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A Minimal Supersymmetric Cosmological Model

Ewan Stewart

KAIST

Beyond the Standard Models ofParticle Physics, Cosmology and Astrophysics

2 February 2010Cape Town, South Africa

Donghui Jeong, Kenji Kadota, Wan-Il Park, EDS hep-ph/0406136Gary N Felder, Hyunbyuk Kim, Wan-Il Park, EDS hep-ph/0703275

Richard Easther, John T Giblin, Eugene A Lim, Wan-Il Park, EDS arXiv:0801.4197Seongcheol Kim, Wan-Il Park, EDS arXiv:0807.3607

A Minimal Supersymmetric Cosmological Model

Ewan Stewart

KAIST

Beyond the Standard Models ofParticle Physics, Cosmology and Astrophysics

2 February 2010Cape Town, South Africa

Donghui Jeong, Kenji Kadota, Wan-Il Park, EDS hep-ph/0406136Gary N Felder, Hyunbyuk Kim, Wan-Il Park, EDS hep-ph/0703275

Richard Easther, John T Giblin, Eugene A Lim, Wan-Il Park, EDS arXiv:0801.4197Seongcheol Kim, Wan-Il Park, EDS arXiv:0807.3607

Standard model of cosmology

(density)1/4

time

mPl

1011 GeV

103 GeV

100 keV

10 K

tPl

10−28 s

10−13 s

10 min

1010 yr

inflationdensity perturbationsgravitational waves?

νR 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

Moduli and gravitinos

Moduli are cosmologically dangerous. Nucleosynthesis constrains

n

s. 10−12

In the early universe

H2 (Ψ−Ψ1)2

m2susy (Ψ−Ψ0)2

∼ MPl

n

s∼ 107

Moduli generated: H . msusy

after

slow-roll inflation: H & minflaton & msusy

Moduli and gravitinos

Moduli are cosmologically dangerous. Nucleosynthesis constrains

n

s. 10−12

In the early universe

H2 (Ψ−Ψ1)2

m2susy (Ψ−Ψ0)2

∼ MPl

n

s∼ 107

Moduli generated: H . msusy

after

slow-roll inflation: H & minflaton & msusy

Moduli and gravitinos

Moduli are cosmologically dangerous. Nucleosynthesis constrains

n

s. 10−12

In the early universe

H2 (Ψ−Ψ1)2

m2susy (Ψ−Ψ0)2

∼ MPl

n

s∼ 107

Moduli generated: H . msusy

after

slow-roll inflation: H & minflaton & msusy

Moduli and gravitinos

Moduli are cosmologically dangerous. Nucleosynthesis constrains

n

s. 10−12

In the early universe

H2 (Ψ−Ψ1)2

m2susy (Ψ−Ψ0)2

∼ MPl

n

s∼ 107

Moduli generated: H . msusy

after

slow-roll inflation: H & minflaton & msusy

Moduli and gravitinos

Moduli are cosmologically dangerous. Nucleosynthesis constrains

n

s. 10−12

In the early universe

H2 (Ψ−Ψ1)2

m2susy (Ψ−Ψ0)2

∼ MPl

n

s∼ 107

Moduli generated: H . msusy

after

slow-roll inflation: H & minflaton & msusy

Moduli and gravitinos

Moduli are cosmologically dangerous. Nucleosynthesis constrains

n

s. 10−12

In the early universe

H2 (Ψ−Ψ1)2

m2susy (Ψ−Ψ0)2

∼ MPl

n

s∼ 107

Moduli generated: H . msusy

after

slow-roll inflation: H & minflaton & msusy

Moduli and gravitinos

Moduli are cosmologically dangerous. Nucleosynthesis constrains

n

s. 10−12

In the early universe

H2 (Ψ−Ψ1)2

m2susy (Ψ−Ψ0)2

∼ MPl

n

s∼ 107

Moduli generated: H . msusy

after

slow-roll inflation: H & minflaton & msusy

Standard model of cosmology

(density)1/4

time

mPl

1011 GeV

103 GeV

100 keV

10 K

tPl

10−28 s

10−13 s

10 min

1010 yr

inflationdensity perturbationsgravitational waves?

νR 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

Standard model of cosmology

(density)1/4

time

mPl

1011 GeV

103 GeV

100 keV

10 K

tPl

10−28 s

10−13 s

10 min

1010 yr

inflationdensity perturbationsgravitational waves?

νR decay matter/antimatter?

moduli, gravitinos, . . . disaster

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

Minimal Supersymmetric Standard Model

W = λuQHu u + λdQHd d + λeLHd e + µHuHd

But

I µ?

I neutrino masses?

I strong CP?

Minimal Supersymmetric Standard Model

W = λuQHu u + λdQHd d + λeLHd e + µHuHd

But

I µ?

I neutrino masses?

I strong CP?

Minimal Supersymmetric Standard Model

W = λuQHu u + λdQHd d + λeLHd e + µHuHd

But

I µ?

I neutrino masses?

I strong CP?

Minimal Supersymmetric Standard Model

W = λuQHu u + λdQHd d + λeLHd e + µHuHd

But

I µ?

I neutrino masses?

I strong CP?

Minimal Supersymmetric Cosmological Model

W = λuQHu u + λdQHd d + λeLHd e +1

2λν (LHu)2 + λµφ

2 HuHd + λχφχχ

MSSM neutrino masses MSSM µ-term drives m2φ < 0

axion

µ = λµφ20

|φ|

V

φ0

V0

Minimal Supersymmetric Cosmological Model

W = λuQHu u + λdQHd d + λeLHd e +1

2λν (LHu)2 + λµφ

2 HuHd + λχφχχ

MSSM

neutrino masses MSSM µ-term drives m2φ < 0

axion

µ = λµφ20

|φ|

V

φ0

V0

Minimal Supersymmetric Cosmological Model

W = λuQHu u + λdQHd d + λeLHd e +1

2λν (LHu)2 + λµφ

2 HuHd + λχφχχ

MSSM neutrino masses

MSSM µ-term drives m2φ < 0

axion

µ = λµφ20

|φ|

V

φ0

V0

Minimal Supersymmetric Cosmological Model

W = λuQHu u + λdQHd d + λeLHd e +1

2λν (LHu)2 + λµφ

2 HuHd + λχφχχ

MSSM neutrino masses MSSM µ-term

drives m2φ < 0

axion

µ = λµφ20

|φ|

V

φ0

V0

Minimal Supersymmetric Cosmological Model

W = λuQHu u + λdQHd d + λeLHd e +1

2λν (LHu)2 + λµφ

2 HuHd + λχφχχ

MSSM neutrino masses MSSM µ-term drives m2φ < 0

axion

µ = λµφ20

|φ|

V

φ0

V0

Minimal Supersymmetric Cosmological Model

W = λuQHu u + λdQHd d + λeLHd e +1

2λν (LHu)2 + λµφ

2 HuHd + λχφχχ

MSSM neutrino masses MSSM µ-term drives m2φ < 0

axion

µ = λµφ20

|φ|

V

φ0

V0

Thermal inflation

|φ|

V

φ0

V0

RADIATIONDOMINATION

Thermal inflation

|φ|

V

φ0

V0

THERMALINFLATION

Thermal inflation

|φ|

V

φ0

V0

THERMALINFLATION

Thermal inflation

|φ|

V

φ0

V0

first orderphase transition

Thermal inflation

|φ|

V

φ0

V0

potential energyconverted to

particles

Thermal inflation

|φ|

V

φ0

V0

MATTERDOMINATION

Key properties of thermal inflation

Forφ0 ∼ 1010 to 1012 GeV

Large dilution

∆ ∼ 1020 =⇒ pre-existing moduli sufficiently diluted

Short duration

N ∼ 10 =⇒primordial perturbationsfrom slow-roll inflation

preserved on large scales

Low energy scale

V1/40 ∼ 106 to 107 GeV =⇒ moduli regenerated with

sufficiently small abundance

Key properties of thermal inflation

Forφ0 ∼ 1010 to 1012 GeV

Large dilution

∆ ∼ 1020 =⇒ pre-existing moduli sufficiently diluted

Short duration

N ∼ 10 =⇒primordial perturbationsfrom slow-roll inflation

preserved on large scales

Low energy scale

V1/40 ∼ 106 to 107 GeV =⇒ moduli regenerated with

sufficiently small abundance

Key properties of thermal inflation

Forφ0 ∼ 1010 to 1012 GeV

Large dilution

∆ ∼ 1020 =⇒ pre-existing moduli sufficiently diluted

Short duration

N ∼ 10 =⇒primordial perturbationsfrom slow-roll inflation

preserved on large scales

Low energy scale

V1/40 ∼ 106 to 107 GeV =⇒ moduli regenerated with

sufficiently small abundance

Key properties of thermal inflation

Forφ0 ∼ 1010 to 1012 GeV

Large dilution

∆ ∼ 1020 =⇒ pre-existing moduli sufficiently diluted

Short duration

N ∼ 10 =⇒primordial perturbationsfrom slow-roll inflation

preserved on large scales

Low energy scale

V1/40 ∼ 106 to 107 GeV =⇒ moduli regenerated with

sufficiently small abundance

Gravitational waves

f

Hz

ΩGW

10−10 10−5 100 105 101010−40

10−35

10−30

10−25

10−20

10−15

10−10

10−5

PRIMORDIALINFLATION

INFLATIONPREHEATING

DECIGO

array

Gravitational waves

f

Hz

ΩGW

10−10 10−5 100 105 101010−40

10−35

10−30

10−25

10−20

10−15

10−10

10−5

PRIMORDIALINFLATION

INFLATIONPREHEATING

THERMAL

INFLATION

DECIGO

array

Baryogenesis

Key assumption

m2LHu

=1

2

(m2

L + m2Hu

)< 0

Implies a dangerous non-MSSM vacuum with

LHu ∼ (109GeV)2

andλdQLd + λeLLe = µLHu

eliminating the µ-term contribution to LHu ’s mass squared.

LHu ,QLd , LLe

V

0

our vacuum

deeper vacuum

Baryogenesis

Key assumption

m2LHu

=1

2

(m2

L + m2Hu

)< 0

Implies a dangerous non-MSSM vacuum with

LHu ∼ (109GeV)2

andλdQLd + λeLLe = µLHu

eliminating the µ-term contribution to LHu ’s mass squared.

LHu ,QLd , LLe

V

0

our vacuum

deeper vacuum

Reduction

W = λuQHu u + λdQHd d + λeLHd e +1

2λν (LHu)2 + λµφ

2HuHd + λχφχχ

L =

(l0

), Hu =

(0hu

), Hd =

(hd

0

), e =

(0)

u =(

0 0 0)

, Q =

(0 0 0

d/√

2 0 0

), d =

(d/√

2 0 0)

φ = φ , χ = 0 , χ = 0

Reduction

W = λuQHu u + λdQHd d + λeLHd e +1

2λν (LHu)2 + λµφ

2HuHd + λχφχχ

L =

(l0

), Hu =

(0hu

), Hd =

(hd

0

), e =

(0)

u =(

0 0 0)

, Q =

(0 0 0

d/√

2 0 0

), d =

(d/√

2 0 0)

φ = φ , χ = 0 , χ = 0

Potential

V = V0 + m2L|l |

2 −m2Hu|hu |2 + m2

Hd|hd |2 − m2

φ|φ|2

+1

2

(m2

Q + m2d

)|d |2 +

1

2

(m2

L + m2e

)|e|2

+

[1

2Aνλν l

2h2u − Aµλµφ

2huhd −1

2Adλdhdd2 +

1

2Aeλehde2 + c.c.

]+∣∣λν lh2

u

∣∣2 +∣∣∣λν l2hu − λµφ2hd

∣∣∣2 +

∣∣∣∣λµφ2hu +1

2λdd2 +

1

2λee

2

∣∣∣∣2+ |λdhdd |2 + |λehde|2 + |2λµφhuhd |2

+1

2g2

(|hu |2 − |hd |2 − |l |2 +

1

2|d |2 +

1

2|e|2)2

drives thermal inflation lhu rolls away

lhu stabilizedwith

fixed phase

φ rolls away

hd forced out

d and e held at origin

lhu returnswith

rotation

φ stabilizedm2φ(φ0) = −αφm2

φ(0)

Potential

V = V0 + m2L|l |

2 −m2Hu|hu |2 + m2

Hd|hd |2 − m2

φ|φ|2

+1

2

(m2

Q + m2d

)|d |2 +

1

2

(m2

L + m2e

)|e|2

+

[1

2Aνλν l

2h2u − Aµλµφ

2huhd −1

2Adλdhdd2 +

1

2Aeλehde2 + c.c.

]+∣∣λν lh2

u

∣∣2 +∣∣∣λν l2hu − λµφ2hd

∣∣∣2 +

∣∣∣∣λµφ2hu +1

2λdd2 +

1

2λee

2

∣∣∣∣2+ |λdhdd |2 + |λehde|2 + |2λµφhuhd |2

+1

2g2

(|hu |2 − |hd |2 − |l |2 +

1

2|d |2 +

1

2|e|2)2

drives thermal inflation

lhu rolls away

lhu stabilizedwith

fixed phase

φ rolls away

hd forced out

d and e held at origin

lhu returnswith

rotation

φ stabilizedm2φ(φ0) = −αφm2

φ(0)

Potential

V = V0 + m2L|l |

2 −m2Hu|hu |2 + m2

Hd|hd |2 − m2

φ|φ|2

+1

2

(m2

Q + m2d

)|d |2 +

1

2

(m2

L + m2e

)|e|2

+

[1

2Aνλν l

2h2u − Aµλµφ

2huhd −1

2Adλdhdd2 +

1

2Aeλehde2 + c.c.

]+∣∣λν lh2

u

∣∣2 +∣∣∣λν l2hu − λµφ2hd

∣∣∣2 +

∣∣∣∣λµφ2hu +1

2λdd2 +

1

2λee

2

∣∣∣∣2+ |λdhdd |2 + |λehde|2 + |2λµφhuhd |2

+1

2g2

(|hu |2 − |hd |2 − |l |2 +

1

2|d |2 +

1

2|e|2)2

drives thermal inflation lhu rolls away

lhu stabilizedwith

fixed phase

φ rolls away

hd forced out

d and e held at origin

lhu returnswith

rotation

φ stabilizedm2φ(φ0) = −αφm2

φ(0)

Potential

V = V0 + m2L|l |

2 −m2Hu|hu |2 + m2

Hd|hd |2 − m2

φ|φ|2

+1

2

(m2

Q + m2d

)|d |2 +

1

2

(m2

L + m2e

)|e|2

+

[1

2Aνλν l

2h2u − Aµλµφ

2huhd −1

2Adλdhdd2 +

1

2Aeλehde2 + c.c.

]+∣∣λν lh2

u

∣∣2 +∣∣∣λν l2hu − λµφ2hd

∣∣∣2 +

∣∣∣∣λµφ2hu +1

2λdd2 +

1

2λee

2

∣∣∣∣2+ |λdhdd |2 + |λehde|2 + |2λµφhuhd |2

+1

2g2

(|hu |2 − |hd |2 − |l |2 +

1

2|d |2 +

1

2|e|2)2

drives thermal inflation lhu rolls away

lhu stabilizedwith

fixed phase

φ rolls away

hd forced out

d and e held at origin

lhu returnswith

rotation

φ stabilizedm2φ(φ0) = −αφm2

φ(0)

Potential

V = V0 + m2L|l |

2 −m2Hu|hu |2 + m2

Hd|hd |2 − m2

φ|φ|2

+1

2

(m2

Q + m2d

)|d |2 +

1

2

(m2

L + m2e

)|e|2

+

[1

2Aνλν l

2h2u − Aµλµφ

2huhd −1

2Adλdhdd2 +

1

2Aeλehde2 + c.c.

]+∣∣λν lh2

u

∣∣2 +∣∣∣λν l2hu − λµφ2hd

∣∣∣2 +

∣∣∣∣λµφ2hu +1

2λdd2 +

1

2λee

2

∣∣∣∣2+ |λdhdd |2 + |λehde|2 + |2λµφhuhd |2

+1

2g2

(|hu |2 − |hd |2 − |l |2 +

1

2|d |2 +

1

2|e|2)2

drives thermal inflation lhu rolls away

lhu stabilizedwith

fixed phase

φ rolls away

hd forced out

d and e held at origin

lhu returnswith

rotation

φ stabilizedm2φ(φ0) = −αφm2

φ(0)

Potential

V = V0 + m2L|l |

2 −m2Hu|hu |2 + m2

Hd|hd |2 − m2

φ|φ|2

+1

2

(m2

Q + m2d

)|d |2 +

1

2

(m2

L + m2e

)|e|2

+

[1

2Aνλν l

2h2u − Aµλµφ

2huhd −1

2Adλdhdd2 +

1

2Aeλehde2 + c.c.

]+∣∣λν lh2

u

∣∣2 +∣∣∣λν l2hu − λµφ2hd

∣∣∣2 +

∣∣∣∣λµφ2hu +1

2λdd2 +

1

2λee

2

∣∣∣∣2+ |λdhdd |2 + |λehde|2 + |2λµφhuhd |2

+1

2g2

(|hu |2 − |hd |2 − |l |2 +

1

2|d |2 +

1

2|e|2)2

drives thermal inflation lhu rolls away

lhu stabilizedwith

fixed phase

φ rolls away

hd forced out

d and e held at origin

lhu returnswith

rotation

φ stabilizedm2φ(φ0) = −αφm2

φ(0)

Potential

V = V0 + m2L|l |

2 −m2Hu|hu |2 + m2

Hd|hd |2 − m2

φ|φ|2

+1

2

(m2

Q + m2d

)|d |2 +

1

2

(m2

L + m2e

)|e|2

+

[1

2Aνλν l

2h2u − Aµλµφ

2huhd −1

2Adλdhdd2 +

1

2Aeλehde2 + c.c.

]+∣∣λν lh2

u

∣∣2 +∣∣∣λν l2hu − λµφ2hd

∣∣∣2 +

∣∣∣∣λµφ2hu +1

2λdd2 +

1

2λee

2

∣∣∣∣2+ |λdhdd |2 + |λehde|2 + |2λµφhuhd |2

+1

2g2

(|hu |2 − |hd |2 − |l |2 +

1

2|d |2 +

1

2|e|2)2

drives thermal inflation lhu rolls away

lhu stabilizedwith

fixed phase

φ rolls away

hd forced out

d and e held at origin

lhu returnswith

rotation

φ stabilizedm2φ(φ0) = −αφm2

φ(0)

Potential

V = V0 + m2L|l |

2 −m2Hu|hu |2 + m2

Hd|hd |2 − m2

φ|φ|2

+1

2

(m2

Q + m2d

)|d |2 +

1

2

(m2

L + m2e

)|e|2

+

[1

2Aνλν l

2h2u − Aµλµφ

2huhd −1

2Adλdhdd2 +

1

2Aeλehde2 + c.c.

]+∣∣λν lh2

u

∣∣2 +∣∣∣λν l2hu − λµφ2hd

∣∣∣2 +

∣∣∣∣λµφ2hu +1

2λdd2 +

1

2λee

2

∣∣∣∣2+ |λdhdd |2 + |λehde|2 + |2λµφhuhd |2

+1

2g2

(|hu |2 − |hd |2 − |l |2 +

1

2|d |2 +

1

2|e|2)2

drives thermal inflation lhu rolls away

lhu stabilizedwith

fixed phase

φ rolls away

hd forced out

d and e held at origin

lhu returnswith

rotation

φ stabilizedm2φ(φ0) = −αφm2

φ(0)

Potential

V = V0 + m2L|l |

2 −m2Hu|hu |2 + m2

Hd|hd |2 + m2

φ(φ) |φ|2

+1

2

(m2

Q + m2d

)|d |2 +

1

2

(m2

L + m2e

)|e|2

+

[1

2Aνλν l

2h2u − Aµλµφ

2huhd −1

2Adλdhdd2 +

1

2Aeλehde2 + c.c.

]+∣∣λν lh2

u

∣∣2 +∣∣∣λν l2hu − λµφ2hd

∣∣∣2 +

∣∣∣∣λµφ2hu +1

2λdd2 +

1

2λee

2

∣∣∣∣2+ |λdhdd |2 + |λehde|2 + |2λµφhuhd |2

+1

2g2

(|hu |2 − |hd |2 − |l |2 +

1

2|d |2 +

1

2|e|2)2

drives thermal inflation lhu rolls away

lhu stabilizedwith

fixed phase

φ rolls away

hd forced out

d and e held at origin

lhu returnswith

rotation

φ stabilizedm2φ(φ0) = −αφm2

φ(0)

Baryogenesis

MODULIDOMINATION

THERMALINFLATION

FLATONDOMINATION

RADIATIONDOMINATION

φ = 0

φ > 0

φ ∼ φ0

φ preheats

φ decays

huhd = 0

hd > 0 ⇒ d = e = 0

lhu = 0

lhu > 0

brought back into origin with rotation⇒ nL < 0

preheating and thermal friction⇒ NL conserved

l , hu , hd decayT > TEW ⇒ nL → nB

dilution ⇒ nB/s ∼ 10−10

nucleosynthesis

Numerical simulation

mt

nL/nAD

0 200 400 600 800 1000−0.15

−0.1

−0.05

0

0.05

0.1

0.15

Baryon asymmetry

nB

s∼

nL

nAD

nAD

nφ

Td

mφ(φ0)

Usingnφ ∼ mφ(φ0)φ2

0 , m2φ(φ0) ∼ αφm2

φ(0) , nAD ∼ mLHu l20

l0 ∼ 109 GeV

√(10−2 eV

mν

)( mLHu

103 GeV

)and

Td ∼ 1 GeV

(1012 GeV

φ0

)(|µ|

103 GeV

)2

gives

nB

s∼ 10−10

(nL/nAD

10−2

)(1012 GeV

φ0

)3 (10−2 eV

mν

)(|µ|

103 GeV

)2 (10−1

αφ

)(mLHu

mφ(0)

)2

which suggestsφ0 ∼ 1012 GeV

Baryon asymmetry

nB

s∼

nL

nAD

nAD

nφ

Td

mφ(φ0)

Usingnφ ∼ mφ(φ0)φ2

0 , m2φ(φ0) ∼ αφm2

φ(0) , nAD ∼ mLHu l20

l0 ∼ 109 GeV

√(10−2 eV

mν

)( mLHu

103 GeV

)and

Td ∼ 1 GeV

(1012 GeV

φ0

)(|µ|

103 GeV

)2

gives

nB

s∼ 10−10

(nL/nAD

10−2

)(1012 GeV

φ0

)3 (10−2 eV

mν

)(|µ|

103 GeV

)2 (10−1

αφ

)(mLHu

mφ(0)

)2

which suggestsφ0 ∼ 1012 GeV

Baryon asymmetry

nB

s∼

nL

nAD

nAD

nφ

Td

mφ(φ0)

Usingnφ ∼ mφ(φ0)φ2

0 , m2φ(φ0) ∼ αφm2

φ(0) , nAD ∼ mLHu l20

l0 ∼ 109 GeV

√(10−2 eV

mν

)( mLHu

103 GeV

)and

Td ∼ 1 GeV

(1012 GeV

φ0

)(|µ|

103 GeV

)2

gives

nB

s∼ 10−10

(nL/nAD

10−2

)(1012 GeV

φ0

)3 (10−2 eV

mν

)(|µ|

103 GeV

)2 (10−1

αφ

)(mLHu

mφ(0)

)2

which suggestsφ0 ∼ 1012 GeV

Dark matter candidates

Peccei-Quinn symmetry

W = λuQHu u + λdQHd d + λeLHd e +1

2λν (LHu)2 + λµφ

2HuHd + λχφχχ

DFSZ axion KSVZ axion

Axion

ma ∼Λ2

QCD

fawhere fa =

√2φ0

N

' 6.2× 10−6 eV

(1012 GeV

fa

)Axino

ma =1

16π2

∑χ

λ2χAχ

∼ 1 to 10 GeV

Dark matter candidates

Peccei-Quinn symmetry

W = λuQHu u + λdQHd d + λeLHd e +1

2λν (LHu)2 + λµφ

2HuHd + λχφχχ

DFSZ axion

KSVZ axion

Axion

ma ∼Λ2

QCD

fawhere fa =

√2φ0

N

' 6.2× 10−6 eV

(1012 GeV

fa

)Axino

ma =1

16π2

∑χ

λ2χAχ

∼ 1 to 10 GeV

Dark matter candidates

Peccei-Quinn symmetry

W = λuQHu u + λdQHd d + λeLHd e +1

2λν (LHu)2 + λµφ

2HuHd + λχφχχ

DFSZ axion KSVZ axion

Axion

ma ∼Λ2

QCD

fawhere fa =

√2φ0

N

' 6.2× 10−6 eV

(1012 GeV

fa

)Axino

ma =1

16π2

∑χ

λ2χAχ

∼ 1 to 10 GeV

Dark matter candidates

Peccei-Quinn symmetry

W = λuQHu u + λdQHd d + λeLHd e +1

2λν (LHu)2 + λµφ

2HuHd + λχφχχ

DFSZ axion KSVZ axion

Axion

ma ∼Λ2

QCD

fawhere fa =

√2φ0

N

' 6.2× 10−6 eV

(1012 GeV

fa

)

Axino

ma =1

16π2

∑χ

λ2χAχ

∼ 1 to 10 GeV

Dark matter candidates

Peccei-Quinn symmetry

W = λuQHu u + λdQHd d + λeLHd e +1

2λν (LHu)2 + λµφ

2HuHd + λχφχχ

DFSZ axion KSVZ axion

Axion

ma ∼Λ2

QCD

fawhere fa =

√2φ0

N

' 6.2× 10−6 eV

(1012 GeV

fa

)Axino

ma =1

16π2

∑χ

λ2χAχ

∼ 1 to 10 GeV

Dark matter genesis

thermal inflation

flaton = saxinomatter domination

firstorder

phasetransition

radiationdomination

decay

axinos

decay

NLSP

decayaxions

QCD phase

transition

Dark matter genesis

thermal inflation

flaton = saxinomatter domination

firstorder

phasetransition

radiationdomination

decay

axinos

decay

NLSP

decayaxions

QCD phase

transition

Dark matter genesis

thermal inflation

flaton = saxinomatter domination

firstorder

phasetransition

radiationdomination

decay

axinos

decay

NLSP

decayaxions

QCD phase

transition

Dark matter genesis

thermal inflation

flaton = saxinomatter domination

firstorder

phasetransition

radiationdomination

decay

axinos

decay

NLSP

decayaxions

QCD phase

transition

Dark matter genesis

thermal inflation

flaton = saxinomatter domination

firstorder

phasetransition

radiationdomination

decay

axinos

decay

NLSP

decay

axionsQCD phase

transition

Dark matter genesis

thermal inflation

flaton = saxinomatter domination

firstorder

phasetransition

radiationdomination

decay

axinos

decay

NLSP

decayaxions

QCD phase

transition

Dark matter genesis

thermal inflation

flaton = saxinomatter domination

firstorder

phasetransition

radiationdomination

decay

axinos

decay

NLSP

decayaxions

QCD phase

transition

Dark matter abundance

Flaton decays late

Td ∼ 1 GeV

(|µ|

103 GeV

)2 (1012 GeV

φ0

)

Axion

Misalignment

Ωa ∼ 3

(fa

1012 GeV

)1.2

×

1 for Td 1 GeV(

Td

1 GeV

)2

for Td 1 GeV

Axino

Flaton decay

Ωa ' 0.04( αa

10−1

)2 ( ma

1 GeV

)3(

1012 GeV

φ0

)2 (1 GeV

Td

)

Thermal NLSP decay

Ωa ∼ 10( ma

1 GeV

)(1012 GeV

φ0

)2

×

1 for Td

mN

7(7Td

mN

)7

for Td mN

7

Dark matter abundance

Flaton decays late

Td ∼ 1 GeV

(|µ|

103 GeV

)2 (1012 GeV

φ0

)

Axion Misalignment

Ωa ∼ 3

(fa

1012 GeV

)1.2

×

1 for Td 1 GeV(

Td

1 GeV

)2

for Td 1 GeV

Axino

Flaton decay

Ωa ' 0.04( αa

10−1

)2 ( ma

1 GeV

)3(

1012 GeV

φ0

)2 (1 GeV

Td

)

Thermal NLSP decay

Ωa ∼ 10( ma

1 GeV

)(1012 GeV

φ0

)2

×

1 for Td

mN

7(7Td

mN

)7

for Td mN

7

Dark matter abundance

Flaton decays late

Td ∼ 1 GeV

(|µ|

103 GeV

)2 (1012 GeV

φ0

)

Axion Misalignment

Ωa ∼ 3

(fa

1012 GeV

)1.2

×

1 for Td 1 GeV(

Td

1 GeV

)2

for Td 1 GeV

Axino Flaton decay

Ωa ' 0.04( αa

10−1

)2 ( ma

1 GeV

)3(

1012 GeV

φ0

)2 (1 GeV

Td

)

Thermal NLSP decay

Ωa ∼ 10( ma

1 GeV

)(1012 GeV

φ0

)2

×

1 for Td

mN

7(7Td

mN

)7

for Td mN

7

Dark matter abundance

Flaton decays late

Td ∼ 1 GeV

(|µ|

103 GeV

)2 (1012 GeV

φ0

)

Axion Misalignment

Ωa ∼ 3

(fa

1012 GeV

)1.2

×

1 for Td 1 GeV(

Td

1 GeV

)2

for Td 1 GeV

Axino Flaton decay

Ωa ' 0.04( αa

10−1

)2 ( ma

1 GeV

)3(

1012 GeV

φ0

)2 (1 GeV

Td

)

Thermal NLSP decay

Ωa ∼ 10( ma

1 GeV

)(1012 GeV

φ0

)2

×

1 for Td

mN

7(7Td

mN

)7

for Td mN

7

Dark matter abundanceFlaton decays late

Td ∼ 1 GeV

(|µ|

103 GeV

)2 (1012 GeV

φ0

)

Axion Misalignment

Ωa ∼ 3

(fa

1012 GeV

)1.2

×

1 for Td 1 GeV(

Td

1 GeV

)2

for Td 1 GeV

Axino Flaton decay

Ωa ' 0.04( αa

10−1

)2 ( ma

1 GeV

)3(

1012 GeV

φ0

)2 (1 GeV

Td

)

Thermal NLSP decay

Ωa ∼ 10( ma

1 GeV

)(1012 GeV

φ0

)2

×

1 for Td

mN

7(7Td

mN

)7

for Td mN

7

Dark matter abundanceFlaton decays late

Td ∼ 1 GeV

(|µ|

103 GeV

)2 (1012 GeV

φ0

)

Axion Misalignment

Ωa ∼ 3

(fa

1012 GeV

)1.2

×

1 for Td 1 GeV(

Td

1 GeV

)2

for Td 1 GeV

Axino Flaton decay

Ωa ' 0.04( αa

10−1

)2 ( ma

1 GeV

)3(

1012 GeV

φ0

)2 (1 GeV

Td

)

Thermal NLSP decay

Ωa ∼ 10( ma

1 GeV

)(1012 GeV

φ0

)2

×

1 for Td

mN

7(7Td

mN

)7

for Td mN

7

Dark matter abundanceFlaton decays late

Td ∼ 1 GeV

(|µ|

103 GeV

)2 (1012 GeV

φ0

)

Axion Misalignment

Ωa ∼ 3

(fa

1012 GeV

)1.2

×

1 for Td 1 GeV(

Td

1 GeV

)2

for Td 1 GeV

Axino Flaton decay

Ωa ' 0.04( αa

10−1

)2 ( ma

1 GeV

)3(

1012 GeV

φ0

)2 (1 GeV

Td

)

Thermal NLSP decay

Ωa ∼ 10( ma

1 GeV

)(1012 GeV

φ0

)2

×

1 for Td

mN

7(7Td

mN

)7

for Td mN

7

Dark matter composition

|µ|GeV

Ω

102 103 10410−2

10−1

100

101

fa = 1012 GeVma = 1 GeV

axions

flatonaxinos

NLSPaxinos

Axino LHC signal

NLSPs produced by the LHC decay to axinos plus Standard Model particles

LHCNLSP

axino

SM

with a decay length

1

ΓN→a∼

16πφ20

m3N

∼ 1 km

(200 GeV

mN

)3 ( φ0

1012 GeV

)2

and well constrained parameters

φ0 ∼ 1012 GeV

ma ' 1 GeV

Axino LHC signal

NLSPs produced by the LHC decay to axinos plus Standard Model particles

LHCNLSP

axino

SM1 km

with a decay length

1

ΓN→a∼

16πφ20

m3N

∼ 1 km

(200 GeV

mN

)3 ( φ0

1012 GeV

)2

and well constrained parameters

φ0 ∼ 1012 GeV

ma ' 1 GeV

Simple model

W = λuQHu u + λdQHd d + λeLHd e +1

2λν (LHu)2 + λµφ

2 HuHd + λχφχχ

MSSM neutrino masses MSSM µ-term drives m2φ < 0

thermal inflationbaryogenesis

axion

/axinodark matter

Simple model

W = λuQHu u + λdQHd d + λeLHd e +1

2λν (LHu)2 + λµφ

2 HuHd + λχφχχ

MSSM neutrino masses MSSM µ-term drives m2φ < 0

thermal inflation

baryogenesis

axion

/axinodark matter

Simple model

W = λuQHu u + λdQHd d + λeLHd e +1

2λν (LHu)2 + λµφ

2 HuHd + λχφχχ

MSSM neutrino masses MSSM µ-term drives m2φ < 0

thermal inflationbaryogenesisaxion

/axinodark matter

Simple model

W = λuQHu u + λdQHd d + λeLHd e +1

2λν (LHu)2 + λµφ

2 HuHd + λχφχχ

MSSM neutrino masses MSSM µ-term drives m2φ < 0

thermal inflationbaryogenesisaxion/axinodark matter

Rich cosmology

(density)1/4

time

mPl

1011 GeV

103 GeV

100 keV

10 K

tPl

10−28 s

10−13 s

10 min

1010 yr

inflationdensity perturbationsgravitational waves?

νR decay matter/antimatter?

moduli, gravitinos, . . . disaster

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

Rich cosmology

(density)1/4

time

mPl

1011 GeV

103 GeV

100 keV

10 K

tPl

10−28 s

10−13 s

10 min

1010 yr

inflationdensity perturbationsgravitational waves?

νR decay matter/antimatter?

moduli, gravitinos, . . . disaster

thermal inflation gravitational waves

φ decayQCD transition axion dark matter?

nucleosynthesis light elements

atom formation microwave backgroundgalaxy formation galaxies

vacuum energy dominates acceleration

Rich cosmology

(density)1/4

time

mPl

1011 GeV

103 GeV

100 keV

10 K

tPl

10−28 s

10−13 s

10 min

1010 yr

inflationdensity perturbationsgravitational waves?

νR decay matter/antimatter?

moduli, gravitinos, . . . disaster

thermal inflation gravitational wavesLHu → 0 matter/antimatter

φ decayQCD transition axion dark matter?

nucleosynthesis light elements

atom formation microwave backgroundgalaxy formation galaxies

vacuum energy dominates acceleration

Rich cosmology

(density)1/4

time

mPl

1011 GeV

103 GeV

100 keV

10 K

tPl

10−28 s

10−13 s

10 min

1010 yr

inflationdensity perturbationsgravitational waves?

νR decay matter/antimatter?

moduli, gravitinos, . . . disaster

thermal inflation gravitational wavesLHu → 0 matter/antimatter

φ decay axino dark matterQCD transition axion dark matter

nucleosynthesis light elements

atom formation microwave backgroundgalaxy formation galaxies

vacuum energy dominates acceleration

Rich cosmology

(density)1/4

time

mPl

1011 GeV

103 GeV

100 keV

10 K

tPl

10−28 s

10−13 s

10 min

1010 yr

inflationdensity perturbationsgravitational waves?

νR decay matter/antimatter?

moduli, gravitinos, . . . disaster

thermal inflation gravitational wavesLHu → 0 matter/antimatter

φ decay axino dark matterQCD transition axion dark matter

nucleosynthesis light elements

atom formation microwave backgroundgalaxy formation galaxies

vacuum energy dominates acceleration

A Minimal Supersymmetric Cosmological Model

IntroductionStandard model of cosmologyModuli and gravitinos

A Minimal Supersymmetric Cosmological ModelMSSMMSCMThermal inflationBaryogenesisDark matter

SummarySimple modelRich cosmology