An optimistic view on inflaton hunt Fumi Takahashi (Tohoku) Mar. 7 - - PowerPoint PPT Presentation

An optimistic view on inflaton hunt

Fumi Takahashi (Tohoku)

• Mar. 7 2019@Tohoku University

Based on Daido, FT, Yin, 1702.03284, 1710.11107, FT and Yin, 1903.00462

• 1. Introduction

The standard model (SM) of particle physics has been tested by numerous experiments with great accuracy.

Is this the end of the story?

?

Is this the end of the story?

No!

?

V

• Inflaton

Very flat potential for slow-roll inflation.

• Dark matter

Cold, neutral, and long-lived.

Direct evidence for the physics beyond the SM!

Success of the ΛCDM model relies on the two unknown degrees of freedom:

Known unknowns in Cosmology

Then, where should we look for ?

Niels Bohr

“We are all agreed that your theory is crazy. The question that divides us is whether it is crazy enough to have a chance

• f being correct.”

(Said to Pauli after his presentation.)

Steven Weinberg

“…My advice is to try crazy ideas and innovative experiments. Something will come up.”

(In answer to “Do you have any advice to

• ffer the next generation?”)

Niels Bohr

“We are all agreed that your theory is crazy. The question that divides us is whether it is crazy enough to have a chance

• f being correct.”

(Said to Pauli after his presentation.)

“The whole history of physics proves that a new discovery is quite likely lurking at the next decimal place.”

• F. K. Richtmyer

So, let us try a crazy idea, which might be lurking at the next decimal place.

I want the inflaton (+DM) that can be probed by ground-based experiments.

So, let us try a crazy idea, which might be lurking at the next decimal place.

2.What is the inflaton?

V

• δφ = H

2π

Inflation

Quantum fluc. Inflaton

V

• δφ = H

2π

Inflation

Quantum fluc. Slow-rolls Inflation Inflaton

V

• δφ = H

2π

Inflation

rolls rapidly Inflation ends Quantum fluc. Slow-rolls Inflation Inflaton

V

• δφ = H

2π

Inflation

rolls rapidly Inflation ends Quantum fluc. Slow-rolls Inflation Inflaton

Decays into SM particles

Reheating

V

• δφ = H

2π

Inflation

rolls rapidly Inflation ends Quantum fluc. Slow-rolls Inflation Inflaton

Decays into SM particles

Reheating

Inflation and density perturbations

The quantum fluctuations lead to slightly different evolution at different points. Fluctuation in time = Fluctuation in volume = Density perturbations

V

• δφ = H

Spectral index: Amplitude:

: CMB normalization

k

10-9

kns−1

ns > 1

ns < 1

Scalar mode perturbations

The potential must be flatter for lower inflation scale.

ns is determined mainly by V’’ for low-scale inflation.

ns = 0.965 ± 0.004

Suppose that the inflaton is so light that it is kinematically accessible for experiments.

Suppose that the inflaton is so light that it is kinematically accessible for experiments. For successful reheating, the light inflaton should have sizable couplings to the SM.

1)

Suppose that the inflaton is so light that it is kinematically accessible for experiments. For successful reheating, the light inflaton should have sizable couplings to the SM.

1)

The inflaton may be produced at experiments

• r astrophysical environment (e.g. inside stars)

Inflaton

Std. Model

Reheating Production

φ fφ OSM

V

• Suppose that the inflaton is so light that it is

kinematically accessible for experiments. The inflaton potential is extremely flat, in spite

• f large couplings to the SM.

2)

V

• Suppose that the inflaton is so light that it is

kinematically accessible for experiments. The inflaton potential is extremely flat, in spite

• f large couplings to the SM.

2)

The flatness of the inflaton potential can be ensured by shift symmetry, if it is an NG boson.

Suppose that the inflaton is so light that it is kinematically accessible for experiments.

The inflaton is likely an axion/ALP with sizable couplings to the SM.

Do we have any testable predictions?

See talks by Kawasaki, Ringwald, and Tokiyasu for axions.

Inflaton = ALP

Let us suppose that the inflaton is an ALP which enjoys a (discrete) shift symmetry,

φ → φ + 2πnf

suppressing dangerous radiative correction. Then, the inflaton potential is periodic, i.e.,

n ∈ Z V (φ) = V (φ + 2πf)

and can be expressed as Fourier series,

V (φ) = X

n∈Z

cnein φ

• Super-Planckian decay constant

required:

• Predicted (ns,r) are not favored

by CMB obs.

Natural inflation

φ/f

• Natural inflation

Only large-field inflation is possible with a single cosine term.

Low-scale axion inflation can be realized with at least two cosine terms: “Multi-natural inflation”

• Axion hilltop inflation

Vinf(φ) = Λ4 ✓ cos ✓φ f + θ ◆ − κ n2 cos ✓nφ f ◆◆ + const. = V0 − λφ4 − θΛ4 f φ + (κ − 1) Λ4 2f 2 φ2 + · · ·

λ ∼ Λ4 f 4

for and |κ 1| ⌧ 1

|θ| ⌧ 1

where

φ

V0

∼ −λφ4

λ ∼ ✓Λ f ◆4 ∼ 10−13

CMB normalization:

independent of V0

Low-scale axion inflation can be realized with at least two cosine terms: “Multi-natural inflation”

• Axion hilltop inflation

Vinf(φ) = Λ4 ✓ cos ✓φ f + θ ◆ − κ n2 cos ✓nφ f ◆◆ + const. = V0 − λφ4 − θΛ4 f φ + (κ − 1) Λ4 2f 2 φ2 + · · ·

λ ∼ Λ4 f 4

The inflaton mass at the minimum, , depends on n.

mφ

• 1

• 1

Even n Odd n

mφ ∼ Λ2/f

mφ ⌧ Λ2/f

• 1

The potential is flat only around the potential maximum.

mφ ∼ Λ2 f

λ ∼ ✓Λ f ◆4 ∼ 10−13

: CMB norm

f ∼ 106mφ

Even n

• 1

The potential is flat only around the potential maximum.

mφ ∼ Λ2 f

λ ∼ ✓Λ f ◆4 ∼ 10−13

: CMB norm

f ∼ 106mφ

Even n

• 1

The potential is flat both around the maximum and minimum.

mφ ∼ 0.1Hinf ∼ 0.1 Λ2 Mp

1 ns = 2M 2

V 00 V ' 2 3 m2

H2

' 0.04

So + CMB norm.

f ∼ 103p mφMp

Odd n

10-15 10-10 10-5 1 105 105 107 109 1011 mϕ[GeV] f[GeV] n=2(even) n=3(odd) Inflection (n=2, θ≃π/4)

FT and Yin,1903.00462

ALP mass and decay constant

• cf. for QCD axion

f ∼ 1012 GeV(ma/6 µeV)−1

f ∼ 103p mφMp

f ∼ 106mφ

10-15 10-10 10-5 1 105 105 107 109 1011 mϕ[GeV] f[GeV] n=2(even) n=3(odd) Inflection (n=2, θ≃π/4)

FT and Yin,1903.00462

ALP mass and decay constant

• cf. for QCD axion

f ∼ 1012 GeV(ma/6 µeV)−1

f ∼ 103p mφMp

f ∼ 106mφ

ALP mass and decay constant

Figure taken from 1205.2671

In the case of the ALP coupled to photons

ALP mass and decay constant

Figure taken from 1205.2671

ALP inflation (Even n) ALP inflation (Odd n)

In the case of the ALP coupled to photons

ALP mass and decay constant

Figure taken from 1205.2671

Q C D a x i

• n

ALP inflation (Even n) ALP inflation (Odd n)

In the case of the ALP coupled to photons

• 3. Inflaton hunt by ground-

based experiments

The case of even n

• 1

1 2 3 4 5 0.5 1.0 1.5

We consider the following ALP inflaton couplings to the SM:

(1) Coupling to photons (or weak gauge bosons at high T) (2) Couplings to the SM fermions

L = cγ α 4π φ f Fµν ˜ F µν ≡ 1 4gφγγφFµν ˜ F µν,

L = X

k

ickmk f φ ¯ ψkγ5ψk,

gφγγ = cγα πf

cγ = X

i

qiQ2

i

φ → φ + βf

where the anomaly coefficient is related to charges of the extra fermions as

The precise value of is model-dependent, and it can be of order 10-2 - 102 without invoking a contrived set-up.

cγ

(1) Coupling to photons (or weak gauge bosons at high T)

L = cγ α 4π φ f Fµν ˜ F µν ≡ 1 4gφγγφFµν ˜ F µν,

Ψi → eiβqiγ5/2Ψi

Ψi

EM charge PQ charge

Parameter regions predicted by ALP inflation (with even n)

For , the predicted region overlaps with the SHiP sensitivity.

n=2

SHiP J-PARK(MR) PIP120 NA62 0.1 0.2 0.5 1 2 10-8 10-7 10-6 10-5 10-4 mϕ[GeV] gϕγγ[GeV-1] cγ=300 cγ=30 cγ=1

cγ & 10

10-15 10-13 10-11 10-9 10-7 10-5 1 10 102 103 104 105 106 107 gϕγγ[GeV-1] TR[GeV] cγ=30 cγ=1

Reheating thru ALP-photon coupling

The ALP inflaton decays into photons, , and also dissipate through scattering, e.g., .

φ → γγ

φ + γ → e+ + e−

10-15 10-13 10-11 10-9 10-7 10-5 1 10 102 103 104 105 106 107 gϕγγ[GeV-1] TR[GeV] cγ=30 cγ=1

Reheating thru ALP-photon coupling

Instantaneous reheating

SHiP

The ALP inflaton decays into photons, , and also dissipate through scattering, e.g., .

φ → γγ

φ + γ → e+ + e−

(2) Couplings to the SM fermions

L = X

k

ickmk f φ ¯ ψkγ5ψk,

Such couplings arise if we introduce two Higgs doublets as in the DFSZ axion model. After integrating out the heavy degrees of freedom, we obtain H1 = H cos β exp  iQH1 φ f

• ,

H2 = ˜ H sin β exp  iQH2 φ f

• ,

tan β ⌘ ⌦ H0

↵ hH0

ci = QH1 or QH2

(i.e. PQ charge of the Higgs that it is coupled to.)

In the case that the inflaton has (universal) Yukawa-like interactions, i.e.,

FT and Yin, 1903.00462

0.1 0.5 1 5 10-9 10-8 10-7 10-6 10-5 10-4 10-3 mϕ[GeV] cf f -1[GeV-1] c

f

=1 c

f

=0.1 c

f

=0.01

SHiP

ci = cf

Reheating thru Yukawa-like couplings

The ALP inflaton decays into the SM fermions (+Higgs if kinematically allowed), and dissipate through thermalscattering.

10-14 10-12 10-10 10-8 10-6 10 102 103 104 105 106 107 108 cf f -1[GeV-1] TR[GeV] cf =1 cf =0.1

FT and Yin, 1903.00462

Reheating thru Yukawa-like couplings

Instantaneous reheating

SHiP

The ALP inflaton decays into the SM fermions (+Higgs if kinematically allowed), and dissipate through thermalscattering.

10-14 10-12 10-10 10-8 10-6 10 102 103 104 105 106 107 108 cf f -1[GeV-1] TR[GeV] cf =1 cf =0.1

FT and Yin, 1903.00462

The case of odd n

• 1

1 2 3 4 5 0.5 1.0 1.5

KSVZ

Q C D a x i

• n

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

• Inflaton (ALP) mass and coupling to photons

gφγγ = cγα πf

cγ = X

qiQ2

ψi → eiβqiγ5/2ψi

L = gφγγ 4 φFµν ˜ F µν

KSVZ

Q C D a x i

• n

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

• Inflaton (ALP) mass and coupling to photons

gφγγ = cγα πf

ALP inflation w/ odd n

cγ = X

qiQ2

ψi → eiβqiγ5/2ψi

L = gφγγ 4 φFµν ˜ F µν

Reheating and ALP DM

• 1

L = gφγγ 4 φFµν ˜ F µν

Inflaton (ALP) condensate Photons, SM particles

Decay & dissipation Remnant

ALP Dark Matter

ALP Dark Radiation

• r HDM

Thermalized

ξ ≡ ρφ ρφ + ρR

• after reheating

As we shall see,

ξ = O(0.01) is required to explain DM.

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

Successful inflation

Successful reheating

CDM

Small-scale structure constraint on ALP CDM

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

Successful inflation

Successful reheating

CDM

Small-scale structure constraint on ALP CDM HDM constraint on thermalized ALP

gφγγ = O(10−11) GeV−1

Inflaton = DM = ALP

within the reach of future axion helioscopes and laser experiments.

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

*Plus, there is a preference for extra cooling of HB stars

gφγγ = (0.29 ± 0.18) × 10−10 GeV−1

“An ALP miracle”

Summary

• Inflaton may be searched for at experiments, if the

inflaton is an NG boson with sizable couplings to SM.

f ∼ 103p mφMp

f ∼ 106mφ

• The predicted relations between the mass and decay

constant are

• SHiP (beam dump exp. at CERN)
• The decay of the axion is same

as the reheating! “Big Bang on Earth”

• IAXO/TASTE (Solar axion search)
• The remnant inflaton can be DM.

“ALP miracle”

• Dark radiation with ∆Neff ' 0.03

mφ = O(0.1 − 1) GeV

mφ = O(0.01 − 1) eV

Even n Odd n