University of Portsmouth Non-Gaussiniaty from multi-field inflation with non-standard kinetic terms Kazuya Koyama University of Portsmouth Arroja, Mizuno, Koyama JCAP0808 015 (0806.0619) Arroja, Mizuno Koyama in preparation Mizuno, Arroja, Koyama, Tanaka in preparation

Primordial curvature perturbations Komatsu et.al. 2008 Proved by CMB anisotropies nearly scale invariant nearly adiabatic nearly Gaussian Generation mechanisms inflation curvaton collapsing universe (Ekpyrotic, cyclic)

Generation of curvature perturbations Delta N formalism curvature perturbations on superhorizon scales = fluctuations in local e-folding number Stewart&Sasaki ’95, Sasaki& Tanaka ‘98, …

Suppose delta N is caused by some field fluctuations at horizon crossing Bispectrum Lyth&Rodriguez ‘05 Local type (‘classical’) (local in real space =non-local in k-space) Equilateral type (‘quantum’) (local in k-space)

Observational constraints local type maximum signal for WMAP5 Equilateral type Smith et.al. ‘09

Theoretical predictions Standard inflation Non-standard scenario Single field K-inflation, DBI inflation Features in potential Ghost inflation Multi field depending on the trajectory DBI inflation curvaton new Ekpyrotic (simplest model) isocurvature perturbations (axion CDM) Maldacena ‘04 Rigopoulos, Shellard, van Tent ’06 Wands and Vernizzi ’06 Yokoyama, Suyama and Tanaka, Sasaki,…

K-inflation Non-canonical kinetic term Field perturbations (leading order in slow-roll) Amendariz-Picon et.al ‘99 sound speed Garriga&Mukhanov ‘99

Bispectrum DBI inflation cf. local-type Aishahiha et.al. ‘04

Trispectrum Contact interaction Scalar exchange the same order as the Chen, Huang & Shui, hep-th/0610235 v5 Arroja, Mizuno & Koyama, to appear soon

Consistency relations Squeezed limit gives a time delay in the horizon crossing time Consistency relations

Shape dependence Equilateral configurations Unlike bispectrum, this does not fix the shape completely

Equilateral trispectrum

Folded kite limit Scalar exchange long-wavelength scalar mode changes the background Seery, Sloth & Vernizzi ‘08,

Maximum Maximum appears for contact scalar exchange

Factorisable approximations? Estimator in CMB DBI

Factorisable form Trispectrum 5 parameters for the shape For equilateral configurations there is angular dependences though they are very weak Cremineli et.al. Kogo and Komatsu‘08,

String theory models (too) large non-Gaussianity Lyth bound for equilateral configurations D3 anti-D3 inflaton Huston et.al ’07, Bean et.al. ’07 Kobayashi et.al ‘08

Multi-field model Adiabatic and entropy decomposition Arroja, Mizuno, Koyama ’08 Renaux-Petel, Steer, Langlois Tanaka‘08 Adiabatic and entropy decomposition adiabatic sound speed entropy sound speed entropy adiabatic

Multi-field k-inflation Huang, Shiu, Underwood ‘07 Multi-field k-inflation Multi-field DBI inflation Easson et.al. ‘07 Langlois&Renaux-Petel’08 Renaux-Petel, Steer, Langlois Tanaka‘08 Unlike k-inflation, the entropy perturbations can develop large non-Gaussianity!

Boost DBI action describes fluctuations of a position of brane Boost Tanaka ‘08, Mizuno, Arroja ,Koyama, Tanaka’09 DBI action describes fluctuations of a position of brane Boost P: brane is at rest P’ : brane is moving

Action P: P’:

Transfer from entropy mode Tensor to scalar ratio Bispectrum k-dependence is the same as single field case! large transfer from entropy mode eases constraints Renaux-Petel, Steer, Langlois Tanaka‘08

Trispectrum (preliminary results) Mizuno, Arroja ,Koyama, Tanaka’09 Equilateral configurations Unlike bispectrum, the shape depends on (consistency relation does not hold for entropy modes)

Summary Single field DBI inflation - Full bispectrum/trispectrum were obtained - Need a fast estimator for trispectrum String theory models - Multi-field models could evade stringent constraints from string theory requirements - Trispectrum has different shape dependence from single field models - Need explicit models to calculate the transfer function Chen, Gong, Koyama & Tasinato work in progress