Practical Applications of Field Theory in Cosmology

Daniel J. H. Chung(UW – Madison)

(PASI 2006)

10/25/2006

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

210/25/2006

Plan

� Lecture 1

� Basic Intro to cosmology

� Fundamental problems

� Inflation

� Lecture 2

� Baryogenesis/Leptogenesis

� Dark Energy

� Outlook

Daniel Chung

310/25/2006

� 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

4

Selected General Background10/25/2006

The Very Basic

Daniel Chung

510/25/2006

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

610/25/2006

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

710/25/2006

Where Field Theory Enters

Einstein equations (Equivalence principle)

Boltzmann Equations

R �� g � � 12

g �� R g �� � 8 � T �� g ��

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

8

[De Groot, Van Leeuwen, Van Weert 1980]

10/25/2006

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 2 d

!2 r 2 sin 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

910/25/2006

Background

/ Einstein

/ Notation and examples

H 0 a ' ta t

H 2 1 ka 2

2 3

3

M pl

8 42 1

G N 8 42 1

2 H ' t 5 3 H 2 5 ka 2

67 P

a ' ' ta t

6 7 16

8 5 3 Pcombine:

alternate:

ordinary matter: decelerate

d 8 a 3 67 P d a 3 perfect fluid energy conservationand adiabatic flow

9 : 1a 3

, w ; 0 < a : t 2

=

3

9 : 1a 4

, w ; 13

< a : t 1

=

2

w 0 P 8 6 equation of state Matter dominated

Radiation dominated

expansion rate

Daniel Chung

1010/25/2006

Basic standard 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 A 70

Daniel Chung

1110/25/2006

Explicit Stress-Energy Components

B Popular Model

CED F CED t 0

a 0

a

4

P D FCED

3

G

tot

H GEI J GEK J Gb

J G

c

J GML

N

X

O PX

Q Pc

R

b , c

S R

b , c t 0

a 0

a

3

P b , c

S 0

TI U 10

V5W

b

X 0.044

Y

c

Z 0.22

[]\ ^ 0.73R`_ S R_ t 0 P _ acb R`_

W

tot

X 1.0

dfe g d e t 0

a 0

a

3

P e g 0

Wih j 0.01

noninteracting particle

energy conservation

negative pressure

P tot

H P I J P K J P b

J P c

J P L

k

c

l 3 H 02m 10

n 46 GeV 4

Daniel Chung

1210/25/2006

Temperature of the Universe

o Equilibrium Thermodynamics

o Photon Temperature = “temperature of universe”

o Entropy (conservation gives T history)

n p g2 q 3

r

f E d 3 p

st g2 u 3

v

f E E d 3 p

P t g2 u 3

v p 2

3 Ef E d 3 p

E w p 2 x m 2

f E y 1

expE z {

T

| 1

}�~ � � 230

2T 4

s � � � pT

� 2 � 245

g * s T T 3g * T � g * S T

}R

� � 230

g * T T 4

Early Universe (T>1 MeV)

today (for massless neutrinos): T � 2.34 � 10

� 4 eV g * S

� 3.9 g *

� 3.36

g * T � 300 GeV � 107SM only:

photons dominate and can be measured!g � � 2 �

can fall exponentiallywith temperature

Daniel Chung

1310/25/2006

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

1410/25/2006

BBN

Start with at .{ n , � , e , p }Produce by the time temperature cooled to .{ D , He3 , He4 } T � 1 MeV

T � 10 MeV

(astro-ph/9905320, 0302431)

n � � p e

Boltzmann equation:

�H

� 1

n X

� n Xeq� g X

2   3

¡ d 3 p

expE ¢ £

T¤ 1

¥ g X

m X T

2  

3

¦

2

exp ¢ m X

¢ £ §

T

short distance reaction rate (e.g. )

1a 3

d n X a 3

dt

¨© ª

X a « ij v n Xeq n a

eq n X n a

n Xeq n a

eq

© n i n j

n ieq n j

eq

main intuition: in equilibrium

until ¬®­ ¯

X a ° ij v na

Various binding energies important!n n

eq

n peq

± e ²

e

³ ²®´ µ

T e

³Q µ

T Q ¶ m n

© m p

¨ 1.293

gravity

MeVe.g.

freeze out

Daniel Chung

1510/25/2006

Chain of events

n · ¸ p en ¸ p e ·

e n ¸ p ·

n N

¹ n N

º n p

º A n AX A

¹ n A A

n N

A=# neutron + # proton

a) T » 10 MeV X n¼ 1

2,X p

¼ 12

n ½ p e ·

b) T ¾ 1 MeV X n

¿ np

¿ exp ÀQ Á

T F

 16

depletes more X n

à 17

X p

Ä 67

n p ¸ D Åc) T Æ 0.1 MeV stops dissociating D

D D ¸ n He3

He3 D ¸ n He4

D n ¸ Å He3

p D ¸ n He3

H3 D ¸ n He4

Because has larger binding energy than other nuclei, most remainingneutrons go into

He4

He4

contains info on gravity

B He4 Ç 28.3 MeV , B He3 Ç 7.72 MeV

Y p

¹ 4 nHe4

nb

¿ 2 e

È 2 É

t D

1 º exp Q

Á

T F

Daniel Chung

1610/25/2006

ObservationHe4 Observe low metallicity HII regions hot enough to photoinize He.

Typically dwarf galaxies are favored w/ z< 0.1Plot as a function of z and look for plateau as Y

He4 z z Ê 0D Relatively small binding energy + rate at which out of equilib

freeze out occurs faster for BBN than in starsmore produced in BBN than in stars

measure high redshift dilute clouds in intergalactic medium (IGM)

n p Ë D ÌBecause determines D abundance while n+p makesup the baryons, D abundance is sensitive to baryon photon ratio:

n D

nb

Í Î

bT

m p

3

Ï

2

e B D

Ï

T

Daniel Chung

1710/25/2006

Constraints on High Energy Theory

Ð Constraints on high energy theory: Recall that freeze out condition:

Ñ

H

Ò 1 short distance reaction rate (e.g. ) Ó®Ô Õ

X a Ö ij vgravityfreeze out

new physics with light degrees of freedom increasedH 2 × Ø

3more neutrons more producedHe4

Bound typically expressed as variation in the number of light Ù

at , 2 Ú(could be any other thermal light particles)

[astro-ph/0408033]

bound on d.o.f.

Daniel Chung

1810/25/2006

Basic problems

Daniel Chung

1910/25/2006

Problems of cosmology

Û What is the composition of dark energy?

Û What is the composition of CDM?

Û Why more baryons than antibaryons?

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

Û Classical singularities of general relativity?

Û Why is the observed cosmological constant small when SM says it should be big?

Û Origin of ultra-high energy cosmic rays?

Daniel Chung

2010/25/2006

What is dark energy?

Recall that normal gas of matter has positive pressure.

Field energy can have negative pressure (like inflation).

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

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

P

Ý

x Þ 13

ß

N

Ý

p N2

Ý

p N2 à m N

2

á 3

Ý

x âÝ

x N

ã

aa

ä å 4 æ

3 M pl2

ç è 3P é 0 ê P ëíì 1

î

3 ï

P ð 12

dñ

dt

2ò V

ñ

Daniel Chung

2110/25/2006

What is cold dark matter?

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

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

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

ó Lensing (gravitational deflection of light from compact objects) agrees with this picture. (Dodelson's lecture)

Û CDM neutrinos would overclose the universe.

Û Physics beyond the standard model necessary!

Daniel Chung

22

(Kusenko's lecture)

10/25/2006

Why more baryons than antibaryons?

ô The absorption spectra measurements, CMB, and BBN agree

ô Naturalness of small dimensionless number?

ô According to SM, at T > 100 GeV.

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

nB

n õö 10÷18

nB

n õø 10

÷ 10

Daniel Chung

2310/25/2006

What is the inflaton?

ù CMB data looks like that expected from inflation

i.e.

1. “no” spatial curvature

2. scale invariant spectra on “superhorizon” scales

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

Daniel Chung

2410/25/2006

Singularities of GR

ú 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)

ú Evidence for black holes exist. Is there a singularity behind the apparent horizon?

ú Big bang singularity naively exists: i.e.

R ûü 6a ' ' t

a t

ý a ' ta t

2

ý ka 2 t

þ 1 ÿ

t 2 ��

Daniel Chung

2510/25/2006

A small cosmological constant?

� Due to SM quantum fluctuations

� On the other hand we observe

�� � � M 4

� � � 10� 12 GeV 4

� Possible values of

Planck scale 1018 GeV

GUT scale 1016 GeV

See-saw scale 1013 GeV

M

Daniel Chung

2610/25/2006

Ultra-high energy cosmic rays

There is a GZK cutoff

at 1019.8 eV due to efficient

Proton cannot ravel more

than 40 Mpc.

Events above 1019.8 eV measured (possibly).

No energetic extragalactic sources within 40 Mpc.

Primary? Source & acceleration mechanism?� p � p

Daniel Chung

2710/25/2006

Inflation

Daniel Chung

2810/25/2006

Motivation: Mostly initial condition problems.

Inflation

kH 2 a 2

� ��� 1Friedmann:

today:k

H 02 a 0

2

� �0

� 1 � 10

� 2

early universe: kH e

2 a e2

� kH 0

2 a 02

a r

a 0

a e

a r

2 � 10

� 2 10

� 4 10

� 6 2 � 10

�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

2910/25/2006

More Motivation

“singularity”

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

causal signals travel beyond naïve horizon

d H

� a t

�

0

t dt 'a t '

� t

1 � 23 1 � w

naïve horizon (with ):

real singularity

w ��� 1

�

3

� 1H

“inside horizon”

“outside horizon”

Daniel Chung

3010/25/2006

Unwanted Relics

G 1

G 2

... SU 3 c

! SU 2 L

! U 1 Y

G 1

Monopoles arise whenever "

2 G i

#

G j

$ In M

% H 3 % T c6 &

M pl3

n M&

s % T c3

M pl3

% 1014

1019

3

% 10

' 15

mM

( 1016 GeV )

M

( 1011

3. Unobserved relic problem

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

unacceptably large!

Daniel Chung

3110/25/2006

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

* Flat patch becomes the entire universe (solves flatness)

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

* Dilutes unwanted relics

* Prediction: scale invariant density perturbations

Inflationds 2 + g, - dx

,

dx

- + dt 2 . a 2 t dx i dx j /

ij

d H

+ a t

0

0

t dt 'a t '

ddt

x a1

1

H

2 0 3 d 2 ad t 2

2 0

causal signals travel beyond naïve horizon

4655 7 1

2 8 39

d 3 k

4

k e

: i k ; x power: /=<<

hor

> k 3

?

2

/

k

2 @ > 10

A 5

x B comoving coordinate separation

Daniel Chung

3210/25/2006

Qualitative description of inflaton

How to choose the potential and initial conditions?

C for about 60 e-folds.

C Inflation must end.

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

C After inflation ends, the universe must reheat to .

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

Action: S D E

d 4 x F g F 12

R G 12

g

HI J H K JI K F V K

single field inflationary models:

d 2 adt 2

L 0 a t f

a t iM e N efold

KT L 10 MeV

Daniel Chung

3310/25/2006

Magic of negative pressure

N Horizon problem

N 60 efolds desired:

d 2 adt 2

O

a P Q 4 R

3 M pl2

S T 3P U 0 V P WYX 1

Z

3 [ (just like dark energy)

[\ 12

d

]

dt

2^ V

]

P P 12

d

_dt

2 Q V _

V d

]

dt

2 W V ]

` d 2 a

dt 2

b H da

dtslow roll inflation

d adt

Z

a\ H V a c ed

dt H

Daniel Chung

3410/25/2006

Quantitative Single FieldSlow Roll approximation

e Negative Pressure and 60 e-folding

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

e Density perturbation amplitude:

f g 12

V '

h

V

2

ij d H

dtH 2

k 1 l m V ' '

n

V

o 1 Nh

t i

g pq

t i

q

t f d

h

2 f r 60

s t

t f

u 1 Vn

min

v 0

scale invariance nearly automatic! 2 w x

60

y 6 z x

60

{ 0.2

indicates source of fine tuning

3 Hd

n

dt

v}| V '

n H 2~ V3

never Planckian

P k

�i V24 � 2 f h

60

� 10

� 5

Daniel Chung

3510/25/2006

Standard Reheating

� Inflaton field decays: e.g.

�

t2 �� 3H � �

tot

�t

�� m 2� �tot2

4

��� 0

L i

�� �� � �

�tot

� � �m 2

m

L � 12

�� 2 � m 2� 2 � L i

��� � 12

�t

� 2� m 2 � 2 � 2 �

4 � m 2

�

t

� 2

2

� m 2 � 22

use following approx:

�t

�R

� 4 H �

R

� �

tot

����

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

3610/25/2006

Why 60 efolds?

¤ Largest scale that we see homogeneous and isotropic:

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

L � a 0

¥

dx � a 0

¥

a dec

a 0 daH a 2

¦ a 0

¥

a dec

a 0 daH 0 a 0

§

a 3

¨

2 a 2

¦ 2H 0

© a 0 X

1H I

ª X a I

« 1H I

ª a 0 X

La I

a 0

sufficiently small

a I

a 0

¬ a I

a e

a e

a 0

­ e ® N a e

a 0max

a e

a 0

¯ a RH

a 0

° g * S t RH

g * S t 0

1

¨

3

T 0

T RH

¯ T 0

T RH

lnT RH

T 0

± 12

ln

²

R0

³ 60 ± ln T RH

1015 GeV

´ N

need enough efolds

H I

¯ T RH2

3

(also for curvature)

Daniel Chung

3710/25/2006

Single Scalar Field ComputationAction: S µ ¶

d 4 x · g · 12

R ¸ 12

g

¹º» ¹ ¼» º ¼ · V ¼gauge degree of freedom: Freedom of slicing the spacetime (splitting perturbed versus unperturbed)

½¿¾ ½

0

À Á Â ½

xperturb :

gÃ Ä Å gà Ä0 Æ Ç a 2 2

È É Êi B

É Ê

i B 2 Ë Ìij

É Êi

Êj E

v Í a ÎÏ ÐÏ

0 ' Ñ

a '

Òa

Óinfinitesimally gauge invariant (same as longitudinal gauge)

dx

Ã

dx

Ägà Ä0 ° a 2 Ô d Ô 2Õ d x 2

ÖØ× Õ a '

Ù

aa

Ú

0 'v

S ° Û

d Ô d 3 x 12

v ' 2Õ Ü

v 2 Ý a '

Ù

aa

Ú

0 '

Þàß 2 a

Ú

'a '

Ù

av 2

' á âäã

Seed formation of galaxies!

constant on constant hypersurface (comoving)

¼Ö ° å

Daniel Chung

3810/25/2006

Power Spectrumquantize: v æ , x ç è d 3 k

2 é 3

ê

2a k v k

æ ë aì kdagger v k

* æ e i k í x

a k , a k ' dagger ç î 3 k ï k '

ðñ , x

ðñ , y ò ó dkk

sin k x ô yk x ô y P õ P ö ÷ k 3

2 ø 2a '

ù

aa

ú

0 '

2

v k2

v k ' ' ë k 2 ï 2 ë p

û2v k

ç 0p ü 3 3 ýÿþ �

v k

��� �� � e

� i k �

2 kboundary condition:

v k

ç é2

ï æ H �1 ï k æ ei

�

212

� � 9 � 4 p2

P k

� � V24 � 2� �

60

� 10

ì 5

��� � a '�

aa

�0 '

v

H �1 � k � �k

�aH � 0

� i 2�� k � 3

�

2

Daniel Chung

3910/25/2006

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

!

aa

"

0 '

#%$ 2 a

"0 '

a '&

av k

' 0v k

� A k

a

(

0 '

a '

)

agrowing mode:

k

*

a H + 0

,

k

a

"

0 '

a '

&

a

- a k v k

. / a0 kdagger v k

* .

1

k , 1

ldagger 2 0

3

k

24 1

k

lim k

5

aH 6 0 7

k are classical random variables!

are constants8

k

Constants on superhorizon scales!

Spectral index: P 9 : k n s

0 1

n s

; 1 < 2 = ; 6 >

d n s

d ln k- 16 ? . 24 ? 2 2 @ ACB V ' V ' ' '

V 2

Shape of the potential is given by nS k

Running of spectral index measurement = measuring potential

Daniel Chung

4010/25/2006

Gravity waves

Tensor perturbations: D

gE FT G 0 00 h ij

P T k H k 3

I2 h + k2 J h K k 2 L k n T

M 1

P T

N 8 H 2

2 O 2

N 16 P P Q

nT

R 1 G R 16 S G R r T

8

r U P T

P R

Consistency relation can rule outsingle field inflation!

In multifield inflation (more realistic):

1 V nT

W r X

8

Daniel Chung

41

(n.b. Some people use theconvention )P T

Y k n T

Z nT

[ r \

8

10/25/2006

What is this good for?

]

t2 ^

0

_ ]

t R

1 _ R

]

t

^

0

_ k 2 c s2 ^

0

` F

^

l

a

2 l _ 1

b ^

0

_ c ad j l k afe a d _ ...

2l g 14 h C l

i 12 h 2

j d kk

k 3 kl

2

2l g 1

fixes the boundary condition to the Boltzmann equation

c s2 ` 1

31

1 _ R R l 3 m

b

4 mon

prq s

TT

k i

l t 0

u k

l

v e i k w x P l k x ySee Dodelson's lecture for more details.

z{

0, x , | z{

0 x , | ' }lC l P l

|~ | '

kt i

� �t i

Daniel Chung

4210/25/2006

Why Is It Difficult to Test Slow-roll Inflation at Colliders?

Daniel Chung

43

Both

and

involve .

N

�

t i

� ��t i

�t f d

�

2 M p

� � 50

M p

� TeV

Order parameter is far away from TeV scale vacuum.

e.g. light fields during inflation heavy fields today���

� � P

� P k

�o� V24 � 2 � �

60

� 10� 5

10/25/2006

Inflationary Model

W � �

1

� ��

1

� �

2

� n � 2M pl

n � 2 � 2�

2

D � � 2� |

�

|2� |

�

|2 � | �

1 |2 � n | �

2 |2

|

�

|2 � | �

|2   � 2 ¡ �

1

� �2

� 0

U � ¢

12 | £ |2 |

�

|2 � ¢

22 |

�

|2n � 4M pl

2n � 4 |�

| 4 � g 2

2

� 2� |

�

|� |

�

|2 2 � soft terms

| � | ¤ n�

2�1

¥

M pl

n � 2 ¥Inflates while

[hep-ph/9405389, hep-ph/0507218]

If

¦¨§ M p

©«ª m 3

¬

2

M p

During inflation, ­ mass TeVª m 3

¬

2

ª® M pDuring inflation, mass­

Daniel Chung

4410/25/2006

Non-canonical Kinetic TermsDaniel Chung

45

Sound speed controls most inflationary observables.

S ¯ °

d 4 x

± 12

± g R ² ± g p X ,

³

X ´ 12

g

µ¶· µ ¸· ¶ ¸c s

2 ¯ ¹ ² p2 X

º

X

¹

¹ ¯ 2 X

º

X p ± p

P k

»½¼ 169

¾

64 ¿ 2 c s 1 À p Á ¾

Observables:

= 1 for canonical

Inflation condition:Xp

dpdX

 1 r ¼ à 8 c s nT

r ÄÅ 8 c s nT

Å 1

(other popular convention: )

10/25/2006

e.g. DBI Inflation

Æ Probe D3 brane moving in approx. AdS 3

Ç S 5

ÈÊÉ r

Ë¨Ì 'DBI

S Í Î 1g s

Ï

d 4 x Î g f

Ð Ñ1 1 Î f Ð

gÒÓ Ô Ò Ð ÔÓ ÐÕ V

Ð

fÖ× Ø

Ö 4Approximate warp factor:AdS 5

Ø× R 4

Ù' 2

V from RR and fields associated with compactification.

c s

Ú 1Û Í 1 Î f Ð d

Ð

dt

2 Ü 1 is possible.

[Leigh 89]

[hep-th/0404084]

Allows inflation even when is reaching the maximum possible“speed.”

d

Ö

dt

Daniel Chung

4610/25/2006

Non-Gaussianity

Ý

k 1

Ý

k 2

Ý

k 3

Þ 2 ß 3 à 3 k 1

á k 2

á k 3 P 3 k 1, k 2, k 3

Ý

k 1

Ý

k 2

Þ 2 ß 3 à 3 k 1

á k 2 P 2 k 1, k 2â

k i

ã k ä 3P n å k æ 3 n æ 1

Intuition: interactions of the inflaton field.

three-point function:

Before: computed 2-point function

çk è é

k ê k 2

3 a 2 d Hdt

ë

[e.g. astro-ph/0210603, hep-th/0404084, astro-ph/0506056, hep-th/0506236, hep-th/0605045]

Estimate: Consider the limit in which k 1ì k 2, k 3

ds 2í î dt 2 ï a 2 t e 2

ð

B x d x 2 ï ...intuitively, one mode is frozen and sets up background:

Ý

x 2

Ý

x 3 B

ñ Ý

e

ò

x 2

Ýe

òx 3

ñ Ýx 2

Ý

x 3

ó Ý

B

d

Ý

x 2

Ý

x 3

d

Ý ó ...three point function must be proportional to

Fourier transforming, one would expect

P 3 k 1, k 2,

ô k 2

ñ P k 1

d P 2 k 2,

ô k 2

d ln k 2

ó k 3

|k 3

õö k 2

ñ O ÷ P k 1 P k 2

Od ln c s

dt1H

P k 1

canonical

noncanon

Daniel Chung

4710/25/2006

Future Prospects

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

ø Polarization:

ø B polarization comes from tensor and lensing (contaminant as far as inflation is concerned).ø B polarization has no contribution from scalar perturbations.ø measuring tensor is important for checking consistency condition (to know if it really is inflation!)ø Unfortunately, typically less than 1% of the scalar spectrumø Nongaussianities

ø Isocurvature

ø Theoretical Problems

ù What is the inflaton? Are there truly natural models?ù Stability of de Sitter space and back reaction. ù More observables to experimentally ascertain inflation.

Daniel Chung

4810/25/2006

Baryogenesis

Daniel Chung

4910/25/2006

Observation

ú In solar system much more baryons than antibaryons

ú Dominance of matter clear on scales < 10 Mpc:

bound on from .

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

n p

û

n p

ü 3 ý 10

þ 4

n 4 He

ÿ

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

5010/25/2006

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

5110/25/2006

Illustration of Sakharov Criteria

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

� Branching ratios:

� Baryon produced:

� Out of equilibrium: otherwise, the other direction produces

r ��

X � a�

X

r ��

X � a�

X

1 � r ��

X � b�X

1 � r ��

X � b�

X

babb

“CP”:

“CP”:

�

B X� r ba

1 � r bb!B X

�" r ba

" 1" r bb!B � !

B X

# !

B X

� ba

" bb

B violation

r " r

CP violation

ba

$ bb r $ r

rephasing invariant

Daniel Chung

5210/25/2006

Boltzmann

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

% Simplification

% Chemical equilibrium of others:

% Kinetic equilibrium of all states:

p

& ''

x

& ( )+*, & p

*

p

, ''

p

& f x

&

, p

& - C f

.

t

/

d 3 p f 0 3 H

/

d 3 p f 1 / d 3 pE

C f n t 1 g2 2 3

/d 3 p f

g X

2 2 3

3 d 3 p X

E X

C f 14 3

d

5

X d

5

a d

5

b d5

c 2 2 4 6 4 p X

0 pa

4 pb

4 pc

7

M X 8 a 9 b 8 c2 f X f a 1 : f b 1 : f c

; M b 8 c 9 X 8 a2 f b f c 1 : f X 1 : f a

d

<

X

= g X

2 > 3

d 3 p X

2 E X

e.g. f b

1 f beq , f c

1 f ceq

e.g. f X

? F t f Xeq , f a

? A t f aeq

Daniel Chung

5310/25/2006

Interference

@ CP violation involves a complex parameter in the Lagrangian:

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

@

CP violation = interference of transition amplitudes :

L A m 2 B

12 C B

22 D m e i EGF

1

F

2

C e H i EF2

F1

I M 3 e i

JLK M a M a I e N i JLK M a M a C mLR2 e i

O B2

B1

C e H i O B

1* B

2*

P

phys

Q RTS UWV S X

M 2 Y M 1Z M 2 e i

[

phys 2 Y M 12 Z M 2

2 Z 2 \

M 1 M 2 e

] i [

phys

M CP 2 ^ M 1

I M 2 e

N i _

phys 2 ^ M 12 I M 2

2 I 2 `

M 1 M 2 e i

_

phys

Daniel Chung

54

M 1

a real

10/25/2006

Cutting

b Recall in the simple example

b Diagrammatically

c

B a c

B X

d c

B X

a ba

e bb

B violation

r e rCP violation

M 2 f M CP 2 ^ g

M 1 M 2 e i

h

phys f M 1 M 2 ei i h

phys

This is 0 unless develops an imaginary part due to virtual states going on shell.

+ interferes

Since the real part of this should be taken (which vanishes unless an internal line goes on shell):

Daniel Chung

55

M 2

M 1 M 2 e ih

phys

[for an example of usage, see hep-ph/0112360 ]

10/25/2006

10/25/2006

Thermal Leptogenesis

j Have only perturbatively significant B-L violating operators.

j Generate L as we have been discussing.

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

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

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

B k 8 N f

l 4 N H

22 N f

l 13 N H

B m L

Daniel Chung

57

[for review, e.g. hep-ph/0401240]

10/25/2006

Boltzmann Eq.

zY neq

d Y n

dz

o p 1H a , i , j , ...

Y n Y a ...

Y neq Y aeq ...

q eq r s a s ... t i s j s ...

u Y i Y j ...

Y ieq Y j

eq ...

v eq i w j w ... x y w a w ...

z z m n

T q eq o K 1 z

K 2 z

{

decay

scatter q eq r s a t i s j s ... o T64 | 4 n }eq

~

m � � m a2

�

ds � s s K 1s

T

� s z 2 s � m n � m a2 s � m n � m a

2

s

� s

(same equation is applicable to dark matter.)

o � v neq

Y i

� n i

s

Daniel Chung

5810/25/2006

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

3

�

2

e

� M �

T c m� � 10

� 1 eV , M � 109 GeV , g *

� 100, m W

� 100 GeV

MT c

3�

2

e

� M �

T c � 0.1(out of equilibrium temperature)

� 10

� 10

Daniel Chung

59

Yukawa information assuming see-saw.

Lepton number generated

10/25/2006

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/0303065

� hep-ph/0208043

� hep-ph/0006119

� hep-ph/9901362

� hep-ph/9901312

� hep-ph/9802240

Daniel Chung

6010/25/2006

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 � T c

� m h

T c

Daniel Chung

6110/25/2006

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!

Daniel Chung

6210/25/2006

Aspects of MSSM

� L soft

� 12

M 3 g g � M 2 w w � M 1 B B

 ¡ ¢ £ ¤ b H d

¢

H u

£ ¤ H u

¢

Q i

£

A u ij U jc   H d Q i A d D j

c   H d L i A e ijE j

c   h.c.

¥ Q i

¦

m Q ij

2 Q j

¦ * ¥ L i

¦

m L ij

2 L j

¦ * ¥ U ic * m U 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

§ ¨ 12

© + © - 0 X T

X 0

© +© -

Chargino mass matrix

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

ª +-« W +-

H u+-

W ¬ ¡ ¢ £ ¤ H u

¢

Q i

£

Y uij U j

c   H d

¢

Q i

£

Y dij D j

c   H d¢

L i

£Y e

ij E jc ¤ ­ 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

cL 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 ° M 2 2 M W sin

±

2 M W sin

± ²Daniel Chung

6310/25/2006

Sakharov conditions

1) Baryon number violation: SU(2) sphaleron

e.g. 1 generation

O B ³ L ´ C hL 1h L 2

w L4

iq L i

q L iq L i

l L i

u L

µ d L d L

¶

e

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

·

EW

¸ k ¹

W

¹

W4 T 4 k º

W

» O 1unbroken phase:

broken phase: ¼¾½ 2.8 ¿ 105 T 4

À

W

4 Á

4

 à 7 exp Ä Ã 10

Å 4 ÆÇ Æ 10

Å 1

ÃÉÈ E sph T

Ê

T

E sph

Ë 2 m W¹

W

Ë 8 Ì Hg

Daniel Chung

64

Í

d 4 x Tr F F + Higgs

10/25/2006

Sakharov conditions

2) CP violation:

In SM:

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

Î

M 2

Ï

Ð

L Ñ 12

M 2 W Rdagger W L

ÒÔÓ h Rdagger hL

Ò h.c.

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

Õ

CP

Ö g W

2 m W

12

m t2 × m u

2 m t2 × m c

2 m c2 × m u

2 m b2 × m d

2 m b2 × m s

2 m s2 × m d

2 j Ø 10

Ù 22

j Ú Û

V cs V us* V ud V cd

* Ü 10

Ý 4

Too small.

Daniel Chung

6510/25/2006

Out of equilibrium3) Phase transition:

Þ T>100 GeV, symmetry is restored.

Þ T<100 GeV, symmetry broken.H

V H ß D T 2 à T 02 H 2 à E T H 3 á

â

T4

H 4

H

V H

z

H ß z

H ã 0

ä äå

w

(Attractive, because almost no new assumption!)

T æ T c

T ç T c

Daniel Chung

6610/25/2006

EW B creation step 1

1. Pick up CP/chiral asymmetry

H ß z H ã 0è

wn bL é n b

L ê 0

nb

ë nb

ì n bL í nb

R ë n bL ë nb

R ì 0

q

sphalerons activesphalerons inactive

B ß 0e.g. 1 generation

u L u R

Daniel Chung

6710/25/2006

EW B creation step 2

H ß z H ã 0î

w

ï

n bL ð n b

L

nb

ñ n b

ì nbL ò n b

R ñ n bL ñ n b

R ó 0

q

sphalerons active

sphalerons inactive

u L

ô d L d L

õ

e

u R

ö u R

u L d L

õ

e

B ÷ 1B ß 0

e.g. 1 generation

Daniel Chung

6810/25/2006

EW B creation step 3

H ø z H ù 0

ú

w

nb

û n b

ì nbL ü n b

R û n bL û nb

R ý 0

q sphalerons active

sphalerons inactive

Daniel Chung

6910/25/2006

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

7010/25/2006

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 nh

� �

Y

nQ

k Q

� nT

k T

� n H

��� n h

k H� �

h

n H

k H

� S H

scattering source

S H

� S Q

nB

c 1

�

EW

v w

� �0

dz nL 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

7110/25/2006

Sufficient CP violation

� Estimate

� Importance

� Large top Yukawa coupling

� Higgs mediated CP asymmetry

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

� � k �

w

�

w4

g s

�

CP f � 10

� 10 �w4 � 10

� 6 g s

� 10

O B � 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

7210/25/2006

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 1 0.05 [Chang et al 2002; Pilaftsis 2002]

Daniel Chung

7310/25/2006

22

22

22

22

3 strong enough phase transition

3 charge and color breaking minima

3 if (suggestive) 3 sufficient diffusion

3 sufficient CP violation

3 sufficient density processed by the sphaleron

0.2 mQ

4 A t

4 0.4 mQ

tan

576 4

mQ

6 1TeV

120 GeV 8 m 9

t R

8 mt

: , M 1,2

; mQ

< = M 1,2

>

T c2 ? 0.05

: , M 1,2

; 2T c

mh

@ 115GeV

mh

6 114 GeV

sketch of parameter regionDaniel Chung

7410/25/2006

Dark Energy

Daniel Chung

75

a ' ' ta t

A B 16

C D 3 P E 0

FG g2 H 3

If E E d 3 p

P G g2 H 3

I p 2

3 Ef E d 3 p

Cannot be particles:

Can be cosmological constant: JK JML K const P K N JML

10/25/2006

Dark Energy Problems

O Why is the cosmological constant small.

O Why is the dark energy domination time period nearly coinciding with the epoch of structure formation?

O Is there a light ( GeV) scalar field associated with dark energy? (e.g. another inflaton, just much lighter)

O What are prospects for measuring dark energy?

10

P 42

Daniel Chung

76

QMR S 10

T 12 GeV 4

10/25/2006

Popular Proposals for CC solution

U Back reaction due to particle creation

V Recent progress in resummation techniques, but outcome still unclear.

U Bottom-up stable tuning approach

V Abott's solution to CC: washboard potential protected by a noncompact global symmetry

W Problem with empty/cold universe may be fixed using supersymmetry and assumptions about nonrenormalizable operatorsW Predictions may include modified gravity and absence of axion detectionU Landscape/anthropic arguments

Daniel Chung

7710/25/2006

Example Daniel Chung

78

a) Dilaton (scalar-tensor gravity) – natural in string theory b) Non-compact global symmetry (e.g. shift symmetry) c) Supersymmetry d) Assumption about non-renormalizable operators

Improve Abbott's “solution”: End up with an empty universe!

Itzhaki's ingredients:

[hep-th/0604190]

problem:

arbitrarily small slopeprotected by symmetry

U X 12

R Y m 2 Z 2Use Dilatonic coupling of the form to obtaine

[ \ 2R

idea:

This leads to a precise relationship between the cosmological constant energy density and at the onset of reheating phase transition.

m 2

R ] 4 V

^ precision determined by slope

10/25/2006

Example continued

Itzhaki's Point: Tuning for reheating DIFFERENT from CC problem

What about the rest of the cosmological constant?

U X 12

R _ m 2 ` 2 R ] 4 V

a

Energy available for reheating? b

RH

c 14

m 2 M p2

m

m

Tune and coupling to ensure acceptable CC at minimum of the phase transition vacuum.

i.e. if , a relationship between and .g

` 4 g

Isn't this tuning the same as the original CC tuning?

Can be protected by SUSY up to SUSY breaking effects of

No, since now, we know exactly what the value of the CC to cancel! (Thisknowledge was provided to us by the Abott's mechanism.)

Isn't this tuning the same as the usual N=1 SUSY protection of CC? M S2

M p

4

No, SUSY breaking generically leads to energy densities and not densities.M S4

M S2

M p

10/25/2006

Problems with Proposal

U Sensitive to assumptions about nonrenrormalizable operators:

U Coupling to SM and reheating scenario not completed (in progress)

U Implications:

d Dilaton -> modifications of gravity near millimeter.

d Low scale scale SUSY breaking.

d Low scale inflation

d axion vev may be fixed (allowing larger Peccei Quinn breaking scales).

tree level stable and predictive CC without UV completionloop corrections

However, does there exist any top don mod which give desired restrictions on the nonrenormalizable operators?

10/25/2006

Tracker Model

e Energy density follows the radiation energy density until a transition to matter domination occurs

d 2 f

dt 2

g 3 H

fih 2

j k 6

f3 l 0e.g.

m npo q j k

M P2

aa Q

r 3 1 s w B

t2

background energy density enters here

n

B

u aa Q

r 3 1 s w B

decreases more slowly than

H 2v w

B

x w

Q

y

3 M p2

start with dominant

n

B

w z {| 1 } 2 1 } w B

4

~ { M p8

3 1 } w B

aa Q

3 1 � w B

�

4large field var:

��� 10 MeV

Daniel Chung

81

V { � � 6

~ 2

Controls the time of onset of quint domination.

Why is the dark energy domination time period nearly coinciding with the epoch of structure formation?

10/25/2006

Problems

� Light Mass: otherwise Q sits at the min of potentialForm of the potential is difficult to protect in QFTAll operators not protected by symmetries should appear in the EFT.

� pheno. problems with Planck mass field variatione.g.

W � N c

� N f

� 3N c

� N f

�

N c

� N f

det Q i Q j1

�

N c

� N f

rad. mass terms

e.g.

m 2 � 2

Q i Q j

� � 2 �ji

c�

M p

n

Tr F

��

F � � gauge coupling timevariation

Also, large vev variation cutoff physics is important lack of predictibility from theory

�7� M p8

3 1 � w B

aa Q

3 1 � w B

�

4

[hep-ph/0005037]

Daniel Chung

8210/25/2006

Tracking Problems

� Tracking requires some tuning of intital conditions

phase portraitof attractors V � � � 4 ��

��

y � V�x � 1

6 M p

d

�

d ln a

(astro-ph/0312450, astro-ph/0403526)

Daniel Chung

8310/25/2006

Other Properties Quintessence

� Lightness of quintessence: like photons, do not cluster appreciably

� CMB sensitivity requires at least few percent level contribution of quintessence at z=1000. Certainly not true for cosmo constant.

� Just like inflatons, non-canonical kinetic terms can change

� Suppression of CMB multipoles on long wavelength is possible with quintessence with . (e.g. astro-ph/0301284)

� Because quintessence needs to be weakly coupled (gravitational strength) to protect its light mass, it cannot be produced at colliders.

c s

� 1

c s.

Daniel Chung

8410/25/2006

Distinguishing CC and Quintessence

� Equation of state

  Clustering and lensing

  Supernovae or any other standard candles

  Integrated Sachs-Wolfe effect (ISW)

  Last scattering surface CMB effects

� Sound speed effects for non-canonical Q

� Interactions of Q with dark matter (DM)

  DM at colliders + DM direct detection + effects of Q during DM freeze out [e.g. astro-ph/0207396]

[e.g. astro-ph/0301284]

Daniel Chung

8510/25/2006

Collaborative score card

¡

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?

¢ What is the dark energy?

¡

What is the 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?

with SUSY

with PQ

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

Daniel Chung

8610/25/2006

OutlookDaniel Chung

87

  Inflation non-trivial tests: correlation of observables

£ B-modes: gravity waves£ running spectral index: measurement of CMB down to short scales£ non-gaussianities: 21-cm line  LHC is turning on: Higgs most likely to be measured

£ unprecedented opportunity for testing EW bgenesis£ leptogenesis is comparatively more difficult to test  DE being non-zero opens up new views

£ e.g. axion PQ scale can be lowered – connection with string theory?£ e.g. inflationary model must be low scale model£ e.g. implications for near-millimeter scale modification of gravity£ e.g. lowscale SUSY breakng  Exciting opportunities to connect HE theory with cosmology sure to be enhanced with LHC results!

10/25/2006