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: ds 2 = h $^{2}$( y )( − dt 2 + a ( t ) $^{2}$dx$^{2}$) + $_{h}$− $^{2}$( y ) g$_{mn}$ ( y ) dy $^{m}$dy$^{n}$, (485) S = − ∫ d $^{4}$xa$^{3}$( t )   T ( φ ) √ 1 − ˙ φ 2 T ( φ ) + V ( φ ) − T ( φ )   , (486) V ( φ ) ≈ m 2 2 φ 2 + V$_{0}$ ( 1 − V$_{0}$ 4 π $^{2}$v 1 φ 4 ) , (487) p ( φ, K ) = − T$_{3}$h $^{4}$( φ ) √ 1 − 2 K /h ( φ ) 4 + T$_{3}$h $^{4}$( φ ) − V ( φ ) , ρ ( φ, K ) = 2 K $^{p$_{,}$}$K − p , (488) c 2 s = $^{p$_{,}$}$K $^{ρ$_{,}$}$K = $^{p$_{,}$}$K $^{p$_{,}$}$K + 2 K $^{p$_{,}$}$KK = 1 − 2 K /h 4 = 1 Γ 2 , (489) 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: 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: where K = ( ˙ φ $^{2}$/ 2 T$_{3}$ ). The speed of sound is given by: 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]. 232