+ Observational constraints on assisted k-inflation Tokyo University of Science Junko Ohashi and...
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Observational constraints on assisted k-inflation
Tokyo University of ScienceJunko Ohashi and Shinji Tsujikawa
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Inflation theory
Big Bang cosmology
1. Motivation
Horizon and flatness problems
Inflation theory
Exponential expansion at energy scale in the early universe
: Starobinsky , Guth , Sato , Kazanas (1980)
Inflaton quantum
fluctuation
Primordial density perturbation
Cosmic Microwave Background temperature perturbation
almost scale invariant consistent with WMAP
observations
theoretical curve
observation
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Inflation occurs around .
2. Inflationary observables
Standard inflation
K-inflation
Scalar Spectral Index :Tensor to Scalar Ratio :Non-Gaussianity Parameter :
(68% CL)
(95% CL)
(95% CL)
is constrained by and .
Inflation occurs around .
For the Lagrangian
Equation of state
Scalar field propagation speed
(order of slow-roll)
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Scalar Spectral Index
Action
Slow variation parameters
Scalar field propagation speed
3. Perturbations
Tensor to Scalar Ratio
Non-Gaussianity Parameter
( Seery and Lidsey, 2005 )
for the primordial density perturbation
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arbitrary function
( is constant )
(Piazza and Tsujikawa , 2004)
Effective single field
4. Assisted k-inflation modelsGeneral multi-field models leading to assisted inflation
is satisfied even if .
Effective single field
( Liddle, Mazumdar, and Schunck 1998 )
In general from the particle physics.condition for
inflation
Inflation occurs due to the multi filed effect.
Assisted inflation mechanism
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with ,
Dilatonic ghost condensate
DBI field
example
Effective single field form of assisted Lagrangian
( const. )
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( const. )
At the fixed point of assisted inflation,
Once is given, then becomes constant.
These two parameters are constant because they are functions of only.
Slow variation parameter
Field propagation speed
Effective single-field system
4. Perturbations for assisted k-inflation
Therefore
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For the Lagrangian
These observables can be represented with one parameter ( , , , or ).
( functions of )
( functions of or )
Assisted inflation
Three Inflationary Observables
Once is given,
Scalar Spectral Index
Non-Gaussianity Parameter
Tensor to Scalar Ratio
( functions of or )
We can constrain the parameter from the CMB observations.
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Canonical field with an exponential potential
(95%CL)
Likelihood analysiswith COSMOMCWMAP (7 year)
data,BAO, and HST
( 95% CL )observation
5. Observational constraints on some models
probability distribution
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Dilatonic ghost condensate
(95%CL)
with the central value of
when
Likelihood analysiswith COSMOMC
probability distribution
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DBI field
Assisted inflation occurs when
changes with arbitrary constant
probability distribution
with the central value of
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+6. Conclusion
Using the CMB likelihood analysis, we have studied the observational constraints on assisted k-inflation models described by the Lagrangian .
We will discuss other models motivated by particle physicswith the future high-precision observations .
We have also extended the analysis to more general functions of .From the observational constraints we have found that the single-power models with are ruled out.
Since it is possible to realize for the k-inflation model, it can be constrained by the observations.
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6. More general modelsLet’s consider the more general functions of in which Class (i) the numerators of and
Linear expansion of andby setting
satisfies
for
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Class (ii) the denominator of
Generalization of DBI model
Under the condition that and
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加速膨張の条件状態方程式
から
正準スカラー場モデル
Ghost condensate
Action
条件を満たすには
ポテンシャル項が効いてインフレーションを起こす
十分なインフレーションを起こすには
運動エネルギー項でインフレーションを起こす
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バイスペクトル
相互作用ハミルトニアン
ハイゼンベルグ描像 相互作用描像
摂動3次オーダーのラグランジアンと関係する.
作用を3次まで展開して を得る
・・・3点相関関数をフーリエ変換したもの
3つの波数ベクトルの長さの関数
Equilateral Local/Squeezed
統計の取り方の違い