Dterm chaotic inflation in supergravity

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D-term chaotic inflationin supergravity

• Masahide Yamaguchi
• (Aoyama Gakuin University)
• arXiv0706.2676
• Collaboration with Kenji Kadota
• 24th Sep 07 _at_KIAS-YITP joint workshop

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Outline

• Introduction
• Inflation models
• How difficult to realize chaotic inflation
  
• in supergravity
• D-term chaotic inflation model in supergravity
• Model
• Dynamics and density perturbations
• Summary and Discussion

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General prediction of inflation

• Global isotropy and homogeneity
• Spatially flat universe
• Almost scale invariant, adiabatic, and Gaussian
  density fluctuations

WMAP results strongly support inflation.
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Inflation models proposed so far

• Old Inflation
• New Inflation
• Hybrid inflation
• Chaotic Inflation

Inflation does not end.
Guth, Sato 81
Linde, Albrecht Steinhardt 82
Fine tuning of initial conditions.
Linde 91
No fine tuning of initial conditions.
Linde 83
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Inflation model building
Slow-roll
Nearly flat potential
Keep flat against radiative corrections
Supersymmetry (Supergravity)
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Scalar potential in supergravity
K Kähler potential
W Superpotential
Due to the factor eK, it has been considered
almost impossible to realize chaotic inflation
in supergravity.
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F-term chaotic inflation in supergravity
(Kawasaki, MY, Yanagida)
Nambu-Goldstone-like shift symmetry
(C a dimensionless real parameter)
e.x.
(m represents the breaking of the shift symmetry)
Chaotic inflation can take place naturally.
However, it may be difficult to associate it
with the low energy effective theory of particle
physics such as GUT.
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D-term chaotic inflation in supergravity
Model
We introduce four superfields charged under U(1)
gauge symmetry and U(1)R symmetry,
The general (renormalizable) superpotential
(a, b, c are real and positive constants, for
simplicity)
We take the canonical Kahler potential, the
minimal gauge kinetic function, and the vanishing
FI term for simplicity.
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Scalar potential
Note that the F-flat direction exists.
The global minimum of the potential is given by
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Realization of chaotic inflation
When the universe starts around the Planck
scale, the global minimum of the potential is not
necessarily realized.
Instead, the almost F-flat condition is first
realized due to the exponential factor eK of
the F-term, if ,
and , for example.
(Note that the dynamics is essentially the
same even if we interchange by
.)
The potential is mostly dominated by the D-term
and chaotic inflation can take place.
plays the role of an inflaton.
Next, we investigate the dynamics in detail.
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Dynamics of the homogeneous mode I
The actual inflation trajectory is slightly
deviated from the exact F-flat direction due to
the presence of the D-term and given by
In fact, f3 and f4 dynamically go to the origin
during inflation because their masses are much
larger than
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Dynamics of the homogeneous mode II
The dynamics is described by the following
effective potential,
Here, we redefine the fields
This trajectory (almost F-flat direction) is a
massless mode and becomes an inflaton, which is
well parametrized by the field f1.
The eigenvalues of the mass matrix are given by
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Dynamics of the homogeneous mode III
The dynamics of the homogeneous mode is
completely described by the following reduced
potential,
Chaotic inflation with the quartic potential is
realized.
That is, though we have introduced four fields,
there is only one massless mode corresponding to
the almost F-flat direction, which is
automatically lifted by the D-term.
In fact, the potential is dominated by the D-term
during inflation,
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Primordial density fluctuations I
We have only one light field.
Only adiabatic mode
Adiabatic condition
We have the relation between df1 and df2.
(Note that df3 and df4 are massive so that we
neglect them.)
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Primordial density fluctuations II
By inserting this relation, the equation of
motion for the perturbation becomes
On the other hand, by use of the adiabatic
condition, the gravitational potential in the
long wave limit is given by
Thus, the density fluctuations are completely
determined by the reduced potential
.
g O(10-6) to explain the primordial density
fluctuations.
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Summary and Discussion

• In this talk, we have presented a D-term chaotic
  inflation
• model in supergravity.
• The gauge coupling g should be g O(10-6) in
  order to
• explain the primordial density fluctuations.
• Even though we presented a toy model of the
  quartic potential
• chaotic inflation, the leading order
  polynomial can be different
• by choosing the non-minimal gauge kinetic
  function.
• As for the reheating, it may require the
  breaking of the gauge
• symmetry after inflation because the inflaton
  cannot directly
• decay into the standard particles due to the
  charge conservation.
• Such a breaking can occur, for instance, by
  the introduction of
• the FI term or a Higgs-like field.