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

2. 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)

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

4. 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)

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

6. 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,…

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

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

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

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

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

14. Equilateral trispectrum

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

16. Maximum
Maximum appears for
contact
scalar exchange

17. Factorisable approximations?
Estimator in CMB
DBI

18. 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,

19. 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

20. 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

21. 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!

22. 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

23. Action
P: P’:

24. 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

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

26. 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