The ALP miracle collaboration with F. Takahashi & W. Yin Ryuji - - PowerPoint PPT Presentation

The ALP miracle

collaboration with F. Takahashi & W. Yin

Ryuji Daido Tohoku Univ.

@PPP2017

1702.03284 JCAP05(2017)044

V

• There are two unknown degree of freedom in the CDM.

(except for the origin of .)

Λ Λ

• 1. Introduction
• Inflaton
• Dark matter

Both are neutral and occupied a significant fraction of the energy density of the Universe.

Very flat potential for slow-roll inflation. Cold, neutral, and long-lived.

V

• Thermal history

Inflaton decays and produce radiation, while DM must be produced somehow.

inflaton radiation DM

ρ

Scale factor ?

Inflaton = DM ?

• cf. Kofman, Linde, Starobinsky `94, Mukaida, Nakayama 1404.1880, Bastero-Gil, Cerezo, Rosa,1501.05539

see also Lerner, McDonald 0909.0520, Okada, Shafi 1007.1672, Khoze 1308.6338 for inflaton WIMP.

If the reheating is incomplete, some of inflaton condensate may remain.

DM=inflaton

radiation

Incomplete reheating!

inflaton

ρ

Scale factor

The remnant inflaton condensate due to incomplete reheating can be dark matter.

What we did

• Inflaton = DM = Axion-like particle (ALP)
• The observed CMB and LSS data fix the relation

between the ALP mass and decay constant.

• Successful reheating and DM abundance point to

specific values within the reach of IAXO.

gφγγ = O(10−11) GeV−1 mφ = O(0.01) eV ,

• 2. Axion and Inflation

Axion is a pseudo NG boson, and enjoys a discrete shift symmetry.

φ → φ + 2πnf

Since dangerous radiative corrections are naturally suppressed, axion is compatible with inflation.

n ∈ Z V (φ) = V (φ + 2πf)

and can be expressed as Fourier series,

∆φ = 2πf

V (φ) = X

n∈Z

cnein φ

f

The axion potential is periodic, i.e.

• 1

1 2 3 4

ϕ/f

0.5 1.0 1.5 2.0

V(ϕ)/Λ4

・Super-Planckian decay constant is required.

Axion and Inflation

The simplest model is the natural inflation.

Freese, Frieman, Olinto `90

・Large field inflation ・Predicted are not favored by recent observations.

• Natural inflation

(ns, r)

• Axion hilltop inflation
• Inflaton is light both during inflation

and in the true min.

Flatness=longevity

m2

φ = V 00(φmin) = −V 00(φmax)

Hilltop inflation can be realized with two cosine terms.

• 1

1 2 3 4 5 0.5 1.0 1.5

Odd n

Vinf(φ) = Λ4 ✓ cos ✓φ f + θ ◆ − κ n2 cos ✓ nφ f ◆◆ + C

upside down symmetric

Czerny, Takahashi 1401.5212, Czerny, Higaki, Takahashi 1403.0410, 1403.5883

• The decay constant can be sub-

Planckian.

f ⌧ MP

= V0 − λφ4 − Λ4θφ f + (κ − 1) Λ4 2f 2 φ2 + . . .

V (φ)/Λ4

(Minimal extension)

Axion and Inflation

• Axion hilltop inflation

λ ' 7.5 ⇥ 10−14 ✓N∗ 50 ◆−3 .

N∗ ' 61 + ln ✓ H∗ Hinf ◆ 1

2

+ ln ✓ Hinf 1014GeV ◆ 1

2

ns ' 1 + 2η(φ∗) ' 1 3 N∗

Planck normalization Spectral index

Hilltop inflation can be realized with two cosine terms.

Vinf(φ) = Λ4 ✓ cos ✓φ f + θ ◆ − κ n2 cos ✓ nφ f ◆◆ + C

(Minimal extension)

= V0 − λφ4 − Λ4θφ f + (κ − 1) Λ4 2f 2 φ2 + . . .

Czerny, Takahashi 1401.5212, Czerny, Higaki, Takahashi 1403.0410, 1403.5883

• 1

1 2 3 4 5 0.5 1.0 1.5

Odd n

upside down symmetric

V (φ)/Λ4

Axion and Inflation

Spectral index

The typical inflaton mass:

mφ ∼ θ

1 3 Λ2

f = O(0.1)Hinf

• 0.06
• 0.04
• 0.020.00 0.02 0.04 0.06 0.08
• 0.01

0.00 0.01 0.02 0.03 0.04 (κ-1)×(f/Mpl)-2 θ×(f/Mpl)-3

• cf. ns ' 1 + 2η(φ∗)

ns = 0.968 ± 0.006

Relation between and

mφ

f

The Planck normalization of density perturbation and the spectral index fix the relation between and ,

mφ

f

: Planck normalization : Friedman eq. : Scalar spectral index

• cf. ns ' 1 + 2η(φ∗)

λ ∼ ✓Λ f ◆4 ∼ 10−13 Λ4 ∼ H2

infM 2 pl

mφ ∼ 0.1Hinf

f ∼ 5 × 107 GeV ⇣n 3 ⌘1/2 ⇣ mφ 1 eV ⌘0.51

K S V Z

QCD axion IAXO ALPS-II 10-4 10-3 10-2 10-1 100 101 102 103 CAST HB 10 -14 10 -13 10 -12 10 -11 10 -10 10 -9

m [eV]

φ

CMB τ EBL X-ray

Telescopes

gφγγ = cγα πf

RD, Takahashi, and Yin 1702.03284 Limits taken from Essig et al 1311.0029

Successful inflation

cγ = X

i

qiQ2

i

ψi → eiβqiγ5/2ψi

φ → φ + βf

L = gφγγ 4 φFµν ˜ F µν

Mass and coupling to photons

The inflaton oscillates about in a quartic potential.

φmin = πf

• 1

1 2 3 4 5 0.5 1.0 1.5

m2

eff(t) = V 00(φamp)

The effective mass, with time, and so, decay and dissipation become inefficient at later times.

= 12λφ2

amp decreases

Incomplete reheating

• 3. Reheating and ALP DM

• 1

1 2 3 4 5 0.5 1.0 1.5

Inflaton (ALP) condensate Photons, SM particles

Decay & dissipation Remnant

ALP Dark Matter

• 3. Reheating and ALP DM

ξ ≡ ρφ ρφ + ρR

• after reheating

・Reheating

✓The decay rate into two photons:

• 1

1 2 3 4 5 0.5 1.0 1.5

✓The dissipation rate is roughly estimated as

• cf. Moroi, Mukaida, Nakayama and Takimoto,1407.7465

Γdec(φ → γγ) = c2

γα2

64π3 m3

eff

f 2 v u u t1 − 2m(th)

γ

meff !2

m2

eff(t) = V 00(φamp) = 12λφ2

amp

m(th)

γ

∼ eT

φ γ γ

Γdis,γ = C c2

γα2T 3

8π2f 2 m2

eff

e4T 2

φ γ e− e+

ξρtot

H ' Γdec + Γdis

Inflation Radiation DM Scale factor

ρ

The remnant inflaton condensate is expressed by

ξ ≡ ρφ ρφ + ρR

• after reheating

・Reheating

gφγγ & 10−11 GeV−1

Solving following equations, we found

ξ . O(0.01)

for successful reheating .

KSVZ

QCD axion IAXO ALPS-II 10-4 10-3 10-2 10-1 100 101 102 103 CAST HB 10 -14 10 -13 10 -12 10 -11 10 -10 10 -9

m [eV]

φ

CMB τ EBL X-ray

Telescopes

Successful inflation

Successful reheating

∝ (φ − φmin)4 ∝ (φ − φmin)2

Quadratic

Quartic

After the reheating, decreases like radiation until the potential becomes quadratic.

ρφ

• ALP condensate as CDM

w ≡ P ρ = n − 2 n + 2

cf. for φn

zc & O(105) by SDSS and Ly-alpha

DM should be formed before

SM radiation

ρφ

quartic

quadratic

Scale factor

Matter-radiation equality

zc

zeq ∼ 3000

DM

Sarkar, Das, Sethi, 1410.7129

ξ . 0.02 ✓g∗s(TR) 106.75 ◆ 1

3 ✓ 3.909

g∗s(Tc) ◆ 1

3 ✓Ωφh2

0.12 ◆ ✓5 × 105 1 + zc ◆ .

• ALP condensate as CDM

• ALP condensate as CDM

ρφ s ' 3 4ξ

3 4 mφTR

p 2λfx

mφ ' 0.07 x−1 ✓ ξ 0.01 ◆− 3

4 ✓Ωφh2

0.12 ◆ eV, & 0.04 x−1 ✓ 106.75 g∗s(TR) ◆ 1

4 ✓g∗s(Tc)

3.909 ◆ 1

4 ✓Ωφh2

0.12 ◆ 1

4 ✓ 1 + zc

5 ⇥ 105 ◆ 3

4

eV,

SM radiation

ρφ

quartic

quadratic

Scale factor

Matter-radiation equality

zc

zeq ∼ 3000

DM

Sarkar, Das, Sethi, 1410.7129

KSVZ

QCD axion IAXO ALPS-II 10-4 10-3 10-2 10-1 100 101 102 103 CAST HB 10 -14 10 -13 10 -12 10 -11 10 -10 10 -9

m [eV]

φ

CMB τ EBL X-ray

Telescopes

Successful inflation

Successful reheating

DM abundance

KSVZ

QCD axion IAXO ALPS-II 10-4 10-3 10-2 10-1 100 101 102 103 CAST HB 10 -14 10 -13 10 -12 10 -11 10 -10 10 -9

m [eV]

φ

CMB τ EBL X-ray

Telescopes

Successful inflation

Successful reheating

HDM constraint

DM abundance

KSVZ

QCD axion IAXO ALPS-II 10-4 10-3 10-2 10-1 100 101 102 103 CAST HB 10 -14 10 -13 10 -12 10 -11 10 -10 10 -9

m [eV]

φ

CMB τ EBL X-ray

Telescopes

Successful inflation

Successful reheating

DM abundance

HDM constraint

KSVZ

QCD axion IAXO ALPS-II 10-4 10-3 10-2 10-1 100 101 102 103 CAST HB 10 -14 10 -13 10 -12 10 -11 10 -10 10 -9

m [eV]

φ

CMB τ EBL X-ray

Telescopes

Successful inflation

Successful reheating

The ALP miracle!

DM abundance

HDM constraint

Summary

• Inflaton = DM = Axion-like particle (ALP)
• The observed CMB and LSS

data fix the relation between the ALP mass and decay const.

• Successful inflation,

reheating and DM abundance point to within the reach of IAXO.

gφγγ = O(10−11) GeV−1 mφ = O(0.01) eV ,

KSVZ

QCD axion IAXO ALPS-II 10-4 10-3 10-2 10-1 100 101 102 103 CAST HB 10 -14 10 -13 10 -12 10 -11 10 -10 10 -9

m [eV]

φ

CMB τ EBL X-ray

Telescopes