observational constraints on assisted k -inflation
DESCRIPTION
Observational constraints on assisted k -inflation. Tokyo University of Science Junko Ohashi and Shinji Tsujikawa. 1. Motivation. Inflation theory. : Starobinsky , Guth , Sato , Kazanas (1980) . Big Bang cosmology. Inflation theory. Exponential expansion at energy scale - PowerPoint PPT PresentationTRANSCRIPT
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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 LagrangianEquation 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. ConclusionUsing 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