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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