Implications of BICEP2 results forparticle physics and cosmology
3rd September 2014
熱場の量子論＠理研

Fuminobu Takahashi(Tohoku)BICEP2

1403.3985

BICEP2

1403.3985

Too good to be true?
Maybe galactic foreground? (cf. Flauger et al 1405.7351)
In any case we will see in the near future.

What if r = O(10-3‒10-1)?
What can we say about inﬂation?

Talk plan
1. What did BICEP2 ﬁnd?
2. Inﬂation models
1. Chaotic inﬂation
2. Natural and Multi-Natural Inﬂation
3. QCD axion and isocurvature
perturbations (時間があれば）4. Conclusions

1. What did BICEP2 ﬁnd?

Cosmic Microwave BackgroundPlanck distribution of CMB

Our Universe was in equilibrium.

CMB photons are characterized by
1. Energy (or temperature)
2. Polarization

CMB temperature sky map

CMB anisotropy angular power spectrum

CMB anisotropy angular power spectrum
Cosmological parameters

CMB polarization
CMB photons are polarized!!

WMAP

CMB polarization
CMB photons are polarized!!

WMAP

Polarization can be easily generatedby Thomson scatterings.

(Taken from W. Huʼs webpage)Polarization can be easily generatedby Thomson scatterings.

(Taken from W. Huʼs webpage)No polarization is generated if the Unvierse
was exactly isotropic.

(Taken from W. Huʼs webpage)No polarization is generated if the Unvierse
was exactly isotropic.

(Taken from W. Huʼs webpage)Polarization is due to quadrupole anisotropy
around electrons at recombination(Taken from W. Huʼs webpage)Polarization is due to quadrupole anisotropy
around electrons at recombination(Taken from W. Huʼs webpage)(Taken from Samtleben et al, ̀07)

E-mode and B-mode are exchanged by rotating thepolarization vector by 45 degrees.

Perturbations of spacetime
Flat FRW Universe:
ds2 =dt2 + a(t)2 ij dxi dxj

Perturbations of spacetime
Flat FRW Universe:ds2 =+ small perturbations

dt2 + a(t)2 ij dxi dxj

Perturbations of spacetime
Flat FRW Universe:
ds2 =dt2 + a(t)2 ij dxi dxj+ small perturbations

The perturbations can be decomposed into
three types.

1. Scalar
2. Vector
3. Tensor

inﬂatonGW

E-mode ONLY

BOTH E-mode
and B-mode

E-mode ONLY

BOTH E-mode
and B-mode

C
H
H
C

C

H

H

C

E-mode ONLY

BOTH E-mode
and B-mode

C
H
H
C

C
Rotationby 45 deg.

H

H

C

E-mode ONLY

BOTH E-mode
and B-mode

BICEP2 found B-mode

Taken from
Chinone’s webpage

Galactic foregrounds?
Planck collaboration, 1405.0871@353 GHz (cf. BICEP2 @150 GHz)
The polarization fraction tends to be higher where
the dust emission is smaller.

2. Inﬂation models

Inﬂation
Accelerated cosmic expansion solves various theoreticalproblems of the std. big bang cosmology.
Guth `81, Sato `80, Starobinsky `80, Kazanas `80, Brout, Englert, Gunzig, `79

One way to realize the inﬂationary expansion is the slowLinde ̀82, Albrecht and Steinhardt ̀82
roll inﬂation.

V⇥ = 2HF

F

Perturbations of spacetime
Flat FRW Universe:
ds2 =dt2 + a(t)2 ij dxi dxj+ small perturbations

The perturbations can be decomposed into
three types.

1. Scalar
2. Vector
3. Tensor

InﬂatonGWScalar mode
It is due to ﬂuctuations in time
induced by the inﬂatonʼsquantum ﬂuctuation.

TimeScalar mode
Amplitude::COBE normalization

Spectral index:

k
10-9

ns 1

ns > 1
ns < 1kTensor mode

It is due to ﬂuctuations ofgraviton itself.

Observation vs Theory
Scalar modeTensor modeV : the inﬂaton potential

Itʼs GUT-scale inﬂation!

Large-ﬁeld inﬂation
The inﬂaton excursion exceeds the Planck scale.

Afterinflation& MP

Duringinflationφ

Lyth bound:
Lyth 1997

GUT-scale, large-ﬁeld inﬂation

GUT-scale, large-ﬁeld inﬂation•

Inﬂation model building in sugra/string

GUT-scale, large-ﬁeld inﬂation•

Inﬂation model building in sugra/string•

Shift symmetry is likely.

GUT-scale, large-ﬁeld inﬂation•

Inﬂation model building in sugra/string••

Shift symmetry is likely.

High reheating temperature:GUT-scale, large-ﬁeld inﬂation•

Inﬂation model building in sugra/string••

Shift symmetry is likely.

High reheating temperature:GUT-scale, large-ﬁeld inﬂation•

Inﬂation model building in sugra/string••

Shift symmetry is likely.

High reheating temperature:•

Thermal leptogenesis is likely.

GUT-scale, large-ﬁeld inﬂation•

Inﬂation model building in sugra/string••

Shift symmetry is likely.

High reheating temperature:•

Thermal leptogenesis is likely.

•

Baryogenesis, dark matter, unwanted relics.

GUT-scale, large-ﬁeld inﬂation•

Inﬂation model building in sugra/string••

Shift symmetry is likely.

High reheating temperature:•

Thermal leptogenesis is likely.

•

Baryogenesis, dark matter, unwanted relics.

•

Symmetry restoration is possible.

GUT-scale, large-ﬁeld inﬂation•

Inﬂation model building in sugra/string•••

Shift symmetry is likely.

High reheating temperature:•

Thermal leptogenesis is likely.

•

Baryogenesis, dark matter, unwanted relics.

•

Symmetry restoration is possible.

The inﬂaton mass is about.

GUT-scale, large-ﬁeld inﬂation•

Inﬂation model building in sugra/string•••

Shift symmetry is likely.

High reheating temperature:•

Thermal leptogenesis is likely.

•

Baryogenesis, dark matter, unwanted relics.

•

Symmetry restoration is possible.

The inﬂaton mass is about.

GUT-scale, large-ﬁeld inﬂation•

Inﬂation model building in sugra/string•••

Shift symmetry is likely.

High reheating temperature:•

Thermal leptogenesis is likely.

•

Baryogenesis, dark matter, unwanted relics.

•

Symmetry restoration is possible.

The inﬂaton mass is about•.

Related to SUSY breaking scale or RH neutrino mass?

GUT-scale, large-ﬁeld inﬂation•

Inﬂation model building in sugra/string•••

High reheating temperature:•

Thermal leptogenesis is likely.

•

Baryogenesis, dark matter, unwanted relics.

•

Symmetry restoration is possible.

The inﬂaton mass is about••

Shift symmetry is likely.

.

Related to SUSY breaking scale or RH neutrino mass?

Too large isocurvature perturbations.

GUT-scale, large-ﬁeld inﬂation•

Inﬂation model building in sugra/string•••

High reheating temperature:•

Thermal leptogenesis is likely.

•

Baryogenesis, dark matter, unwanted relics.

•

Symmetry restoration is possible.

The inﬂaton mass is about••

Shift symmetry is likely.

.

Related to SUSY breaking scale or RH neutrino mass?

Too large isocurvature perturbations.
•

The QCD axion less likely? PQ symmetry restoration?

Various large-ﬁeld inﬂation models
Quadratic chaotic inﬂation
Linde ̀83

Natural inﬂation

2.0

Freese et al, ̀90
1.5

1.0

0.5

-4

-2

2

4

Predicted values of (ns, r)

Planck, 1303.5802

Predicted values of (ns, r)
Quadratic
chaotic inﬂ

Planck, 1303.5802

Predicted values of (ns, r)
Quadratic
chaotic inﬂ

Natural inﬂ

Planck, 1303.5802

Various large-ﬁeld inﬂation models
Polynomial chaotic inﬂation
Destri, de Vega, Sanchez [astro-ph/0703417]
Nakayama, FT, Yanagida 1303.7315(see also Kobayashi, Seto 1403.5055
Kallosh, Linde, Wesphal 1405.0270)

Nakayama, FT, Yanagida, 1303.7315

Multi-Natural inﬂation (MNI)
Czerny, FT 1401.5212
Czerny, Higaki FT 1403.0410, 1403.5883

Sub-Planckian decay constants are allowed
as hilltop inﬂation can be realized.
Czerny, FT, 1401.5212

Various large-ﬁeld inﬂation models
Polynomial chaotic inﬂation
Destri, de Vega, Sanchez [astro-ph/0703417]
Nakayama, FT, Yanagida 1303.7315(see also Kobayashi, Seto 1403.5055
Kallosh, Linde, Wesphal 1405.0270)

Nakayama, FT, Yanagida, 1303.7315

Multi-Natural inﬂation (MNI)
Czerny, FT 1401.5212
Czerny, Higaki FT 1403.0410, 1403.5883

Sub-Planckian decay constants are allowed
as hilltop inﬂation can be realized.
Czerny, FT, 1401.5212

Various large-ﬁeld inﬂation models
Polynomial chaotic inﬂation
Destri, de Vega, Sanchez [astro-ph/0703417]
Nakayama, FT, Yanagida 1303.7315(see also Kobayashi, Seto 1403.5055
Kallosh, Linde, Wesphal 1405.0270)

Nakayama, FT, Yanagida, 1303.7315

Multi-Natural inﬂation (MNI)
Czerny, FT 1401.5212
Czerny, Higaki FT 1403.0410, 1403.5883

Sub-Planckian decay constants are allowed
as hilltop inﬂation can be realized.
Czerny, FT, 1401.5212

Chaotic inﬂation in SUGRA
Kawasaki, Yamaguchi, Yanagida, hep-ph/0004243 ,hep-ph/0011104

To have a good control over the inﬂaton ﬁeld values greater than
the Planck scale, we impose a shift symmetry;

which is explicitly broken by the superpotential.

even forPolynomial chaotic inﬂation in SUGRA
Nakayama, FT, Yanagida 1303.7315,1305.5099(cf. Kallosh, Linde, Westphal 1405.0270)

V
ns = 1 + 2
V
r=8

V
V

3

V
V

2

2

1303.7315

1303.7315

Natural and Multi-Natural Inﬂation- Natural inﬂation

Freese, Frieman, Olinto ̀90

Only large-ﬁeld inﬂation is possible,and f is bounded below:

Natural and Multi-Natural Inﬂation- Natural inﬂation

Freese, Frieman, Olinto ̀90

Only large-ﬁeld inﬂation is possible,and f is bounded below:- Multi-Natural inﬂation

Czerny, FT 1401.5212, Czerny, Higaki, FT 1403.0410, 1403.5883

For Nsource = 2, various values of (ns,r) are
possible as in the polynomial chaotic inf.
No lower bound on the decay constants.

1403.5883

Natural and Multi-Natural Inﬂation- Natural inﬂation

Freese, Frieman, Olinto ̀90

Only large-ﬁeld inﬂation is possible,and f is bounded below:- Multi-Natural inﬂation

Czerny, FT 1401.5212, Czerny, Higaki, FT 1403.0410, 1403.5883

For Nsource = 2, various values of (ns,r) are
possible as in the polynomial chaotic inf.
No lower bound on the decay constants.

1403.5883

Axion hilltop inﬂation
Czerny, FT 1401.5212(Small-ﬁeld Multi-Natural inﬂation) Czerny, Higaki FT 1403.0410
Hilltop quartic inﬂation (new inﬂation) can be realized byrequiring a ﬂat-top potential in multi-natural inﬂation.
2.0

1.5

1.0

for

and

Axion hilltop inﬂation is possible for f < MP.

0.5

4

2

2

•

Simple realization of hilltop inﬂation by axion.

•

The potential shape is under control.

•

Spectral index can give a better ﬁt to the
Planck data by a slight shift of the phase.

4

Axion hilltop inﬂation
Czerny, FT 1401.5212(Small-ﬁeld Multi-Natural inﬂation) Czerny, Higaki FT 1403.0410
Hilltop quartic inﬂation (new inﬂation) can be realized byrequiring a ﬂat-top potential in multi-natural inﬂation.
2.0

1.5

Quartic
1.0

for

and

hilltop

Axion hilltop inﬂation is possible for f < MP.

0.5

4

2

2

•

Simple realization of hilltop inﬂation by axion.

•

The potential shape is under control.

•

Spectral index can give a better ﬁt to the
Planck data by a slight shift of the phase.

4

Aligned Natural Inﬂation
Kim, Nilles, Peloso, hep-ph/0409138
Czerny, Higaki, FT 1403.5883, Harigaya and Ibe 1404.3511, Choi, Kim, Yun, 1404.6209, Higaki, FT,
1404.6923, Tye, Won, 1404.6988, Kappl, Krippendorf, Nilles, 1404.7127, Bachlechner et al, 1404.7496,
Ben-Dayan, Pedro, Westphal,1404.7773 ,Long, McAllister, McGuirk 1404.7852

The eﬀectively large decay constant can be realized by
the alignment of two (or more) axion potentials.

• Two axions:If n1/n2 = m1/m2, there is a ﬂat direction; the corresponding
decay constant would be inﬁnite.
If n1/n2 ≈ m1/m2, there is a relatively light direction; thecorresponding decay constant can be larger than f1 or f2.

Aligned Natural Inﬂation
Kim, Nilles, Peloso, hep-ph/0409138

Taken from 1404.6209 by Choi, Kim, Yun

Aligned Natural Inﬂation
Kim, Nilles, Peloso, hep-ph/0409138• Two axions:For, the eﬀective decay constant isSome hierarchy among the anomaly coeﬃcients are needed
to realize a large enhancement of O(100).

Aligned Natural Inﬂation• Multiple axions:

For a moderately large N (> 5 or so), the eﬀective decay
constant can be enhanced w/o hierarchy among the anomaly
Choi, Kim, Yun, 1404.6209
coeﬃcients.
Prob. dist. was studied in detail for various cases incl.
Higaki, FT, 1404.6923

Aligned Natural Inﬂation• Prob dist for the enhancement of the decay constant
We generated integer-valued
random matrix

1
0.5

0.1
0.05

0.01
0.005

Enhancement becomes
likely for larger Naxion.
15

20

30

50

70

100

150 200

300

Higaki, FT, 1404.6923

Aligned Natural Inﬂation• Prob dist for the enhancement of the decay constant
We generated integer-valued
random matrix

The enhancement along
The lightest

multiple directions ishighly unlikely.
The inﬂaton is the

3rd

2nd lightest

lightest axion!

Higaki, FT, 1404.6923

Aligned Natural Inﬂation• Prob dist for the enhancement of the decay constant
We generated integer-valued
random matrix

The enhancement is lesslikely for larger Nsource.

Higaki, FT, 1404.6923

Axion Landscape!

For

Higaki, FT 1404.6923, many axions may form a mini-landscape.

• Eternal inﬂation takes place inlocal minima.
• A ﬂat direction arises by the KNP
mechanism.
• Slow-roll inﬂation starts along theﬂat direction after the tunneling
event.
• Negative curvature/suppression atlarge scales if the total e-folding isjust 50-60.

Linde ̀95, Freivogel et al ̀05,
Yamauchi et al ̀11, Bousso et al ̀13

Any little something extra?

•Isocurvature perturbations•Running spectral index

Axion isocurvature perturbations

ρ

Adiabatic perturbation
photonIsocurvature perturbationρ
photonDM/baryonx(Planck+WMAP polarization)

DM/baryonxThe QCD axion is a plausible candidate forDM with isocurvature perturbations.

Ta = Hinf /2
QCD

T

QCD

a

Isocurvature constraint on Hinfr = 0.01109
108

r = ⌦a /⌦DM

r=1

107

H inf / GeV

r = 0.1

106
105
104
103
102
101
100
10-1
10-2
10-3

109

1010

1011

1012

fa / GeV

1013

1014

Kobayashi, Kurematsu, FT, 1304.0922

Isocurvature constraint on Hinfr = 0.01109
108

r = ⌦a /⌦DM

r=1

107

H inf / GeV

r = 0.1

106
105

Hinf

10

1013

1014

7 8

GeV

104
103
102
101
100
10-1
10-2
10-3

109

1010

1011

1012

fa / GeV

Kobayashi, Kurematsu, FT, 1304.0922

Isocurvature constraint on Hinfr = 0.01109
108

r = ⌦a /⌦DM

r=1

107

H inf / GeV

r = 0.1

106

Hinf

105

10

7 8

GeV

104
103
102

Anharmonic
effects

101
100
10-1
10-2
10-3

109

1010

1011

1012

fa / GeV

1013

1014

Kobayashi, Kurematsu, FT, 1304.0922

Solutions•

Restoration of Peccei-Quinn symmetry during
inﬂation.

Taken fromM. Kawasakiʼs slide

Solutions•

Restoration of Peccei-Quinn symmetry during
inﬂation.
• Axions are produced from domain walls andaxion DM is possible for fa = 1010GeV.
Hiramatsu, Kawasaki, Saikawa and Sekiguchi, 1202.5851,1207.3166

Solutions•

Restoration of Peccei-Quinn symmetry during
inﬂation.
• Axions are produced from domain walls andaxion DM is possible for fa = 1010GeV.
Hiramatsu, Kawasaki, Saikawa and Sekiguchi, 1202.5851,1207.3166•(Super-)Planckian saxion ﬁeld value during
inﬂation. (Saxion could be the inﬂaton)
Axion: phase component
Saxion: radial component

1016
1015

BICEP21014

H inf / GeV

1013
1012
1011
1010
109
108
107

axion CDM

106

is assumed.

105
104

109

1010

1011

1012 1013

fa / GeV

1014 1015

1016

Higaki, Jeong, FT, 1403.4186

Solutions•

Restoration of Peccei-Quinn symmetry during
inﬂation.
• Axions are produced from domain walls andaxion DM is possible for fa = 1010GeV.
Hiramatsu, Kawasaki, Saikawa and Sekiguchi, 1202.5851,1207.3166

Super-Planckian saxion ﬁeld value during
inﬂation. (Saxion could be the inﬂaton)• Heavy axions during inﬂation.
••

Stronger QCD during inﬂation•

Enhanced explicit PQ breaking Dine, Anisimov hep-ph/0405256

Dvali, hep-ph/9505253
Jeong, FT 1304.8131

Higaki, Jeong, FT, 1403.4186

Conclusions•

If r =O(0.001-0.1), we can get information of the very
early Universe at the GUT-scale.

•

Large-ﬁeld inﬂation realized by shift symmetry.
•

Chaotic inﬂation/(multi-)natural inﬂation lead to various
values of (ns,r).

•Axion landscape•

Eternal inﬂation and subsequent slow-roll inﬂation
realized in a uniﬁed manner.

••(Multi-)natural inﬂation by the KNP mechanism•

Just 50-60 e-foldings may lead to negative curvature.

Anything extra？
•

Axion CDM Isocurvature perturbations.

•

Running spectral index /spatial curvature, etc.