fixed now. As for the previous model the solution in the next order of iteration can be obtained leading to the following perturbations outside the horizon: where Putting everything in place, the gauge invariant quantity would be: In the next section, we shall investigate the effect of these improvements on the gauge invariant quantity on the power spectrum of perturbations for Case I which is a realistic model. The freezing of gauge invariant quantity after exiting from the horizon proposes cosmological observable quantities such as correlation function, Φ( q ) which is the Fourier transform of 2- point function and gives us some information about the inhomogeneities. It is given by the relation: Using the results of the previous section we can easily obtain the correlation function for the first case (Λ$_{0}$ = 0) as 19 Φ( q ) ∝ q − 3 ∣ ∣ ∣ ( 1 + iK 6 π 2 ( q q$_{0}$$^{)}$$^{2}$$^{(}$ 1 − ( τ$_{0}$ τ ) 2 ) ) ∣ ∣ ∣ 2 (62) 〈 R$_{q}$R ∗ q ′ 〉 = (2 π ) $^{3}$δ ( q + q $^{′}$)Φ( q ) . (61) R o $_{q}$( T ) = − iK ′′ 4 π Q − 3 q $^{[}$1 − i a$_{0}$z$_{1}$ 96 Q − 2 q [( Q$_{q}$ T ) 4 − ( Q$_{q}$ T$_{0}$ ) $^{4}$)] $^{]}$. (60) V Improved power spectrum F ′ 3 = − i 24 π Q − 2 q [( Q$_{q}$ T ) 4 − ( Q$_{q}$ T$_{0}$ ) $^{4}$)] . (59) R$_{q}$ ( T ) −→ R o $_{q}$( T ) = − iK ′′ 8 π Γ(3) Q − 3 q $^{[}$1 + a$_{0}$z$_{1}$π 4 F ′ 3 ] (58)