Ewan Stewart- A Minimal Supersymmetric Cosmological Model

8/3/2019 Ewan Stewart- A Minimal Supersymmetric Cosmological Model

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A Minimal Supersymmetric Cosmological Model

Ewan Stewart

KAIST

YKIS 2010 Symposium:Cosmology - The Next Generation

28 June 2010YITP, Kyoto University

D Jeong, K Kadota, W-I Park, EDS hep-ph/0406136G N Felder, H Kim, W-I Park, EDS hep-ph/0703275

R Easther, J T Giblin, E A Lim, W-I Park, EDS arXiv:0801.4197S Kim, W-I Park, EDS arXiv:0807.3607
http://cosmology.kaist.ac.kr/http://www2.yukawa.kyoto-u.ac.jp/~ykis2010/YKIS2010/http://www2.yukawa.kyoto-u.ac.jp/~ykis2010/YKIS2010/http://arxiv.org/pdf/hep-ph/0406136http://arxiv.org/pdf/hep-ph/0703275http://arxiv.org/pdf/0801.4197http://arxiv.org/pdf/0807.3607http://arxiv.org/pdf/0807.3607http://arxiv.org/pdf/0801.4197http://arxiv.org/pdf/hep-ph/0703275http://arxiv.org/pdf/hep-ph/0406136http://www2.yukawa.kyoto-u.ac.jp/~ykis2010/YKIS2010/http://www2.yukawa.kyoto-u.ac.jp/~ykis2010/YKIS2010/http://cosmology.kaist.ac.kr/http://find/http://goback/


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Standard model of cosmology(density)1/4

time

mPl

1011GeV

103GeV

100 keV

10K

tPl

1028 s

1013 s

10min

1010 yr

inflationdensity perturbationsgravitational waves?

R decay matter/antimatter?

electroweak transition matter/antimatter?neutralino freeze out neutralino dark matter?

QCD transition axion dark matter?

nucleosynthesis light elements

atom formation microwave backgroundgalaxy formation galaxies

vacuum energy dominates acceleration
http://find/


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Moduli and gravitinos

Moduli are cosmologically dangerous. Nucleosynthesis constrains

ns 1012
http://find/


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ns 1012

In the early universe

H2 (

1)2
http://find/


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ns 1012


H2 (

1)2

m2susy (0)2

MPl
http://find/


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ns 1012


m2susy (0)2

MPl

ns 107

Moduli generated: H msusy
http://find/


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ns 1012


m2susy (0)2

MPl

ns 107


slow-roll inflation: H minflaton msusy
http://find/


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ns 1012


m2susy (0)2

MPl

ns 107


after

slow-roll inflation: H minflaton msusy
http://find/


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time

mPl

1011GeV

103GeV

100 keV

10K

tPl

1028 s

1013 s

10min

1010 yr

inflation

density perturbations

gravitational waves?






http://find/


11/91


time

mPl

1011GeV

103GeV

100 keV

10K

tPl

1028 s

1013 s

10min

1010 yr

inflation

density perturbations

gravitational waves?


moduli, gravitinos, . . . disaster





http://find/


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Minimal Supersymmetric Standard Model

W = uQHuu+ dQHdd+ eLHde+ HuHd
http://find/


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But

?
http://find/


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But

?

neutrino masses?
http://find/


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But

?

neutrino masses?

strong CP?
http://find/


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Minimal Supersymmetric Cosmological Model

W = uQHuu+ dQHdd+ eLHde+1

2 (LHu)

2+

2HuHd+
http://find/


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2 (LHu)

2+

2HuHd+

MSSM

S C
http://find/


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2 (LHu)

2+

2HuHd+

MSSM neutrino masses

Mi i l S i C l i l M d l
http://find/


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2 (LHu)

2+

2HuHd+

MSSM neutrino masses MSSM -term

= 2

0

Mi i l S i C l i l M d l
http://find/


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2 (LHu)

2+

2HuHd+

MSSM neutrino masses MSSM -term drives m2 < 0

= 2

0

||

V

0

V0

Mi i l S t i C l i l M d l
http://find/


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2 (LHu)

2+

2HuHd+


axion = 2

0

||

V

0

V0

Th l i fl ti
http://find/


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Thermal inflation

|

|

V

0

V0

RADIATIONDOMINATION

The al i flatio
http://find/


23/91

Thermal inflation

|

|

V

0

V0THERMALINFLATION

Thermal inflation
http://find/


24/91

Thermal inflation

|

|

V

0

V0THERMALINFLATION

Thermal inflation
http://find/


25/91

Thermal inflation

|

|

V

0

V0

first orderphase transition

Thermal inflation
http://find/


26/91

Thermal inflation

|

|

V

0

V0

potential energyconverted to

particles

Thermal inflation
http://find/


27/91

Thermal inflation

|

|

V

0

V0MATTER

DOMINATION

Key properties of thermal inflation
http://find/


28/91


For0

1010 to 1012GeV

http://find/


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For0

1010 to 1012GeV

Large dilution

1020 = pre-existing moduli sufficiently diluted

http://find/


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For0

1010 to 1012GeV

Large dilution


Short duration

N 10 =primordial perturbationsfrom slow-roll inflation

preserved on large scales

http://find/


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For0

1010 to 1012GeV

Large dilution


Short duration

N 10 =primordial perturbationsfrom slow-roll inflation

preserved on large scales

Low energy scale

V1/40

106 to 107GeV = moduli regenerated withsufficiently small abundance

First order phase transition
http://find/


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First order phase transitionFirst order phase transition since 0 Tc m.

http://find/


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pFirst order phase transition since 0 Tc m. Typical bubble size

103 to 105 1

H 105 to 103 1

m

http://find/


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103 to 105 1

H 105 to 103 1

m

Flaton decays late

Td 10GeV||

103GeV2

1011GeV

0

http://find/


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103 to 105 1

H 105 to 103 1

m

Flaton decays late

Td 10GeV||

103GeV2

1011GeV

0 Gravitational waves generated with frequency

f 10Hz

/H

104

V0a

3c/da

3d

10

1/3V

1/40

106.5GeV

2/3Td

10GeV

1/3

http://find/


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103 to 105 1

H 105 to 103 1

m

Flaton decays late

Td 10GeV||

103GeV2

1011GeV


f 10Hz

/H

104

V0a

3c/da

3d

10

1/3V

1/40

106.5GeV

2/3Td

10GeV

1/3

and density

GW 1020

104

/H

2V0a

3c/da

3d

10

4/3106.5GeV

V1/40

4/3Td

10GeV

4/3

http://find/


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First order phase transition since 0 Tc m. Typical bubble size

103 to 105 1

H 105 to 103 1

m

Flaton decays late

Td 10GeV||

103GeV2

1011GeV


f 10Hz

/H

104

V0a

3c/da

3d

10

1/3

and density

GW 1020

104

/H

2V0a

3c/da

3d

10

4/31011GeV

0

2

Gravitational waves
http://find/


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f

Hz

GW

1010 105 100 105 10101040

1035

1030

1025

1020

1015

1010

105

PRIMORDIALINFLATION

INFLATIONPREHEATINGDECIGO

Gravitational waves
http://find/


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f

Hz

GW

1010 105 100 105 10101040

1035

1030

1025

1020

1015

1010

105

PRIMORDIALINFLATION

INFLATIONPREHEATING

DECIGO

Gravitational waves
http://find/


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f

Hz

GW

1010 105 100 105 10101040

1035

1030

1025

1020

1015

1010

105

PRIMORDIALINFLATION

INFLATIONPREHEATING

THERMALINFLATION

DECIGO

Baryogenesis
http://find/


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Key assumption

m2LHu =1

2 m2

L + m2

Hu < 0

Baryogenesis
http://find/


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Key assumption

m2LHu =1

2 m2

L + m2

Hu < 0Implies a dangerous non-MSSM vacuum with

LHu (109GeV)2

and

dQLd+ eLLe= LHu

eliminating the -term contribution to LHus mass squared.

LHu,QLd, LLe

V

0

our vacuum

deeper vacuum

Reduction
http://find/


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2 (LHu)

2 + 2HuHd +

Reduction
http://find/


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2 (LHu)

2 + 2HuHd +

L = l

e/2

, Hu = 0

hu

, Hd = hd

0

, e=e/2

u=

0 0 0

, Q=

0 0 0

d/

2 0 0

, d=

d/

2 0 0

= , = 0 , = 0

Potential
http://find/


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V0 + m2

L|l|2 m2Hu|hu|2 + m2Hd|hd|2 + m2d|d|2 + m2e|e|2 m2||2

+

1

2A l

2h2u 1

2Addhdd

2 12Aeehde

2 A2huhd + c.c.

+ lh2u2 + l2hu 2hd2 +

2hu + 12 dd2 + 12 ee22

+ |dhdd|2 + |ehde|2 + |2huhd|2

+ 12g2|hu|2 |hd|2 |l|2 + 1

2|d|2 + 1

2|e|22

Potential
http://find/


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V0 + m2


+

1

2A l

2h2u 1

2Addhdd

2 12Aeehde

2 A2huhd + c.c.

+ lh2u2 + l2hu 2hd2 +

2hu + 12 dd2 + 12 ee22


+ 12g2|hu|2 |hd|2 |l|2 + 1

2|d|2 + 1

2|e|22

drives thermal inflation

Potential
http://find/


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V0 + m2


+

1

2A l

2h2u 1

2Addhdd

2 12Aeehde

2 A2huhd + c.c.

+ lh2u2 + l2hu 2hd2 +

2hu + 12 dd2 + 12 ee22


+ 12g2|hu|2 |hd|2 |l|2 + 1

2|d|2 + 1

2|e|22

drives thermal inflation lhu rolls away

Potential
http://find/


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V0 + m2


+

1

2A l

2h2u 1

2Addhdd

2 12Aeehde

2 A2huhd + c.c.

+ lh2u2 + l2hu 2hd2 +

2hu + 12 dd2 + 12 ee22


+ 12g2|hu|2 |hd|2 |l|2 + 1

2|d|2 + 1

2|e|22


lhu stabilized

withfixed phase

Potential
http://find/


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V0 + m2


+

1

2A l

2h2u 1

2Addhdd

2 12Aeehde

2 A2huhd + c.c.

+ lh2u2 + l2hu 2hd2 +

2hu + 12 dd2 + 12 ee22


+ 12g2|hu|2 |hd|2 |l|2 + 12 |d|2 + 12 |e|2

2


lhu stabilized

withfixed phase

rolls away

Potential
http://find/


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V0 + m2


+

1

2A l

2h2u 1

2Addhdd

2 12Aeehde

2 A2huhd + c.c.

+ lh2u2 + l2hu 2hd2 +

2hu + 12 dd2 + 12 ee22


+ 12g2|hu|2 |hd|2 |l|2 + 12 |d|2 + 12 |e|2

2


lhu stabilized

withfixed phase

rolls away

hd forced out

Potential
http://find/


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V0 + m2


+

1

2A l

2h2u 1

2Addhdd

2 12Aeehde

2 A2huhd + c.c.

+ lh2u2 + l2hu 2hd2 +

2hu + 12 dd2 + 12 ee22


+ 12g2|hu|2 |hd|2 |l|2 + 12 |d|2 + 12 |e|2

2


lhu stabilized

withfixed phase

rolls away

hd forced out

d and eheld at origin

Potential
http://find/


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V0 + m2


+

1

2A l

2h2u 1

2Addhdd

2 12Aeehde

2 A2huhd + c.c.

+ lh2u2 + l2hu 2hd2 +

2hu + 12 dd2 + 12 ee22


+ 12g2|hu|2 |hd|2 |l|2 + 12 |d|2 + 12 |e|2

2


lhu stabilized

withfixed phase

rolls away

hd forced out


lhu returnswith

rotation

Potential

rolls away stabilized
http://find/


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V0 + m2

L|l|2 m2Hu|hu|2 + m2Hd|hd|2 + m2d|d|2 + m2e|e|2 + m2() ||2

+

1

2A l

2h2u 1

2Addhdd

2 12Aeehde

2 A2huhd + c.c.

+ lh2u2 + l2hu 2hd2 +

2hu + 12 dd2 + 12 ee22


+ 12g2|hu|2 |hd|2 |l|2 + 12 |d|2 + 12 |e|2

2


lhu stabilized

withfixed phase hd forced out


lhu returnswith

rotation

stabilizedm2(0) = m2(0)

Baryogenesis
http://find/


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MODULIDOMINATION

THERMALINFLATION

FLATONDOMINATION

RADIATIONDOMINATION

= 0

> 0

0

preheats

decays

huhd = 0

hd > 0 d= e= 0

lhu = 0

lhu > 0

brought back into origin with rotation

nL < 0preheating and thermal friction

NL conservedl, hu, hd decay

T > TEW nL nBdilution nB/s 1010

nucleosynthesis

Numerical simulation

Lattice 1283 box size = 200m1 Fourier modes
http://find/


55/91

Lattice 128 , box size = 200m , Fourier modes0.033m k 3.5m.

CP phase

arg (BA) =

20 CP+ CP0 +

20CP

Initial conditions

= 4m + l = l0 + l

hd = hd

Constraints

D = 2 with = 4.8 103l0j0 = 0

Algorithm Adaptive constrained gauge invariant leapfrog typealgorithm. Exactly conserves the constraints and charges,

and has good energy conservation.

Numerical simulationnL/nAD
http://find/


56/91

mt0 200 400 600 800 1000

0.15

0.1

0.05

0

0.05

0.1

0.15

Baryon asymmetry

n n n T
http://find/


57/91

nB

s nL

nAD

nAD

n

Td

m(0)

Baryon asymmetry

n n n T
http://find/


58/91

nB

s nL

nAD

nAD

n

Td

m(0)

Using

n m(0) 20 , m2(0) m2(0) , nAD mLHul20

l0 109GeV102 eV

m

mLHuTeV

and

Td 1GeV

1012GeV

0

||TeV

2gives

nB

s 1010

nL/nAD

102

1012GeV

0

3102 eV

m

||TeV

2101

mLHum(0)

2

Baryon asymmetry

nB nL nAD Td
http://find/


59/91

nB

s nL

nAD

nAD

n

Td

m(0)

Using

n m(0) 20 , m2(0) m2(0) , nAD mLHul20

l0 109GeV102 eV

m

mLHuTeV

and

Td 1GeV

1012GeV

0

||TeV

2gives

nB

s 1010

nL/nAD

102

1012GeV

0

3102 eV

m

||TeV

2101

mLHum(0)

2

which suggests0

1012GeV

Dark matter candidates

P i Q i
http://find/


60/91

Peccei-Quinn symmetry

W = uQHuu+ dQHdd+ eLHde+

1

2 (LHu)

2

+

2

HuHd +


P i Q i t DFSZ axion
http://find/


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1

2 (LHu)

2

+

2

HuHd +

DFSZ axion


Peccei Quinn symmetry DFSZ axion KSVZ axion
http://find/


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1

2 (LHu)

2

+

2

HuHd +

S S


http://find/


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1

2 (LHu)

2

+

2

HuHd +

Axion

ma 2QCDfa where fa =

2 0N

6.2 106 eV

1012GeV

fa


http://find/


64/91


W = u

QHu

u+ d

QHd

d+

e

LHd

e+

1

2 (LHu

)

2

+

2

Hu

Hd

+

Axion

ma 2QCDfa where fa =

2 0N

6.2 106 eV

1012GeV

fa

Axino

ma =1

162

2A

1 to 10GeV

Dark matter genesis
http://find/


65/91

thermal inflation

Dark matter genesis
http://find/


66/91

thermal inflation

flaton = saxino

matter domination

firstorder

phasetransition

Dark matter genesis
http://find/


67/91

thermal inflation

flaton = saxino

matter domination

firstorder

phasetransition

radiationdomination

decay

Dark matter genesis
http://find/


68/91

thermal inflation

flaton = saxino

matter domination

firstorder

phasetransition

radiationdomination

decay

axinos

decay

Dark matter genesis
http://find/


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thermal inflation

flaton = saxinomatter domination

firstorder

phasetransition

radiationdomination

decay

axinos

decay

NLSP

decay

Dark matter genesis
http://find/


70/91

thermal inflation


firstorder

phasetransition

radiationdomination

decay

axinos

decay

NLSP

decayaxions

QCD phase

transition

Dark matter genesis
http://find/


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thermal inflation


firstorder

phasetransition

radiationdomination

decay

axinos

decay

NLSP

decayaxions

QCD phase

transition

Dark matter abundance
http://find/


72/91

Axion

Axino

http://find/


73/91

Axion Misalignment

a 3

fa

1012GeV

1.2

Axino

http://find/


74/91

Axion Misalignment

a 3

fa

1012GeV

1.2

Axino Flaton decay

a 0.04 a

101

2 ma1GeV

31012GeV0

21GeV

Td

http://find/


75/91

Axion Misalignment

a 3

fa

1012GeV

1.2

Axino Flaton decay

a 0.04 a

101

2 ma1GeV

31012GeV0

21GeV

Td

Thermal NLSP decay

a 10 ma

1GeV

1012GeV0

2

Dark matter abundanceFlaton decays late || 21012GeV
http://find/


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Td 1GeV ||

103GeV

10 GeV

0

Axion Misalignment

a 3

fa

1012GeV

1.2

Axino Flaton decay

a 0.04 a

101

2 ma1GeV

31012GeV0

21GeV

Td

Thermal NLSP decay

a 10 ma

1GeV

1012GeV0

2

Dark matter abundanceFlaton decays late || 21012GeV
http://find/


77/91

Td 1GeV ||

103GeV

10 GeV

0

Axion Misalignment

a 3

fa

1012GeV

1.2

1 for Td 1GeV

Td

1GeV2

for Td 1GeV

Axino Flaton decay

a 0.04 a

101

2 ma1GeV

31012GeV0

21GeV

Td

Thermal NLSP decay

a 10 ma

1GeV

1012GeV0

2

Dark matter abundanceFlaton decays late

T G V

|| 21012GeV
http://find/


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Td 1GeV ||

103GeV

10 GeV

0

Axion Misalignment

a 3

fa

1012GeV

1.2

1 for Td 1GeV

Td

1GeV2

for Td 1GeV

Axino Flaton decay

a 0.04 a

101

2 ma1GeV

31012GeV0

21GeV

Td

Thermal NLSP decay

a 10 ma

1GeV

1012GeV0

2

1 for Td mN7

7TdmN

7for Td mN

7

Dark matter composition
http://find/


79/91

||GeV102 103 104

102

101

100

101

fa = 1012GeV

ma = 1GeV

axions

flatonaxinos

NLSPaxinos

Axino LHC signal

NLSPs produced by the LHC decay to axinos plus Standard Modelparticles
http://find/


80/91

p

LHCNLSP

axino

SM

Axino LHC signal

NLSPs produced by the LHC decay to axinos plus Standard Modelparticles
http://find/


81/91

p

LHCNLSP

axino

SM1 km

with a decay length

1

Na 16

20

m3N

1 km

200GeV

mN

30

1012GeV

2

and well constrained parameters

0 1012GeV

ma 1GeV

Simple model

MSSM drives m2 < 0
http://find/


82/91


2

(LHu)2

+ 2HuHd +


axion

Simple model

MSSM t drives m2 < 0
http://find/


83/91


2

(LHu)2

+ 2HuHd +

MSSM neutrino masses MSSM -term drives m < 0

thermal inflationaxion

Simple model

MSSM MSSM t drives m2 < 0
http://find/


84/91


2

(LHu)2

+ 2HuHd +


thermal inflationbaryogenesis axion

Simple model

MSSM i MSSM term drives m2 < 0
http://find/


85/91


2

(LHu)2

+ 2HuHd +


thermal inflationbaryogenesis axion/axinodark matter

Rich cosmology(density)1/4

mPl tPli fl i density perturbations
http://find/


86/91

time

1011GeV

103GeV

100 keV

10K

1028 s

1013 s

10min

1010 yr

inflation density perturbationsgravitational waves?









mPl tPli fl ti density perturbations
http://find/


87/91

time

1011GeV

103GeV

100 keV

10K

1028 s

1013 s

10min

1010 yr

inflation density perturbationsgravitational waves?



thermal inflation gravitational waves

decayQCD transition axion dark matter?





mPl tPlinflation density perturbations
http://find/


88/91

time

1011GeV

103GeV

100 keV

10K

1028 s

1013 s

10min

1010 yr

inflation y pgravitational waves?



thermal inflation gravitational wavesLHu

0 matter/antimatter

decayQCD transition axion dark matter?





http://find/


89/91

time

1011GeV

103GeV

100 keV

10K

1028 s

1013 s

10min

1010 yr





0 matter/antimatter

decay axino dark matterQCD transition axion dark matter





http://find/


90/91

time

1011GeV

103GeV

100 keV

10K

1028 s

1013 s

10min

1010 yr





0 matter/antimatter

decay axino dark matterQCD transition axion dark matter




A Minimal Supersymmetric Cosmological Model

Introduction
http://find/


91/91

IntroductionStandard model of cosmologyModuli and gravitinos

A Minimal Supersymmetric Cosmological ModelMSSMMSCMThermal inflationBaryogenesisDark matter

SummarySimple modelRich cosmology
http://find/

Documents

Ewan Stewart- A Minimal Supersymmetric Cosmological Model