Dark Energy In Hybrid Inflation

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Dark Energy In Hybrid Inflation

• Seongcheol Kim
• (KAIST)

Based on Phys. Rev. D75 063520(2007)
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• CONTENTS
• 1. Introduction
• 2. Idea
• 3. Model Building
• 4. SUSY Realization
• 5. Summary

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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 ?CDM, 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?

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IDEA
1. Inflation stage
Scalar field
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?

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IDEA

• Combining the onset of present acceleration with
  the primordial 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 field which plays no role during
  the inflaton rolls down its potential and only
  works to finish inflation.

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MODEL BUILDING
Inflation end of inflation
quintessence field all fields are

start to roll settled down

1st phase transition
2nd phase transition
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1st Stage Primordial Inflation

• 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
  .

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2nd Stage Phase transition between? and ?
The waterfall field ? oscillates at the minimum
and decays so that the Universe is reheated.
We assumes that the critical point of waterfall
field is earlier than the minimum point of the
potential
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2nd Stage Phase transition between? and ?

• Waterfall condition
• 1. The absolute value of the effective mass
  square of ? is much larger than H2
• 2. The time scale for ? to roll down from ?c to 0
  be much shorter than H-1
• Amplitude of density perturbation

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3rd Stage Phase transition between ? and s
We assumed that the critical point of waterfall
field is earlier than the minimum point of the
potential
The minimum along s direction is
The minimum of the potential when all fields
are settled down
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3 Kinds of Vacuum
1. positive vacuum 2. zero vacuum 3.
negative vacuum density density density
usual quintessential inflation
Similar to ?CDM
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SUSY REALIZATION

• 1. Hybrid Inflation
• superpotential
• where ?1 and ?2 are pair of superfields in
  non-trivial representations of some gauge group
  under which ? is neutral.
• the effective potential
• By simply adding a mass term which
  softly breaks supersymmetry, we see that the
  hybrid inflation scenario is possible.

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SUSY REALIZATION

• 2. Our Model
• D-term contribution
• The coupled term of ? and s has a negative sign.
• We use ? and s oppositely charged under U(1)
  symmetry.
• ? and ? are charged with same sign.
• The coupled terms

but

• We do not consider F-term contribution
• 2. 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.

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Summary

• We have investigated a simple model based on
  hybrid inflation.
• The quintessence field s is coupled to the
  waterfall field ? so that ? rolls toward
  , s 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.