Multi-fieldDBI inflation

Sébastien Renaux-Petel(APC, Paris)

Based on David Langlois, S. R-P, arXiv:0801.1085 [hep-th], JCAP David Langlois, S. R-P, D. Steer & T. Tanaka, arXiv:0804.3139 [hep-th], PRL David Langlois, S. R-P, D. Steer & T. Tanaka, arXiv:0806.0336 [hep-th], PRD

UniverseNet, Oxford, 24.09.08

Outline

I : Action and background

II : Linear perturbations

III : Non-Gaussianities

Sébastien Renaux-Petel, APC

Introduction

• After 25 years of existence, inflation has been so far verysuccessful to account for observational data.

• Many high energy physics models involve several scalarfields. If several scalar fields are light enough duringinflation multi-field inflation !

• Models with non-standard kinetic terms: k-inflation, DBIinflation, …

• Multi-field extension and perturbations ?

Sébastien Renaux-Petel, APC

DBI inflation

– Brane inflation: inflaton as the distancebetween two branes

– Moving D3-brane in a higher-dimensionalbackground

The dynamics is governed by a Dirac-Born-Infeld action

Aim : take into account all the internal coordinates

Multi-field effective description

Sébastien Renaux-Petel, APC

[ Easson et al. ’07;Huang et al. ’07 ]

DBI action

Background : homogeneous fields

Including potential terms

Sébastien Renaux-Petel, APC

with

Action

DBI actionMultiple inhomogeneous fields

Terms which vanish for

- one field

- multiple homogeneous fields

Lorentz covariance allows to consider

Essential for perturbations

The object of our work

Sébastien Renaux-Petel, APC

A taste of DBI inflation

• In the homogeneous, one field, situation,

1. Slow-roll regime:

2. “Relativistic” regime:

[Silverstein, Tong ’04; Alishahiha, Silverstein, Tong’04]

Sébastien Renaux-Petel, APC

A taste of DBI inflation• How can we achieve inflation ?

1. Slow-roll regime:

for a potential dominated inflation

2. “Relativistic” regime:

with

Sébastien Renaux-Petel, APC

Linear perturbations : one field• Second-order action

• Canonically normalizedfield (in conformal time)

• Equation of motion in theslow-varying regime

• Amplification atsound horizoncrossing

Sébastien Renaux-Petel, APC

: field perturbation in the flat gauge

Linear perturbations : two fieldsTrajectory

in field space

Entropydirection Adiabatic

direction

• Adiabatic / Entropy decomposition

Linear perturbations : two fieldsTrajectory

in field space

Entropydirection Adiabatic

direction

• Adiabatic / Entropy decomposition

• Second-order action:

• Canonically normalized field

Linear perturbations : two fieldsTrajectory

in field space

Entropydirection Adiabatic

direction

• Adiabatic / Entropy decomposition

• Second-order action:

• Canonically normalized field

Enhancement ofisocurvature perturbations

Primordial spectra

• Curvature perturbation

• In the multi-field case, can evolve on large scales

• Tensor modes

[ same as single-field k-inflation: Garriga & Mukhanov ’99 ]

Feeding of curvatureperturbation by entropy

perturbations

Sébastien Renaux-Petel, APC

Non-Gaussianities

Slow-roll inflation

Planck accuracy:

Single-field DBISébastien Renaux-Petel, APC

Non-Gaussianities : influence ofisocurvature perturbations

• Third order action

• Shape of unaltered

• Amplitude

Non-Linearity parameterreduced by entropy

perturbations

Very important formodel-building

Sébastien Renaux-Petel, APC

Conclusions

• Angular motion of the D3-brane have importantobservational consequences:

- enhancement of isocurvature perturbations with respectto the adiabatic one.

- amplitude of non-Gaussianities reduced.

• General analysis of the perturbations in multi-fieldmodels with non-canonical kinetic terms

– Multi-field extension of k-inflation– Particular case: multi-field DBI inflation

Sébastien Renaux-Petel, APC