content_image/374384.jpg content_image/374387.jpg content_image/374385.jpg content_image/374388.jpg content_image/374386.jpg
inflation [87, 89, 90]. 

Another variant of brane inflation has been discussed in the context of DBI (Dirac Born- Infeld) action [239, 920], where a D 3 brane rolls fast with almost a relativistic velocity, v = 16 / 27, for a particular case of KS-throat [921]. Inside a warped throat, the 4 d metric is given by: 

<img src='content_image/374384.jpg'>

The DBI action for a D 3 brane is given by the brane position, φ ( t ), from the bottom of the throat: 

where T ( φ ) = T$_{3}$h $^{4}$( φ ) and h ( φ ) is the warp factor depending on the brane position. For a slow-roll inflation, the action yields the standard kinetic term ≈ ˙ φ $^{2}$/ 2. The potential is given by a phenomenological mass term, and the coulomb potential between D 3 and D 3 brane: 2 

where V$_{0}$ = 2 T$_{3}$h 4 A is the brane tension at the bottom of the throat, where h$_{A}$ ∼ 0 . 2 − 10 − $^{3}$. The DBI inflation is quite similar to the K-inflation picture [155], where inflation is driven by a non-canonical kinetic term, a simple analogy can also be made with a fluid dynamical picture, where an equation of state can be determined via: 

<img src='content_image/374387.jpg'>

where K = ( ˙ φ $^{2}$/ 2 T$_{3}$ ). The speed of sound is given by: 

<img src='content_image/374385.jpg'>

<img src='content_image/374388.jpg'>

<img src='content_image/374386.jpg'>

where Γ is a relativistic factor. Besides matching the amplitude of the perturbations and the scalar tilt, n$_{s}$ ∼ 0 . 98, there is a possibility of generating large non-Gaussianity towards the end of inflation. The value of f$_{NL}$ is determined by the relativistic motion of the brane, when Γ ≫ 1, | f$_{NL}$ | ≈ 0 . 32Γ $^{2}$. For | f$_{NL}$ | < 300, gives Γ ≤ 32 [239, 922]. The tensor to scalar ratio depends on the choice of initial conditions and it drops significantly as Γ ≫ 1 [923]. 

