yields: and the perturbed energy-momentum conservation equation gives: These are constraints on the perturbation evolutions, by which we shall obtain the IMSE in the next subsection. Note that the perturbation equations differ from the non–improved ones only in changing G$_{0}$ to G ( t ) as it is expected in the equation of motion improvement method. Assuming that the inhomogenity of CMB to be produced by the perturbation of the background inflation field ¯ ϕ , the action functional would be: B IMSE The dynamics of the model is given by the Friedmann equation for the classical background 9 S = S$_{Gravity}$ + ∫ d $^{4}$x √ − g$^{[}$ − 1 2 g $^{αβ}$∂$_{α}$ ¯ ϕ∂$_{β}$ ¯ ϕ − V ( ¯ ϕ ) − 2 M 2 $_{pl}$Λ$^{]}$ . (20) where M 2 pl = (8 πG$_{0}$ ) − 1 2 is the reduced Planck mass. ∂$_{j}$ [ δp + ∇ $^{2}$π S + ∂$_{0}$ [(¯ ρ + ¯ p ) δu ] + 3˙ a a (¯ ρ + ¯ p ) δu + 1 2 (¯ ρ + ¯ p ) E$^{]}$ = 0 (18) δ ˙ ρ + 3˙ a a ( δρ + δp ) + ∇ 2 [ − a − $^{1}$(¯ ρ + ¯ p ) F + a − $^{2}$(¯ ρ + ¯ p ) δu + ˙ a a π S ] + 1 2 (¯ ρ + ¯ p ) ∂$_{0}$ $^{[}$3 A + ∇ $^{2}$B ] = 0 . (19) − 4 πG ( t ) a 2 $^{[}$δρ − δp − ∇ $^{2}$π S ] = 1 2 a ˙ a ˙ E + $^{(}$2˙ a 2 + a ¨ a $^{)}$E + 1 2 ∇ $^{2}$A − 1 2 a 2 ¨ A − 3 a ˙ a ˙ A − 1 2 a ˙ ∇ 2 ˙ B + ˙ a ∇ $^{2}$F (14) 8 πG ( t ) a (¯ ρ + ¯ p ) ∂$_{j}$δu = − ˙ a∂$_{j}$E + a∂$_{j}$ ˙ A (16) ∂$_{j}$∂$_{k}$ $^{[}$16 πG ( t ) a $^{2}$π S + E + A − a 2 ¨ B − 3 a ˙ a ˙ B + 2 a ˙ F + 4˙ aF ] = 0 (15) − 4 πG ( t ) $^{[}$δρ + 3 δp + ∇ $^{2}$π S ] = − 1 2 a $_{2}$∇ $^{2}$E − 3˙ a 2 a ˙ E − 1 a ∇ 2 ˙ F − ˙ a a $_{2}$∇ $^{2}$F + 3 2 ¨ A + 3˙ a a ˙ A − 3¨ a a E + 1 2 ∇ 2 ¨ B + ˙ a a ∇ 2 ˙ B (17)