YA, T. Inami, Y. Kawamura, & Y. Koyama, [arXiv:1504.06905] · We propose the inflationary cosmology based on the 5-dimensional gravity + gauge theory. In our model, two scalar fields,

Yugo Abe (Shinshu University)

GRaB100@NTU, July 10, 2015

In collaboration with

T. Inami (NTU), Y. Kawamura (Shinshu U), Y. Koyama (NCTS)

YA, T. Inami, Y. Kawamura, & Y. Koyama, [arXiv:1504.06905]

We propose the inflationary cosmology based on the 5-dimensional gravity + gauge theory.

In our model, two scalar fields, radion and gauge-Higgs , are obtained from 5d-gravity field and 5d-gauge field after compactification.

- Can the effective potential be identified with inflaton potential?

- If possible, which scalar fields has the role of inflaton?

- Where did inflaton come from? Gravity, gauge theory or both?

- In string theory point of view, radion appears from closed string and gauge-Higgs appears from open string.

Our focus 0

What kind of symmetry can control scalar potential?

5D gravity + gauge theory

1-loop scalar potential (finite) = inflaton potential

Fine-tuning problem on inflationary cosmology

5D gauge symmetry

5D general coordinate transformation invariance

Problem

Cause

Our solution 3

2

1

Slow-roll inflation scenario -0 1

Inflation is the rapidly accelerated expansion of space at early stage of our universe.

From the particle physics point of view, the slow-roll inflation can be explained using a scalar potential (inflaton potential).

Slow-roll approximation( ) gives vacuum conditions and

, where and .

Friedmann eqs.

inflation solution

: scale factor

: Newton const.

: curvature

Inflation theory is the dynamics of scalar field(s) “inflaton”.

Constraints on inflaton potential -1 1 1) slow-roll conditions : flatness of potential

1) spectral index : amount of scale dependence of fluctuation

2) e-folding number : period in which inflation continues

1) curvature perturbation : reproduce the temperature fluctuations of CMB

1) tensor to scalar ratio : energy scale of inflation

1) quantum gravity correction is negligible.

(*: at the horizon exit)

(observations)

(observations)

(observations)

( : observations)

Fine-tuning parameters of inflaton potential

If we take the inflaton potential as .

is required by inflation constraints.

However considering quantum effects, all of terms which allowed by symmetries may appear.

Coefficients should be fine-tuned.

Furthermore, inflation occurs where ….

( : reduced Planck mass)

The inflaton potential is just given by hand or is derived from a theory. our way.

I will explain later.

( : cut-off)

Fine-tuning problem on inflational cosmology -2 1

What kind of symmetry can control scalar potential?

Scalar field doesn’t have a 4d symmetry of controlling the potential.

The serious divergent term appears from the quantum correction.

We must balance the relation between and .

On the other hand,

Where does the fine-tuning come from?

The gauge and gravity field doesn’t have the mass term, thanks to the gauge symmetry and general coordinate transformation invariance.

2 -0

How control to 4d scalar potential?

Only to evaluate .

Tree level Quantum level

・Higher-dimensional gauge symmetry ・Higher-dimensional general coordinate transformation invariance

cf. 4d gauge symmetry

Our answer : Higher-dimensional theory 2 -1

5d gauge field includes 4d gauge field and 4d scalar field .

Scalar fields are the extra components of the higher-dimensional fields.

Gauge-Higgs

5d gravity field includes 4d gravity field , 4d U(1) gauge field and 4d scalar field .

(V.E.V of radion is related to the size of the extra space)

,

Radion

5-dimensional gauge and gravity field -0 3

5d gauge theory -1 3

where,

at tree level (after compactification)

1-loop level

expansion

where V.E.V. of 4D scalar field :

5D gauge symmetry control the potential of 4D scalar filed.

5d gravity theory -2 3

expansion

1-loop level

at tree level (after compactification)

where V.E.V. of 4D scalar field :

5D general coordinate transformation invariance control the potential of 4D scalar filed.

Inflation from higher-dimensional theory

• 5d U(1) gauge theory : Extranatural inflation model

(2003. N. Arkani-Hamed et al.)

• 5d gravity theory : Radion inflation model

(2013. Fukazawa, Inami, Koyama)

Incomplete : Gauge coupling const. is too small.

Incomplete : 4D cosmological const. is introduced by hand.

where,

3 -3

5d gravity + gauge theory : Our model

where,

( YA, T. Inami, Y. Kawamura & Y. Koyama, PTEP 2014 [arXiv:1404.5125] )

Both Gauge-Higgs and Radion are higher-dimension origin.

However, each property and behavior differ from each other.

We can calculate the finite one-loop potential , thanks to the 5D gauge symmetry and 5D general coordinate transformation invariance.

Can our potential fulfill the constraints of inflation parameters?

5d gravity + gauge theory -4 3

Loop diagrams

n

n

n

n

+ +

+ +

+ +

-5 3

Our one-loop potential -6 3

Gauge-Higgs Radion : number of U(1)charged matter : U(1)charged matter mass : number of neutral matter : neutral matter mass : 5d cosmological constant

: compactification circumference

We investigate which scalar field has the dominant contribution to the inflaton potential and can be identified with the inflaton.

a. Single field inflation

a-1. inflaton = radion

a-2. inflaton = gauge-Higgs

b. Hybrid inflation

b-1. inflaton = radion, waterfall = gauge-Higgs

b-2. inflaton = gauge-Higgs, waterfall = radion

c. Multi inflaton inflation (Future work : We need complex analyses.)

What kind of inflation did we choose?

Possibilities of our inflation model -7 3

inflaton

inflaton

a. Single field inflation -8 3 a-1. radion inflation

( : reduced radion field)

a-2. gauge-higgs inflation (Extranatural)

inflaton

inflaton

a-2. gauge-higgs inflation (Extranatural)

a. Single field inflation -8 3 a-1. radion inflation

( : reduced radion field)

The case of radion inflation does not fulfill the slow-roll conditions.

b. Hybrid inflation -9 3 b-1. radion hybrid inflation

b-2. gauge-higgs hybrid inflation (Extranatural)

waterfall

inflaton

waterfall inflaton

b. Hybrid inflation -9 3 b-1. radion hybrid inflation

b-2. gauge-higgs hybrid inflation (Extranatural)

waterfall

inflaton

waterfall inflaton

The case of radion hybrid inflation does not fulfill the slow-roll conditions.

Besides the vacuum of potential, radion direction is the first rolling direction.

In our model, gauge-Higgs inflation can occur.

This model is large field inflation.

However, we could evaluate the potential without serious fine-tuning.

Radion is very important in determining the physical parameters, especially gauge coupling, matter masses and compactification scale.

charged fermion mass

neutral fermion mass

1/( circumference)

4d gauge coupling

inflaton mass

tensor to scalar ratio

Summary -F 3

Gauge-Higgs is inflaton. What is the role of radion?

- Can the effective potential be identified with inflaton potential?

- If possible, which scalar fields has the role of inflaton?

- Where did inflaton come from? Gravity, gauge theory or both?

- In string theory point of view, radion appears from closed string and gauge-Higgs appears from open string.

Our focus again 4 Our effective potential can cause inflation.

Gauge-Higgs is inflaton.

Inflation appears from gauge field. However, radion is also essential.

What is the origin of inflaton? “Closed string VS Open string”

Our result could indicate that the quantum theory of gravity such as string theory is necessary to understand the mechanism of inflation more properly.

- It would be interesting to study the inflation based on the effective potential relating several scalar fields such as the dilaton, the moduli (including the radion) and the gauge-Higgs in the framework of string theory.

Shape of our potential E x.1 The matter mass ratio change the shape of our effective potential.

: U(1)charged matter mass

: neutral matter mass

Multi field inflation case

If ,

, and are larger than Planck.

For example, the trajectry something like this is expected.

Multi inflaton inflation E x.2