DBI inflation - University of mctp/SciPrgPgs/events/2011... Multi-field DBI inflation • DBI inflation

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  • DBI inflation

    •  A natural inflation model that can generate large equilateral NG

    •  Inflaton is identified as a position modulus of a probe brane in extra-dimesnions

    A small sound speed enhances NG

    •  Single field models in string theory are severely constrained

    1

    D3

    anti-D3

    inflaton

    2 35 1 108

    equi NL

    s

    f c

    = −

    UVφ φ< 716 10sr c ε −= <

    1 4 0.04 0.013sn ε− ±: :

    equil 300NLf >

    Huston et.al ’07, Bean et.al. ’07

    Silverstein & Tong ‘03

  • Multi-field DBI inflation •  DBI inflation is naturally multi-field (i.e. 6 extra-dimensions = 6 fields)

    •  Multi-field effects could ameliorate the problem •  Trispectrum is easier to detect

    2

    δσ

    adiabatic

    entropy 2 116

    1s RS r c

    T ε=

    +

    2 2 35 1 1 108 1

    equi NL

    s RS

    f c T

    = − +

    ,H HS s s

    ζ δσ δ σ

    = = & &

    * *RST Sζ ζ= +

    2 2equi equi NL RS NLT fτ ∝

    Renaux-Petel, et.al ’08, ‘09, Arroja, Mizuno Koyama ‘08

    Arroja, Mizuno Koyama ‘Tanaka ’09, Mizuno Arroja Koyama ’09, Renaux-Petel ‘09

  • DBI Galileons •  Single field extension including higher order derivative

    interactions

    •  A probe brane in 5D A general brane action that gives the 2nd order e.o.m

    3

    ( )21 2 1s

    h g K

    c

    µν µν µ ν

    µν µ ν

    µ

    φ φ

    γ φ

    γ φ−

    = + ∂ ∂

    = − ∂ ∂

    = = + ∂

    ( )4 1 2 3 4[ ] KGBS d x h K R hα α α α= − + + +∫

    (5) (5)

    (5) (5)

    [ ] [ ]GB

    R g R gGB

    K K

    [ ]R h

    DBI Relativistic Galileon terms

    de Rham & Tolley ’10, Burrage et.al. ’11, Goon et.al.’11, Mizuno Koyama ’10, …

  • Multi-field DBI Galileons

    •  In higher-codimensions n>1, it becomes multi-field model and for even n>3, the only possible term is the induced gravity term

    •  In non-relativistic limit

    4

    ( )4 1 2 [ ]S d x h R hα α= − − +∫ , 1,2,..I Ih Iµν µν µ νη φ φ= + ∂ ∂ =

    2( ) 1φ∂

  • Model •  Embed a brane in 10-dimensions

    •  Induced metric

    •  Action

    5

    Renaux-Petel, Mizuno, Koyama ‘11

  • Equations of motion

    6

  • Background

    •  Friedman equation

    •  In the relativistic regime, induced gravity gives a term that breaks the null energy condition

    •  Conditions for inflation

    7

    2

    2 3 1/21, 1D p D

    Mc fV M c h

    >>

  • Second-order action

    Avoid instabilities

    Sound speeds Entropic sound speeds are always smaller than adiabatic one and they become the same in the DBI inflation

    Linear perturbations

    8

    adiabatic

    entropy

    2 2

    2 1/2 D

    fH M c h

    α =

    1 ( 1) 9 D

    cα <

  • Non-Gaussianity

    9

    2 2

    2 1/2 D

    fH M c h

    α =

    •  Two parameters Mostly it gives equilateral NG but for some choice of

    parameters, there appears orthogonal type NG

  • 10

    log Dc

    α

    0RST =

    DBI

    equilateral orthogonal

    Single field

    0equiNLf <

    0equiNLf >

    0orthogNLf

  • 11

    log Dc

    α

    10RST =

    DBI

    equilateral orthogonal

    Multi field

    0equiNLf <

    0equiNLf >

    0orthogNLf

  • Conclusion •  Multi-field DBI galileon a probe brane action with induced gravity

    •  Induced gravity may break the energy condition need to check the ghost condition on non-slow roll inflation background

    •  Slow-roll inflation can be realised if

    •  Cosmological perturbations are controlled by two parmaeters

    constraints on these parameters are obtained It is possible to create orthogonal type NG and positive

    12

    2

    2 3 1/21, 1D p D

    Mc fV M c h

    >>