Figure 2: Relative deviation of improved correlation function from the non–improved one versus the normalized wave number. ϵ = 0 . 300 for solid curve, ϵ = 0 . 030 for dotted curve, and ϵ = 0 . 003 for dashed curve. In order to obtain the power spectrum, note that the improved form of G ( t ) (6) quickly approaches to G$_{0}$ for larger times, and thus can be considered constant after inflation and in the radiation and matter dominated era. This means that the non–improved growth of perturbations works also in this case and the transfer function has not any improvement and is given by the standard one [18]. Therefore the power spectrum is given by: where T is the transfer function [18], κ = √ 2 q/q$_{EQ}$ , q$_{EQ}$ ≃ Ω$_{M}$ h $^{2}$/ 13 . 6Mpc (with Ω$_{M}$ the matter density parameter, and H = h × 100km/sec Mpc) is the exit wave number at radiation–matter equality time, and The result is plotted in figure (3) and the improved power spectrum is compared with the non–improved one. P ( κ ) ∝ κ T $^{2}$( κ )Φ( κ ) (63) Φ( κ ) ∝ 1 + Im ( K ) 6 π 2 κ 2 + Re ( K ) 2 + Im ( K ) 2 144 π 4 κ $^{4}$. (64) 21