for some positive constants c and C . In all these class of models the spectral tilt comes out to be close to the observed limit, n$_{s}$ ∼ 0 . 96, with no significant gravity waves and no cosmic string strings are produced aftermath of inflation [905, 906]. In the above models, if the string loop corrections are included, for instance the Kaluza-Klein loop corrections to the potential arising from the wrapping of the D 7 brane around a cycle, T$_{3}$ , then the overall potential can be modified to admit a saddle point and the point of inflection [908]. When the loop corrections dominate the potential, the potential with canonical kinetic term takes the form: V$_{inf}$ ≈ V$_{0}$ + W 2 0 ν 2 ( $_{Ae}$− 2 κϕ − B ν $_{e}$− κϕ/ 2 + C ν $_{2}$e κϕ ) (482) where A, B, C are tunable constants and B could be chosen to be negative, T$_{1}$ = e $^{κϕ}$, and κ = 2 $_{/}$√$_{3, and}$ ν determines the large internal volume which determines the string scale, M$_{s}$ . The field range for ϕ is such that it can take large VEVs, i.e. ϕ ∼ O (1 − 10) M$_{P}$ , where the tensor to scalar ratio can be made appreciable, i.e. r ∼ 0 . 005 [908]. B. Brane inflation The position of various branes along with their motion can lead to inflation. Let us imagine that there is a gas of Dp branes in p + 1 space-time dimensions. Their stress energy tensor leads to an equation of state [909] p$_{p}$ = [ p + 1 d v 2 − p d ] ρ$_{d}$ , (483) where p$_{p}$ is the pressure and ρ$_{p}$ is the energy density of the gas of p branes. In a relativistic limit, v 2 → 1, a gas of branes behaves as a relativistic fluid with an equation of state, w ≡ p$_{p}$/ρ$_{p}$ = 1 /d , while in the non-relativistic case, v 2 → 0, we obtain w = − p/d , a negative pressure which could lead to a power law inflation with a scale factor a ∝ t 2 / ( d p ) for d = p +1. This would inflate the entire p + 1 dimensional bulk. A stringy realization would require that the dilaton be fixed at all times. A bound state of fractionally charged branes in 10 d universe can also lead to a high entropy state, with an initial correlation length larger than the string scale, as discussed in [910]. These scenarios are helpful in setting up the initial conditions for the universe. First of all they provide a homogeneous Hubble patch with a large causal horizon (bigger than the string scale), where subsequent phases of inflation can take place. 230