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+ Observational constraints on assisted k-inflation Tokyo University of Science Junko Ohashi and Shinji Tsujikawa

+ Observational constraints on assisted k-inflation Tokyo University of Science Junko Ohashi and Shinji Tsujikawa

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Page 1: + Observational constraints on assisted k-inflation Tokyo University of Science Junko Ohashi and Shinji Tsujikawa

+

Observational constraints on assisted k-inflation

Tokyo University of ScienceJunko Ohashi and Shinji Tsujikawa

Page 2: + Observational constraints on assisted k-inflation Tokyo University of Science Junko 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

Page 3: + Observational constraints on assisted k-inflation Tokyo University of Science Junko Ohashi and Shinji Tsujikawa

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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)

Page 4: + Observational constraints on assisted k-inflation Tokyo University of Science Junko Ohashi and Shinji Tsujikawa

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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

Page 5: + Observational constraints on assisted k-inflation Tokyo University of Science Junko Ohashi and Shinji Tsujikawa

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

Page 6: + Observational constraints on assisted k-inflation Tokyo University of Science Junko Ohashi and Shinji Tsujikawa

with ,

Dilatonic ghost condensate

DBI field

example

Effective single field form of assisted Lagrangian

(    const. )

Page 7: + Observational constraints on assisted k-inflation Tokyo University of Science Junko Ohashi and Shinji Tsujikawa

(    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

Page 8: + Observational constraints on assisted k-inflation Tokyo University of Science Junko Ohashi and Shinji Tsujikawa

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.

Page 9: + Observational constraints on assisted k-inflation Tokyo University of Science Junko Ohashi and Shinji Tsujikawa

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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

Page 10: + Observational constraints on assisted k-inflation Tokyo University of Science Junko Ohashi and Shinji Tsujikawa

Dilatonic ghost condensate

(95%CL)

with the central value of

when

Likelihood analysiswith COSMOMC

probability distribution

Page 11: + Observational constraints on assisted k-inflation Tokyo University of Science Junko Ohashi and Shinji Tsujikawa

DBI field

Assisted inflation occurs when

changes with arbitrary constant

probability distribution

with the central value of

Page 12: + Observational constraints on assisted k-inflation Tokyo University of Science Junko Ohashi and Shinji Tsujikawa

+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.

Page 13: + Observational constraints on assisted k-inflation Tokyo University of Science Junko Ohashi and Shinji Tsujikawa

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Page 14: + Observational constraints on assisted k-inflation Tokyo University of Science Junko Ohashi and Shinji Tsujikawa

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

Page 15: + Observational constraints on assisted k-inflation Tokyo University of Science Junko Ohashi and Shinji Tsujikawa

Class (ii) the denominator of

Generalization of DBI model

Under the condition that and

Page 16: + Observational constraints on assisted k-inflation Tokyo University of Science Junko Ohashi and Shinji Tsujikawa

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

Page 17: + Observational constraints on assisted k-inflation Tokyo University of Science Junko Ohashi and Shinji Tsujikawa

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