An Introduction to Cosmologyhep.wisc.edu/~sheaff/PASI2006/chung_silafae05.pdf · An Introduction to Cosmology Daniel J. H. Chung (UW Œ Madison) 07/22/2004 . UNITS The most natural

An Introduction to Cosmology

Daniel J. H. Chung(UW – Madison)

07/22/2004

UNITS

� The most natural units to use:

� Consequence:

mass= energy= GeV

length=time=1/GeV

If , dimensionless.

Sometimes normal units wil be used in the talk.

� � c � 1

� � c � M pl

8 �� 1

Daniel Chung

207/22/2004

Plan

� Lecture 1 (Basics)

� Basic Intro to cosmology and its problems

� Inflation

� Baryogenesis/Leptogenesis

� Lecture 2 (Connecting High Energy and Cosmo)

� Electroweak Baryogenesis

� Dark Matter

� Outlook and Conclusions

Daniel Chung

307/22/2004

The Very Basic

Daniel Chung

407/22/2004

What is cosmology?

� Study of the origin and large scale structure of the universe

� Large scale > 10 kpc (= 30,000 lyr ; galaxy size).

� Largest scale observed (around 10,000 Mpc).

� Traditionally: gravitational and thermal history

� 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)

Daniel Chung

507/22/2004

Observational foundations

� 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.

� Cosmic rays (neutrino, positron, antiproton, ultra-high energy, etc.)

Daniel Chung

607/22/2004

Theory

� Einstein equations (Equivalence principle)

� Boltzmann Equations

R � 12

g � R � 8 � T �

S � 116 �

�

d 4 x � g R � �

d 4 x � g L M

Put in known fields(more later . . .)

p

� ��

x

� � ��� ��

p

�

p� �

�p

� f x

�

, p

� C f

Collision term;Approximation

Daniel Chung

707/22/2004

Homogeneity and Isotropy

� “on the average” Homogeneity and isotropy

� Stress Tensor: Perfect fluid

� Open Problem: Is the naïve averaging of the background density correct?

ds 2 � dt 2 � a 2 t dr 2

1 � kr 2

� r 2d

� 2 � r 2sin 2 �

d � 2

�characterizes the curvature of space at a fixed time

T � ! " t # P t u � u # P t g � 3 R $ 6 k

%

a 2 & 0.01 H 2 ' 10

( 44 GeV 2

e.g. T 00

$ ) T 11

$ a 2 P

Daniel Chung

807/22/2004

Background

* Einstein

* Notation and examples

H + a ' ta t

H 2 , ka 2

- .

3

M pl

8 /- 1

G N 8 /- 1

2 H ' t 2 , 3 H 2 , ka 2

-0 P

a ' ' ta t

1 2 16

3 4 3 Pcombine:

alternate:

ordinary matter: decelerate

d 3 a 3 1 2 P d a 3 perfect fluid energy conservationand adiabatic flow

5 6 1a 3

, w 7 0 8 a 6 t 2

9

3

5 6 1a 4

, w 7 13

8 a 6 t 1

9

2

w : P . - equation of state Matter dominated

Radiation dominated

expansion rate

Daniel Chung

907/22/2004

Basic picture emerging

; T00

contains the following fraction of the total

< 73 % “dark energy” defined by its negative pressure

< 22 % cold dark matter

< 4.4 % in baryons (protons and neutrons)

< 0.6 % neutrinos

< 0.005 % in photons

; The universe is spatially flat to about 1 %.

; a(t) is expanding with km/s/Mpc.

; Energy density was homogeneous and isotropic to 1 part in 105 about 15 billion years ago.

H = ddt

ln a t > 70

Daniel Chung

1007/22/2004

Explicit Stress-Energy Components

? Popular Model

@BA C @ A t 0

a 0

a

4

P A C@ A

3

D

tot

E DBF G DBH G Db

G D

c

G DJI

K

X

L MX

N Mc

@

b ,c

C @

b , c t 0

a 0

a

3

P b , c

C 0

O F P 10

Q5O

b

R 0.044

O

c

R 0.22

O I R 0.73@TS C @TS t 0 P S UWV @TS

O

tot

R 1.0

@YX C @X t 0

a 0

a

3

P X C 0

O H P 0.01

noninteracting particle

energy conservation

negative pressure

P tot

E P F G P H G P b

G P c

G P I

Z

c

[ 3 H 02\ 10

] 46 GeV 4

Daniel Chung

1107/22/2004

Temperature of the Universe

^ Equilibrium Thermodynamics

^ Photon Temperature = “temperature of universe”

^ Entropy (conservation gives T history)

n _ g2 ` 3

a

f E d 3 p

bc g2 d 3

e

f E E d 3 p

P c g2 d 3

e p 2

3 Ef E d 3 p

E f p 2 g m 2

f E _ 1

expE h i

T

j 1

kml n o 2

302 T 4

s n k p pT

q 2 o 2

45g * s T T 3

g * T r g * S T

kR

q o 2

30g * T T 4

Early Universe (T>1 MeV)

today (for massless neutrinos): T s 2.34 t 10

u 4 eV g * S

s 3.9 g *

s 3.36

g * T v 300 GeV w 107SM only:

photons dominate and can be measured!g x y 2 z

can fall exponentiallywith temperature

Daniel Chung

1207/22/2004

Equilibrium?

{ Equilibrium conditions:

| Kinetic equilibrium:

} maintains same temperature} particle number does not change

| Chemical equilibrium:

} maintains same temperature} particle number changes} particle number is determined by temperature

{ Boltzmann equations govern approach to equilibrium

{ Out of equilibrium:

} Kinetic: decoupled} Chemical: freeze out

X Y ~ X Z Y and Z in equilib with photon

X Y ~ Z

��� H

Y and Z in equilib with photon

Daniel Chung

1307/22/2004

Decoupled Species Temperature

� Theorem: Let be the temperature of particle after decoupling and be the temperature of the photon after decoupling. Suppose decouples at temperature .

[Proof] Separate conservation of entropy:

Total conservation of entropy:

T � �

T �

T �

T �� g * S T �

g * S T D

1

�

3

�

T D

s � t D a 3 t D

� s � t 0 a 3 t 0

s tot t D a 3 t D

� s tot t 0 a 3 t 0

�

H

� 1

Daniel Chung

1407/22/2004

Exercise

� 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:

T X

� 4311

457

1

�

3

T � � 1.5 � 10

� 4 eV

Daniel Chung

1507/22/2004

IntroductionDaniel Chung

1607/22/2004

Problems of cosmology

� What is the composition of dark energy?

� What is the composition of CDM?

� Why more baryons than antibaryons?

� 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?

Daniel Chung

1707/22/2004

Rest of the Lectures

� First, a general introduction to these problems.

� Second focus on selected topics.

� Inflation

� Baryogenesis

� Dark Matter

� Collaborative scorecard between problems of physics beyond the standard model and cosmology.

Daniel Chung

1807/22/2004

What is dark energy?

Recall that normal gas of matter has positive pressure.

Field energy can have negative pressure (like inflation).

� Why is the energy density nearly coincident with the matter density today?

� If a dynamical field explains the coincidence, how can such a small mass scale (cosmological time scale) be protected?

P

�

x � 13

�

N

�

p N2

�

p N2 � m N

2

� 3

�

x ��

x N

�

aa

� � 4 �

3 M pl2

� � 3P   0 ¡ P ¢ �1 £

3 �

P � 12

d¤

dt

2

� V ¤

07/22/2004

What is cold dark matter?

� Definition: dark matter that is nonrelativistic at the time of matter radiation equality.

� Can it be all in cold baryons not emitting light?

� BBN (chemistry of producing elements heavier than hydrogen) says no.

� Microlensing (gravitational deflection of light from compact objects) agrees with this picture.

� CDM neutrinos would overclose the universe.

� Physics beyond the standard model necessary!

Daniel Chung

2007/22/2004

Why more baryons than antibaryons?

¥ The absorption spectra measurements, CMB, and BBN agree

¥ Naturalness of small dimensionless number?

¥ According to SM, at T > 100 GeV.

¥ Probability that the small number is from mere thermal fluctuation is very small.

n B

n ¦§ 10¨ 18

n B

n ¦© 10

¨10

Daniel Chung

2107/22/2004

What is the inflaton?

ª CMB data looks like that expected from inflation

i.e.

1. “no” spatial curvature

2. scale invariant spectra on “superhorizon” scales

ª Similar in negative pressure characterization as dark energy; no known particle can produce this

Daniel Chung

2207/22/2004

Singularities of GR

« 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.

R ¬­ 6a ' ' ta t

® a ' ta t

2

® ka 2 t

¯ 1 °

t 2 ±²

Daniel Chung

2307/22/2004

A small cosmological constant?

³ Due to SM quantum fluctuations

³ On the other hand we observe

´µ ¶ · M 4

µ ¶ · 10¸ 12 GeV 4

³ Possible values of

¹ Planck scale 1018 GeV

¹ GUT scale 1016 GeV

¹ See-saw scale 1013 GeV

M

Daniel Chung

2407/22/2004

Ultra-high energy cosmic rays

º There is a GZK cutoff

at 1019.8 eV due to efficient

º Proton cannot ravel more

than 40 Mpc.

º Events above 1019.8 eV measured (possibly).

º No energetic extragalactic sources within 40 Mpc.

º Primary? Source & acceleration mechanism?» p ¼½ p

Daniel Chung

2507/22/2004

Motivation: Mostly initial condition problems.

Inflation

kH 2a 2

¾ ¿ÁÀ 1Friedmann:

today:k

H 02 a 0

2

¾ ¿

0

À 1 Â 10

à 2

early universe: kH e

2 ae2

¾ kH 0

2 a 02

a r

a 0

ae

a r

2

 10

à 2 10

à 4 10

à 6 2 ¾ 10

à 18

at nucleosynthesis

time dependent

1. Flatness Problem

Why small?Initial spatial curvature had to be finely tuned for universe to be this old and flat. Why?

Daniel Chung

2607/22/2004

More Motivation

“singularity”

2. Horizon/causality problem: Why homogeneous and isotropic on “acausal scales?

causal signals travel beyond naïve horizon

d H

Ä a t

Å

0

t dt 'a t '

Ä t

1 Æ 23 1 Ç w

naïve horizon (with ):

real singularity

w ÈÊÉ 1

Ë

3

Ì 1H

“inside horizon”

“outside horizon”

Daniel Chung

2707/22/2004

Unwanted Relics

G 1

Í G 2

Í ... Í SU 3 c

Î SU 2 L

Î U 1 Y

G 1

Monopoles arise whenever Ï

2 G i

Ð

G j

Ñ I

n M

Ò H 3 Ò T c6 Ð

M pl3

n MÐ

s Ò T c3

M pl3

Ò 1014

1019

3

Ò 10

Ó15

m M

Ò 1016 GeV Í Ô

M

Ò 1011

3. Unobserved relic problem

e.g. Suppose the SM is embedded in a larger theory with gauge group

unacceptably large!

Daniel Chung

2807/22/2004

Õ Inflationary solution: Blow up a small flat patch into the entire universe

Õ Flat patch becomes the entire universe (solves flatness)

Õ Lengthen the time it takes to reach the singularity (horizon)

Õ Dilutes unwanted relics

Õ Prediction: scale invariant density perturbations

Inflationds 2 Ö g× Ø dx

×

dx

Ø Ö dt 2 Ù a 2 t dx i dx j Ú

ij

d H

Û a t

Ü

0

t dt 'a t '

ddt

x a1

Ý

H

Þ 0 ß d 2 ad t 2

Þ 0

causal signals travel beyond naïve horizon

àâáá ã 1

2 ä 3å

d 3 k

à

k e

æ i k ç x power: Úéèè

hor

ê k 3

ë

2

Ú

k

2 ìê 10

í 5

x î comoving coordinate separation

Daniel Chung

2907/22/2004

Qualitative description of inflaton

How to choose the potential and initial conditions?

ï for about 60 e-folds.

ï Inflation must end.

ï Spatial inhomogeneities of must be sufficiently small to be consistent with cosmology (too big = too many black holes, too small = not enough structure).

ï After inflation ends, the universe must reheat to .

ï After inflation ends, unwanted relics must not be created (e.g. low enough temperature).

Action: S ð ñ

d 4 x ò g

ò12

R ó 12

g

ôõ ö ô ÷ öõ ÷ ò V ÷

single field inflationary models:

d 2 adt 2

ø 0 a t f

a t iù e N efold

÷

T ú 10 MeV

Daniel Chung

3007/22/2004

Magic of negative pressure

û Horizon problem

û 60 efolds desired:

d 2 adt 2

ü

a ý þ 4 ÿ

3 M pl2

� � 3P � 0 � P � þ1 ü

3 � (just like dark energy)

� ý 12

d

�

dt

2 � V �

P ý 12

d

�dt

2

þ V �

� d

�

dt

2 � V �

d 2

dt 2

� H d

dtslow roll inflation

d adt

�

a H � a � e�

dt H

Daniel Chung

3107/22/2004

Quantitative Single FieldSlow Roll approximation

� Negative Pressure and 60 e-folding

� End of inflation: with at the minimum of the potential

� Density perturbation amplitude:

� � 12

V '

�

V

2

�� d H

dtH 2

� 1 � � V ' '

�

V

� 1 N�

t i

� ��

t i

�

t f d

�

2 � � 60

� �

t f

� 1 V�

min� 0

scale invariance nearly automatic! 2 � �

60

� 6 � �

60

� 0.2

indicates source of fine tuning

3 Hd

�

dt

� �V '

� H 2 V3

never Planckian

P k

!� V24 " 2 � �

60

# 10

$5

Daniel Chung

3207/22/2004

Standard Reheating

% Inflaton field decays: e.g.

&

t2 '( 3H ( )

tot

&t

'( m 2( )tot2

4

'+* 0

L i

,- ./ 0 0

)tot

1 2m 2

m

L , 12

3/ 2 4 m 2/ 2 4 L i

576 * 12

&t

' 2( m 2 ' 2 8 2 9

4 : m 2

&

t

' 2

2

* m 2 ' 22

use following approx:

&t

5R

( 4 H 5

R

)

tot

565

R

; < 230

g * T T 4= reheating temperature as a function of time

estimate:

T RH

> 0.2 200g *

1

?

4 @

tot M pl

Daniel Chung

3307/22/2004

Why 60 efolds?

A Largest scale that we see homogeneous and isotropic:

A inflation can take place only if homogeneous (small patch of comoving coordinate size > X became the observable universe):

L B a 0

C

dx B a 0

C

a dec

a 0 daH a 2

D a 0

C

a dec

a 0 daH 0 a 0

E

a 3

F

2 a 2

D 2H 0

G a 0 X

1H I

H X a I

I 1H I

H a 0 X

La I

a 0

sufficiently small

a I

a 0

J a I

a e

a e

a 0

K e LN a e

a 0max

a e

a 0

M a RH

a 0

N g * S t RH

g * S t 0

1

F

3

T 0

T RH

M T 0

T RH

lnT RH

T 0

O 12

ln

P

R0

Q 60 O ln T RH

1015 GeV

R N

need enough efolds

H I

D T RH2

3

(also for curvature)

Daniel Chung

3407/22/2004

Single Scalar Field ComputationAction: S S T

d 4 x U g U12

R V 12

g

WXY W ZY X Z U V Zgauge degree of freedom: Freedom of slicing the spacetime (splitting perturbed versus unperturbed)

[]\ [

0

^ _ ` [

xperturb :

ga b B ga b0 c d a 2 2

e f gi B

f g

i B 2 h iij

f gi

gj E

v j a kl ml

0 ' n

a '

oa

pinfinitesimally gauge invariant (same as longitudinal gauge)

dx

q

dx

rg q r0 N a 2 s d s 2t d x 2

uwv f a '

x

aa

y

0 'v

S z {

d c d 3 x 12

v ' 2 f |

v 2 } a '

x

aa

y

0 '

~�� 2 a

y

'a '

x

av 2

' � ���

Seed formation of galaxies!

constant on constant hypersurface (comoving)

���� �

Daniel Chung

3507/22/2004

Power Spectrumquantize: v � , x � � d 3 k

2 � 3

�

2a k v k

� � a� kdagger v k

* � e i k � x

a k , a k ' dagger � � 3 k � k '

�� , x

�� , y � � dkk

sin k x � yk x � y P � P � � k 3

2 �2a '

�

aa

�

0 '

2

v k2

v k ' '   k 2 � 2   p

¡2v k

� 0p � 3 3 ¢ � £

v k

¤¦¥ §¨ © e

¨ i k ¥

2 kboundary condition:

v k

� ª2

� « H ¬1 � k « ei

­

212

® ¬ ¯ ° 9 ± 4 p2

² P k

³µ´ V24 ¶ 2· ¸

60

¹ 10

� 5

º °¼» a '½

aa

¸0 '

v

H¾ 1 � k « ¿k

ÀaH Á 0

� i 2 ª� k « 3

À

2

Daniel Chung

3607/22/2004

Quantum to “Classical” TransitionOn large scales: v k ' ' Â a '

Ã

aa

Ä

0 '

ÅÇÆ 2 a

Ä0 '

a 'Ã

av k

È 0

v k

¿ A k

a

Ä

0 '

a '

Ã

agrowing mode:

k

É

a H Ê 0

Ë

k

a

Ä

0 '

a '

Ã

a

� a k v k

Ì Í aÎ kdagger v k

* Ì

Ï

k , Ï

ldagger � 0

Ð

k

�Ñ Ï

k

limk

Ò

aH Ó 0 Ô

k are classical random variables!

are constantsÕ

k

Constants on superhorizon scales!

Spectral index: P Ö × k n s

Ø 1n s

� 2 ÙÑ 6 Úd n s

d ln kÛ 16 ÜÝ Þ 24 Ü 2 Þ 2 ß ß Û V ' V ' ' '

V 2

Shape of the potential is given by n S k

Running of spectral index measurement = measuring potential

Daniel Chung

3707/22/2004

Gravity waves

Tensor perturbations: à

gá âT ã 0 00 h ij

P T k ä k 3

8 å2 h + k2 æ h ç k 2 è k nT

é 1

P T

ê H 2

2 ë 2

ê 2 ì P í

nT

î 1 ã î 2 ï ã î r

r ð P T

P R

Consistency relation givesevidence for single field inflation.

In multifield inflation (more realistic):

1 ñ n T

ò r

Daniel Chung

3807/22/2004

What is this good for?

ó

t2 ô

0

õ ó

t R

1 õ R

ó

t

ô

0

õ k 2 c s2 ô

0

ö F

ô

l

÷

2 l õ 1

ø ô

0

õ ù ÷ú j l k ÷üû ÷ ú õ ...

2l õ 14 ý C l

ö 12 ý 2

þ d kk

k 3 ôl

2

2l õ 1

fixes the boundary condition to the Boltzmann equation

c s2 ö 1

31

1 õ R R ÿ 3 �

b

4 ���

ô ��

TT

���

l � 0

�

l

e i k � x P l k �

“acoustic oscillations”

ô ÷

0, x , � ô ÷

0 x , � ' ölC l P l

�� � '

ôt i

� �

t i

Daniel Chung

3907/22/2004

“Recent” Developments

� Transferring power from isocurvature to curvature perturbations.

� 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.

Daniel Chung

4007/22/2004

Future Prospects

� Running of the spectral index will be better known with future experiments such as Planck.

� 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

� What is the inflaton? Are there truly natural models?

� Stability of de Sitter space and back reaction.

� More observables to experimentally ascertain inflation.

Daniel Chung

4107/22/2004

Baryogenesis

Daniel Chung

4207/22/2004

Observation

� In solar system much more baryons than antibaryons

� Dominance of matter clear on scales < 10 Mpc:

bound on from .

� Other constraints: distortion of CBR, diffuse -ray.

n p

�

n p

� 3 � 10

� 4

n 4 He

�

n 4 He

� 3 � 10

� 8 ?

pp � 3 p � pexplained by

� p p � 0 � 2 �

!

[e.g. Cohen and de Rujula 1997] void+ -

Daniel Chung

4307/22/2004

Is there a problem?

" SM contains nonperturbative baryon number violating operators that erase B+L

" These become efficient when erases preexisting B+L

" Otherwise, an aesthetic initial condition problem

" Starting from initial conditions why

T # T c

$ 100 GeV

% & n B

n '( 6 ) 10

* 10

n B

& n b+ n b

, 0

-naive

. 10

/ 18naively, and not separated.

Daniel Chung

4407/22/2004

Illustration of Sakharov Criteria

0 Suppose “X” carrying 0 baryon number can decay only into “a” carrying baryon number and “b” carrying baryon number .

0 Branching ratios:

0 Baryon produced:

0 Out of equilibrium: otherwise, the other direction produces

r 12

X 3 a2

X

r 45

X 6 a

5

X

1 7 r 45

X 6 b

5X

1 7 r 45

X 6 b

5

X

b ab b

“CP”:

“CP”:

8

B X1 r b a

9 1 : r b b;B X

<= r b a

= 1= r b b;B < ;

B X

> ;

B X

< b a

= b b

B violation

r = r

CP violation

b a

= b b r = r

rephasing invariant

Daniel Chung

4507/22/2004

Boltzmann

? Phase space evolution (useful B-genesis, dark matter, CMB):

? Simplification

? Chemical equilibrium of others:

? Kinetic equilibrium of all states:

p

@ AA

x

@ B CEDF @ p

D

p

F AA

p

@ f x

@

, p

@ G C f

H

t

I

d 3 p f J 3 H

I

d 3 p f K I d 3 pE

C f n t L g2 M 3

Nd 3 p f

g X

2 O 3

P d 3 p X

E X

C f KQ P

d

R

X d

R

a d

R

b dR

c 2 O 4 S 4 p X

J p a

Q p b

Q p c

T

M X U a V b U c2 f X f a 1 W f b 1 W f c

Q M b U c V X U a2 f b f c 1 W f X 1 W f a

d

R

X

X g X

2 O 3

d 3 p X

2 E X

e.g. f b

K f beq , f c

K f ceq

e.g. f X

K F t f Xeq , f a

K A t f aeq

Daniel Chung

4607/22/2004

Interference

Y CP violation involves a complex parameter in the Lagrangian:

Y In this Lagrangian, there is only one physical phase (phase that cannot be removed by field redefinition).

Y

CP violation = interference of transition amplitudes :

L Z m 2 [

12 \ [

22 ] m e i ^`_

1

_

2

\ e a i ^_2

_1

b M 3 e i

ced f a f a b e g i ced f a f a \ m LR2 e i

h [2

[1

\ e a i h [

1* [

2*

i

phys

j kml npo l q

M 2 j M 1r M 2 e i

s

phys 2 j M 12 r M 2

2 r 2 t

M 1 M 2 e

u i s

phys

M CP 2 v M 1

b M 2 e

u i s

phys 2 v M 12 b M 2

2 b 2 w

M 1 M 2 e i

s

phys

Daniel Chung

4707/22/2004

Cutting

x Recall in the simple example

x Diagrammatically

y

B v y

B X

z y

B X

v b a

{ b b

B violation

r { rCP violation

M 2 | M CP 2 j }

M 1 M 2 e i

~

phys | M 1 M 2 e� i ~

phys

This is 0 unless the non-CP violating part develops an imaginarypart due to virtual states going on shell.

+ interferes

Since the real part of this should be taken:

Daniel Chung

4807/22/2004

Thermal Leptogenesis

� Have only perturbatively significant B-L violating operators.

� Generate L as we have been discussing.

� Convert L into B through the B+L violating sphaleron.

� Theoretical attractiveness: L-violating operators natural in seesaw neutrino masses

� “uncomfortable” aspect: in gravity mediated SUSY breaking models, gravitino bound strongly constrains it.

B j 8 N f

� 4 N H

22 N f

� 13 N H

B � L

Daniel Chung

4907/22/2004

Boltzmann Eq.

zY �eq

d Y �

dz

j �1H a , i , j , ...

Y � Y a ...

Y �eq Y aeq ...

� eq � � a � ... � i � j � ...

� Y i Y j ...

Y ieq Y j

eq ...

� eq i � j � ... � � � a � ...

z v m �

T � eq j K 1 z

K 2 z

�

decay

scatter �eq � � a � i � j � ... � T64 � 4 n �eq

�

m � � m a2

�

ds � s s K 1s

T

� s v 2 s � m � � ma2 s � m � � ma

2

s

� s

(same equation is applicable to dark matter.)

� � v neq

Y i

� n i

s

Daniel Chung

5007/22/2004

Leptogenesis Estimate1) Assume temperature of the universe is high enough

right-handed neutrinos are in equilibrium (fixes initial cond.)

Typically, CP conserving reactions control this.

2) Temperature falls:

3) When the right handed neutrino abundance falls below L density, the lepton number freezes out.

�

� v n�

RT � T 2

M pl

� right handed neutrinos go out of equilibrium

� ��

CP m � Mg * v 2

MT c

e

�M �

T c m�   10

¡ 1 eV , M   109 GeV , g *

  100, mW

  100GeV

MT c

e

¢M £

T c ¤ 0.1 (out of equilibrium temperature)

  10

¡ 10

Daniel Chung

5107/22/2004

End of Lecture 1

¥ General Cosmology

¦ Edward Kolb and Michael Turner, THE EARLY UNIVERSE.

¦ Scott Dodelson, MODERN COSMOLOGY

¥ Inflationary references

¦ 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.

¦ Hu and Sugiyama, astro-ph/9411008.

¥ General Baryogenesis

¦ Kolb and Wolfram, Nucl. Phys. B 172, 224 (1980).

¥ Cosmology related to supersymmetry

¦ Chung, Everett, Kane, King, Lykken, and Wang hep-ph/0312378.

Daniel Chung

5207/22/2004

People and References for EW baryogenesis

§ Incomplete list of ewbgenesis people:Ambjorn, Arnold, Bodeker, Brhlik,

Carena, Chang, Cline, Cohen, Davoudiasl, 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,

Wagner, Westphal Weinstock, Worah, Yaffe...

§ “Randomly” selected “overview” references

¥ hep-ph/0312378¥ hep-ph/0208043

¥ hep-ph/0006119

¥ hep-ph/9901362

¥ hep-ph/9901312

¥ hep-ph/9802240

Daniel Chung

5307/22/2004

EW Motivation

¨ In minimal SM, EW phase transition is inevitable!

EW symmetry restoration

¨ An exciting era:

probing at LHC and its microphysics Nearly everything at associated with SM measurable

¨ Almost no cosmological probe to this era

© Explaining the baryon asymmetry of the universe

© Establishing thermal equilibrium for WIMPs close

T ª T c

« m h

T c

Daniel Chung

5407/22/2004

Why worry about electroweak baryogenesis scenario instead of

leptogenesis?

¬ Leptogenesis

­ Computationally simpler: spatially homogeneous

­ 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:

­ Squeezed by gravitino bound

¬ EW Baryogenesis is physics at 100 GeV

­ Almost everything about it can be lab probed in principle

­ In SM and MSSM, EW phase transition occurred!

m ® ¯ U MNS m ® diag R RT m ® diag U MNSdagger

Daniel Chung

5507/22/2004

Aspects of MSSM

° Lsoft

± 12

M 3 g g ² M 2 w w ² M 1 B B

²³µ´ ¶ ° b H d

´

H u

¶ ° H u

´

Q i

¶

A u ij U jc ² H d Q i A d D j

c ² H d L i A e ijE j

c ² h.c.

·Q i

´

mQ ij

2 Q j

´ * · L i

´

m L ij

2 L j

´ * · U ic * mU ij

2 U jc · D i

c * m D ij

2 D jc · E i

c * m E ij

2 E jc

· m H d

2 H d2 · m H u

H u2

Lc

¸ ¹12

º + º - 0 X T

X 0

º +º -

Chargino mass matrix

soft susy breaking (definition: does not introduce quadratic divergence)

º +-» W +-

H u+-

W ± ³´ ¶ ° H u

´

Q i

¶

Y uij U j

c ² H d

´

Q i

¶

Y dij D j

c ² H d´

L i

¶Y e

ij E jc ° ¼ H d

´

H u

¶

Q i

¸ Q L iQ L i

U i

¸ U L i

c U L i

cD i

¸ D L i

c D L i

c L i

± E L iE L i

E i

¸ E L i

c E L i

c H u

¸ H u H u H d

± H d H d

supersymmetric Yukawa and mass term

X ½ M 2 2 M W sin

¾

2 M W sin

¾ ¼Daniel Chung

5607/22/2004

Sakharov conditions

1) Baryon number violation: SU(2) sphaleron

e.g. 1 generation

O B ¿ L À C h L 1h L 2

w L4

iq L i

q L iq L i

l L i

u L

Á d L d L

Â

e

recall: 1) B-violation, 2) CP violation, 3) out of equilibrium

Ã

EW

Ä k Å

W

Å

W4 T 4 k Æ

W

Ç O 1unbroken phase:

broken phase: ÈÊÉ 2.8 Ë 105 T 4

Ì

W

4 Í

4

Î Ï 7 exp Ð Ï 10

Ñ 4 ÒÓ Ò 10

Ñ 1

ÏÕÔ E sph T

Ö

T

E sph

× 2 mWÌ

W

× 8 Í Hg

Daniel Chung

5707/22/2004

Sakharov conditions

2) CP violation:

In SM:

In MSSM, soft SUSY breaking phases: e.g.

Ø

M 2

Ù

Ú

L Û 12

M 2 W Rdagger W L

Ü Ù h Rdagger h L

Ü h.c.

recall: 1) B-violation, 2) CP violation, 3) out of equilibrium

Ý

CP

Þ g W

2 mW

12

mt2 ß mu

2 mt2 ß mc

2 mc2 ß mu

2 m b2 ß md

2 m b2 ß m s

2 m s2 ß md

2 j à 10

á 22

j â ã

V cs V us* V ud V cd

* ä 10

á 4

Too small.

Daniel Chung

5807/22/2004

Out of equilibrium3) Phase transition:

å T>100 GeV, symmetry is restored.

å T<100 GeV, symmetry broken.H

V H æ D T 2 ç T 02 H 2 ç E T H 3 è

é

T

4H 4

H

V H

z

H ê z

H ê 0

ë ëì

w

(Attractive, because almost no new assumption!)

T í T c

T î T c

Daniel Chung

5907/22/2004

EW B creation step 1

1. Pick up CP/chiral asymmetry

H ê z H ê 0ï

wn bL ð n b

L ñ 0

n b

ð n b

ê n bL ò n b

R ð n bL ð n b

R ê 0

q

sphalerons activesphalerons inactive

B ê 0e.g. 1 generation

u L u R

Daniel Chung

6007/22/2004

EW B creation step 2

H ê z H ê 0ó

w

ô

n bL õ n b

L

n b

õ n b

ê n bL ö n b

R õ n bL õ n b

R ÷ 0

q

sphalerons active

sphalerons inactive

u L

ø d L d L

ù

e

u R

ø u R

u L d L

ù

e

B ê 1B ê 0

e.g. 1 generation

Daniel Chung

6107/22/2004

EW B creation step 3

H ê z H ê 0

ú

w

n b

û n b

ê n bL ü n b

R û n bL û n b

R ý 0

q sphalerons active

sphalerons inactive

Daniel Chung

6207/22/2004

Computational Steps

þ 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.

þ Solve for SU(2) charged left handed fermions

þ Integrate sphaleron transition sourced by above.

Daniel Chung

6307/22/2004

Schematically

ÿ One of massaged diffusion equations

ÿ Source term = CP violating, Higgs field gradient

� flow of current w/ background force�

ÿ

v w

�

z n H

� D h

�

z2 n h

� �

Y

nQ

k Q

� n T

k T

� n H

��� n h

k H� �

h

n H

k H

� S H

scattering source

S H

� S Q

n B

c 1

�

EW

v w

� �0

dz n L z exp c 2 z

�

EW

v w

n L z exp f 1 z

f 3

0

�dx S H x exp � f 2 x

1�

H

Daniel Chung

6407/22/2004

Uncertainties

� Source uncertainty (off diagonal term)

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

m A

� 300 GeV M 2

� �

S H

� D h

�

M 2

�

M 22 � � 2

�

z2 v 1

�

z v 2

� v 2

�

z v 1 F 1 z�

z m 1

� F 2 z

�

z m 2

Daniel Chung

6507/22/2004

Resonance

� Consider mass matrix

M z � m 1

� z� z m 2

� � � �1 z 0

0

�2 z

�

z

������ ! 4 � �

z

�

m 1

" m 22 # 4 � 2 m 1

# m 2

! m 1

" m 22

S H

$ D h

%

M 2

&M 2

2 # & 2�

z2 v 1

�z v 2

" v 2

�

z v 1 F 1 z

�

z m 1

# F 2 z

�

z m 2

Daniel Chung

6607/22/2004

Source of source discrepancy

' CQSW has “interaction” term; never diagonal

' CKJPSW uses WKB-like approximation

' Dispute unsettled

L int

( x ) z * +

Rdagger M * +

L

, h.c.

-

z2 . f 2 /10 0

2

z2 , f d

2 + ( 0

+3 12 f d

exp i

4

dz f d

f d2 ( U f 2 V dagger + ( V +

Daniel Chung

6707/22/2004

55

55

55

55

6 strong enough phase transition

6 charge and color breaking minima

6 if (suggestive) 6 sufficient diffusion

6 sufficient CP violation

6 sufficient density processed by the sphaleron

0.2 mQ

7 At

7 0.4 m Q

tan

8:9 4

mQ

9 1 TeV

120 GeV ; m <

t R

; mt

= , M 1,2

; mQ

> = M 1,2

?

T c2 9 0.05

= , M 1,2

; 2 T c

m h

; 115 GeV

m h

9 114 GeV

sketch of parameter regionDaniel Chung

6807/22/2004

sketch of parameter region

55

55

55

55

6 strong enough phase transition

6 charge and color breaking minima

6 if (suggestive)6 sufficient diffusion

6 sufficient CP violation

6 sufficient density processed by the sphaleron

0.2 mQ

7 At

7 0.4 m Q

tan

8:9 4

mQ

9 1 TeV

120 GeV ; m <

t R

; mt

= , M 1,2

; mQ

> = M 1,2

?

T c2 9 0.05

= , M 1,2

; 2 T c

m h

; 115 GeV

m h

9 114 GeV

Daniel Chung

6907/22/2004

sketch of parameter region

55

55

55

55

6 strong enough phase transition

6 charge and color breaking minima

6 if (suggestive)6 sufficient diffusion

6 sufficient CP violation

6 sufficient density processed by the sphaleron

0.2 mQ

7 At

7 0.4 m Q

tan

8:9 4

mQ

9 1 TeV

120 GeV ; m <

t R

; mt

= , M 1,2

; mQ

> = M 1,2

?

T c2 9 0.05

= , M 1,2

; 2 T c

m h

; 115 GeV

m h

9 114 GeV

Daniel Chung

7007/22/2004

sketch of parameter region

55

55

55

55

6 strong enough phase transition

6 charge and color breaking minima

6 if (suggestive)6 sufficient diffusion

6 sufficient CP violation

6 sufficient density processed by the sphaleron

0.2 mQ

7 At

7 0.4 m Q

tan

8:9 4

mQ

9 1 TeV

120 GeV ; m <

t R

; mt

= , M 1,2

; mQ

> = M 1,2

?

T c2 @ 0.05

A , M 1,2

B 2 T c

m h

B 115 GeV

m h

@ 114 GeV

Daniel Chung

7107/22/2004

Strong enough phase transition

C To protect the baryon number

C In the MSSM ,

ED

T cE F

T c

G 1.3H

V IJ E T

F 3 K D

4

F 4

L

V M N T2 O mU

2 P Q

t RT P 0.15 M z

2 cos 2

R P mt2 1 N A t

N S T

tan

R 2

mQ2

3

U

2

mQ2 V mU

2 , mt2

mt2W mU

2 K 0.15 M Z2 cos 2

X K m t2 1J At

J Y Z

tan

X 2

mQ2

mt

[ mt

A t

[ 0.4 mQ

m H2W D

v 2

m H

[ 115 GeV

Daniel Chung

7207/22/2004

Source Term

\ Interaction Lagrangian

\ The CP violating current is proportional to the CP violating propagator correction.

]

L ^ x _ z ` a

Rdagger M ` a

L

b a

Ldagger M `dagger a

R

c

S RR x , y d e

d 4 w S RR x , w w f z gU z M g z V dagger z S LR w , y h h.c.

derivative

U M V dagger ^ m 1 z 0

0 m 2 z

S h

^ D h

i

z2 1

2lim r j 0 Tr

]

S RR z b r2

, z _ r2

b ...mass suppressed

k S h

l S QM Ql 1 TeV M 1,2 , m n M Qif

Daniel Chung

7307/22/2004

Sufficient CP violation

o Estimate

o Importance

p Large top Yukawa couplingp Higgs mediated CP asymmetry

Chargino, Higgs(ino), neutralinos, (s)quark

qr k s

w

s

w4

g s

t

CP f r 10

u 10 vw4 w 10

x 6 g s

y 10

O B z L { h L 1h L 2

w L4

iq L i

q L iq L i

l L i

f | v W

} 0.1 ~ �

CP

� 10

� 2e.g.

�CP

} � M w

�

T c2

Daniel Chung

7407/22/2004

EDM

� experimental EDM bounds

� Theoretical constraints complicated & uncertain

� e.g. without cancellations,

d e

� 1.6 � 10

� 27 e cm [Regan et al 2002]

d n

� 12 � 10

� 26 e cm [Lamoreaux et al 2002]

d Hg

� 2.33 � 10

� 28 e cm [Romalis et al 2001]

Arg M 2

� � 0.05 [Chang et al 2002; Pilaftsis 2002]

Daniel Chung

7507/22/2004

Sufficient density

� For there to be sufficiently large current

otherwise

� Critical temperature

n P� n P� g2 � 2

�

m

�

dE E E 2� m 2 11 � exp E� � �

T� 1

1 � exp E � � �

T

� g � T 2

6

T c

� 100 GeV

� , M 1,2� 2 T c

� 2g m T2 �

3

�

2

sinh � �T exp � m �

T

Daniel Chung

7607/22/2004

EW bgenesis Prospects

� 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� There is a dispute of the strength of the source term when M 2

��

M 2

¡

Daniel Chung

7707/22/2004

Recent collaborative progress

Daniel Chung

7807/22/2004

Cosmology and High Energy Physics

¢ renormalization group flow cosmological time flow.

£ Integrating out degrees of freedom in field theory is most of the time not invertible.£ Entropy producing events evolution noninvariant under time reversal.

¢ What are some recent collaborative efforts between high energy physics and cosmology?

¢ Any prospects for further success?

¤

¥

Daniel Chung

7907/22/2004

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?

Daniel Chung

8007/22/2004

Lightness of Higgs

§ Precision electroweak data & LEP direct search

§ Quantum fluctuations

§ Unnatural if

114 GeV ¨ m H

¨ 200 GeV

H

m H2 © m H

0 2 ª « ¬ 2

¬ 2 ­ m H2

§ Possible values of ® Planck scale 1018 GeV® GUT scale 1016 GeV® See-saw scale 1013 GeV

§ What generates low ?

¬

H

¬Daniel Chung

8107/22/2004

Origin of the electroweak scale

¦ The value of the Higgs field permeating the universe is much smaller than what we might expect from short distance scales.

¦ As before, the possible values are

¯ 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.

H ° 100 GeV

Daniel Chung

8207/22/2004

Unification of coupling

¦ Because of “backreaction” (renormalization) coupling constants depend on energy scale (or length scale).

¦ Is this an accident?

Daniel Chung

8307/22/2004

Incorporating quantum gravity

± All fields are quantized according to the SM.

± Gravity appears in SM.

± Quantize gravity as well.

± Gravity becomes non-predictive!

S SM

© ²

d 4 x ³ g L SM

gravity!

´

S GR

© ²

d 4 x ³ g c 21 R 2 µ c 22 Ra b Rab µ ... µ c 31 R 3 µ ...

undetermined!

Daniel Chung

8407/22/2004

Strong CP problem

¶ The strong interactions (responsible for holding the nucleus together) contains

which is the analog of the CP violating term

in Maxwell theory.

¶ Absence of electric dipole moment of the neutron requires .

¶ The problem: to explain this small number.

LCP

© · ¸

d 4 x ¹ g º »¼ ½ ¾Tr F » ¼ F ½ ¾

¸

d 4 x ¹ g¿

E À¿

B

·ÂÁ 10Ã 9

Daniel Chung

8507/22/2004

Collaborative score card

Ä

Why is the Higgs field light?

Ä

What is the origin of electroweak symmetry

breaking?

Ä

Is it simply an accident that the gauge

couplings seem to meet?

Å How is gravity incorporated into the SM?

Ä

Why is the CP violation from QCD small?

Å What is the dark energy?

Ä

What is the CDM?

Ä

Why more baryons than antibaryons?

Å If inflation solves the cosmological initial condition problems, what is the inflaton?

Å Classical singularities of general relativity?Å Why is the observed cosmological constant

small when SM says it should be big?

Å Origin of ultra-high energy cosmic rays?

with SUSY

with PQ

Many other speculative connections exist.Not very convincing yet, unfortunately.Restricting to particle physics.

Daniel Chung

8607/22/2004

Supersymmetry (SUSY)

Æ (N=1 SUSY) a symmetry exchanging bosons and fermions

examples: SM new particle

Æ Key feature: “Solves”

Ç Why is the Higgs field light?Ç (partially) Is gauge coupling unification an accident?

f È b

electron spin 1

É2 Ê selectron spin 0

Higgs spin 0 Ê Higgsino spin 1

É

2

graviton spin 2 Ê gravitino spin 3

É

2

Daniel Chung

8707/22/2004

Lightness of Higgs

Ë In SM, the trouble was

Ë With SUSY

Cancellation of the quantum back reaction! The Higgs mass is stabilized!

H

m H2 Ì m H

0 2 Í Î Ï 2H

Ð

m H2 ÌÑ Î Ï 2

H H

ÒÒ

Daniel Chung

8807/22/2004

Unification of coupling

Ó “Accident” is more and more looking not like an accident!

Daniel Chung

8907/22/2004

Ensuring the proton stability

Ô General theme in physics: Every new solution has a new set of problems.Ô Recall in SM, proton is very stable due to accidental symm. Ô The MSSM (minimal supersymmetric standard model) obtained by supersymmeterizing the SM contains baryon number violating operator which leads to proton decays

Ô To ensure such operators do not appear: conserve R-parity (a new quantum number natural in SUSY).Ô Conservation of R-charge forbids an R-charged particle to decay to a non-R-charged final states.

Õ lightest R-charged particle is stable!

p Ö× 0 Ø e +

Daniel Chung

9007/22/2004

LSP Neutralino dark matterÓ Direct detection

Ù Earth's orbit around the sun

annual modulationÙ diurnal modulation can also

be sought with direction

sensitive detectors (DRIFT)Ù theoretical uncertainties:Ú local density of dark matter: 4-5Ú nuclear physics of detector: 2-3

subtractadd

Daniel Chung

9107/22/2004

Indirect detection

Û collect in the sun by elastic scattering

Û can escape effeciently (no muons in the sun)

Û neutrinos produce muons

Ü ÜÝßÞ

Ý Þ

à -

ÝáÞnp

à -ÝÞ

W +

W -

detected

Daniel Chung

9207/22/2004

Neutrino telescope reach

â Saturation effect:â Optimistically,

â Theoretical uncertainty: similar to direct detection (i.e. 10)

ã

A

Ì C2

tanh2 t C C A

Daniel Chung

9307/22/2004

Other cosmic rays

Ó Gamma rays, radiowaves, antimatter,...

Ó HEAT shows an “excess” of positrons at 10 GeV.

Ù Explanation in terms of LSPs speculative

ä Greater uncertainty in modelling (as much as 103)

ä Need a better dark matter distribution of the galaxy (perhaps by lensing?)

Daniel Chung

9407/22/2004

Summary of LSP

å In some region of parameter space (large higgsino component and LSP heavy), the only detection method:

å Even if LSP is not the dominant CDM (say 1%), direct detectors and neutrino telescopes can detect CDM.

æ æèç é é

æ æ ç é Z

Daniel Chung

9507/22/2004

More Opinions

Ù string theory (we still do not have the standard model)Ù brane world & large extra dimensions (too arbitrary)Ù moduli problem (good guidance to restricting string theory related speculations); above is a subsetÙ long distance modifications of gravity (surprisingly difficult)Ù self-interacting dark matter (better simulations)Ù CMB and inflation (no connection to SM yet)Ù Self-tuning cosmological constant (unsuccessful thus far)Ù New aspects of reheating (curvature perturb. not frozen)Ù Transplanckian physics (ill motivated)

Daniel Chung

9607/22/2004

Outlook

Ù Supersymmetry is probably the best motivated.ê 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.ê MSSM EW baryogenesis almost ruled out. A good example of how collider data affects cosmology.ê Neutrinos and leptogenesis look promising. (Still plagued by gravitino progblem within SUSY.)ê As the scorecard suggests, there is much to still connect.ê CMB physics (polarization) will tell us more about inflation, but still needs connection to particle physics. Hopefully will not remain an island.

Daniel Chung

9707/22/2004