we see that it can be decomposed as: in which S$_{0}$ ( τ ) = d dτ ln ( aH ′ H 2 $^{)}$, and S$_{I}$ ( τ ) = G ′ 2 G H H ′ d dτ ln ( G $^{2}$H ′ G $^{′}$H 3 ) is the improved part. It can be seen that in the non–improved limit, where G and Λ are constants, MSE (8) is recovered. In this section the solution of the IMSE for two cases will be obtained. First, for a model in which Λ$_{0}$ = 0 and it remains zero as time passing. Second, for the Λ-inflation model. We shall see that IMSE can be solved iteratively for both cases. The Fridemann equation and conservation equation in this case are Considering the well–known exponential potential V ( ϕ ) = ge − λϕ , where g and λ are arbitrary real constants, the perturbed H = H$_{0}$ + ˜ ωH$_{1}$ and ϕ = ϕ$_{0}$ + ˜ ωϕ$_{1}$ seem to be appropriate solutions for (29) and (30) up to first order. Substituting G ( t ) from (6), gives H$_{1}$ and its’ time evolution, ˙ H$_{1}$ , up to O (1) : 12 S ( τ ) = S$_{0}$ ( τ ) + S$_{I}$ ( τ ) (28) IV Solutions of IMSE A Case I: Λ$_{0}$ = 0 H 2 = 8 πG ( t ) 3 $^{(}$1 2 ˙ ϕ 2 + V ( ϕ )$^{)}$ (29) ˙ H = − 4 πG ( t ) ˙ ϕ 2 + H ˙ G ( t ) 2 G ( t ) . (30) ˜ ωH$_{1}$ = 8 πG$_{0}$ 3 ϵ λ ˜ ω ˙ ϕ$_{1}$ − λ 6 3 − ϵ ϵ ˜ ωϕ$_{1}$ t − 8 πG$_{0}$ 3 ϵ λ 2 ˜ ωt 2 pl t 3 − 3 − ϵ 6 ϵ ˜ ωt 2 pl t 3 (31) ˜ ω ˙ H$_{1}$ = 16 πG$_{0}$ λ 2 ˜ ωt 2 pl t 4 − 16 πG$_{0}$ λ ˜ ω ˙ ϕ$_{1}$ t + 1 ϵ ˜ ωt 2 pl t 4 (32)