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

+ Inflation theoryBig 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 theoretica l curve observation

+ Inflation occurs around. 2. Inflationary observables Standard inflation K-inflation Scalar Spectral Index ： Tensor to Scalar Ratio ： Non-Gaussianity Parameter ： (68% CL) (95% CL) is constrained by and. Inflation occurs around. For the Lagrangian Equation of stateScalar field propagation speed (order of slow-roll)

+ Scalar Spectral Index Action Slow variation parametersScalar field propagation speed 3. Perturbations Tensor to Scalar Ratio Non-Gaussianity Parameter ( Seery and Lidsey, 2005 ) for the primordial density perturbation

arbitrary function （ is constant ） (Piazza and Tsujikawa, 2004) Effective single field 4. Assisted k-inflation models General 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

with, Dilatonic ghost condensate DBI field example Effective single field form of assisted Lagrangian ( 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

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.

+ Canonical field with an exponential potential (95%CL) Likelihood analysis with COSMOMC WMAP (7 year) data, BAO, and HST ( 95% CL ) observation 5. Observational constraints on some models probability distribution

Dilatonic ghost condensate (95%CL ) with the central value of when Likelihood analysis with COSMOMC probability distribution

DBI field Assisted inflation occurs when changes with arbitrary constant probability distribution with the central value of

+ 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 physics with 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.

+

6. More general models Let’s consider the more general functions of in which Class (i) the numerators of and Linear expansion of and by setting satisfies for

Class (ii) the denominator of Generalization of DBI model Under the condition that and

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

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 EquilateralLocal/Squeezed 統計の取り方 の違い