Dark Energy In Hybrid Inflation

Seongcheol Kim(KAIST)

Based on Phys. Rev. D75: 063520(2007)

CONTENTS

1. Introduction

2. Idea

3. Model Building

4. SUSY Realization

5. Summary

INTRODUCTION* Observations say that the Universe is composed of 70% unknown form energy. We call it “Dark Energy”.

* There are many models to explain the Dark Energy. For example ΛCDM, quintessence, anthropic principle...

* Our model is based on the quintessence model.

* Our model comes from a question. How can we couple the early accelerated expansion, and the current one together?

IDEA

Scalar field

1. Inflation stage

1st phase transition

2. End of Inflation

and start Standard Cosmology

2nd phase transition

3. Scalar filed slowly rolls again

• There are 3 scalar fields and 2 phase transitions

• How can we combine 3rd scalar field with the others?

IDEA Combining the onset of present acceleration with the primordi

al inflation by indirectly coupling the inflaton with the quintessence field.

Inflation lasts for a long enough time without being disturbed by the interaction with the quintessence field.

Directly coupling the quintessence field with some different fi

eld which plays no role during the inflaton rolls down its potential and only works to finish inflation.

2222 )(4

1

2

1),,(

MmV 22

2

2g

222 )(

4

1 M 22

2

2h

inflaton

waterfall field

quintessence field

MODEL BUILDING

0

0

c

0

roll start to

c

roll start to

0

c

0

0

0

1st phase transition 2nd phase transition

Inflation end of inflation quintessence field all fields are

start to roll settled down

1st Stage : Primordial Inflation

(trapped) 0

0 (trapped) 0

0 / if2222

2222

Mhm

MgmgMc

g

Mc

during lasts stage This

This process is almost same as hybrid inflation when we assume these.

1. The vacuum density is much larger than the potential energy density of the inflaton field.

2. The vacuum energy V(0,0,0) is dominated by .

)(2

1 22

22

MM

mH

Pl

22

MM

/2M

2nd Stage : Phase transition betweenф and ψ

(trapped) 0

0

)( roll start to is

0 / if

2222

2222

Mhm

MgmgM

c

c

We assumes that the critical point of waterfall field is earlier than the minimum point of the potential

M

h

Mc 0

c

c

c

The waterfall field ψ oscillates at the minimum and decays so that the Universe is reheated.

Ψ field

2nd Stage : Phase transition betweenф and ψ

* Waterfall condition1. The absolute value of the effective mass square of ψ is much large

r than H2

2. The time scale for ф to roll down from фc to 0 be much shorter than H-1

* Amplitude of density perturbation

2322 212 plmmMHm

231 24 plgmmMHt

GeV10~ then GeV10~ ,10~ ~ if e.g. 11212 Mmg

510~/

3rd Stage : Phase transition between ψ and σ

roll start to is

0

/ if2222

Mhm

hMc

M

h

Mc 0

* We assumed that the critical point of waterfall field is earlier than the minimum point of the potential

* The minimum along σ direction is : 0222

20

MMh

* The minimum of the potential when all fields are settled down

)2(4

2222

22

0

MhMMh

V

c

c

c σ field

3 Kinds of Vacuum

-0.5 0.5 1 1.5 2z

-1

-0.5

0.5

1w

-0.5 0.5 1 1.5 2z

-1

1

2

3

w

2222 2 MMhM

-0.5 0.5 1 1.5 2z

-1

-0.5

0.5

1

w

1. positive vacuum 2. zero vacuum 3. negative vacuum density density density

2222 MhM 2222 MhM

Similar to ΛCDM usual quintessential inflation

SUSY REALIZATION

1. Hybrid Inflationsuperpotential :where ψ1 and ψ2 are pair of superfields in non-trivial representations of some gauge group under which ф is neutral.

the effective potential :

By simply adding a mass term which softly breaks supersymmetry, we see that the hybrid inflation scenario is possible.

)( 221 W

2221

22

21

22 ||)|||(||| V

2/22m

SUSY REALIZATION

2. Our ModelD-term contributionThe coupled term of ψ and σ has a negative sign.We use ψ and σ oppositely charged under U(1) symmetry.

ф and ψ are charged with same sign.

The coupled terms2

12222

22

1222 ||)||(||)](||[

22

222

)|||(|2

21

222

)||||(2

but 1. We do not consider F-term contribution2. In globally supersymmetric theories the scalar potential does not allow negative value.3. A more detailed analysis of our model and associated problems should be addressed in the context of supergravity.

Summary We have investigated a simple model based on hybrid inflatio

n.

The quintessence field σ is coupled to the waterfall field ψ so that ψ rolls toward , σ begins to move along the effective potential.

The true minimum of the effective potential depends on our choice of the parameters, allowing the vacuum state with positive, negative and zero energy.

This model could be realized in supersymmetric theories via D

-term contribution, but including F-term parts and supergravity effects makes investigation of our model challenging.

/0 M