the scorecard suggests, there is much to still connect. CMB physics (polarization) will tell us more about inflation, but still needs connection to particle physics. Hopefully will not remain an island.
