+

Observational constraints on assisted k-inflation

Tokyo University of ScienceJunko Ohashi and Shinji Tsujikawa

+

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

+

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)

+

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

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

with ,

Dilatonic ghost condensate

DBI field

example

Effective single field form of assisted Lagrangian

( 　　 const. ）

( 　　 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 analysiswith COSMOMCWMAP (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 analysiswith COSMOMC

probability distribution

DBI field

Assisted inflation occurs when

changes with arbitrary constant

probability distribution

with the central value of

+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.

+

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

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

Equilateral Local/Squeezed

統計の取り方の違い