content_image/298198.jpg content_image/298197.jpg content_image/298195.jpg content_image/298194.jpg content_image/298193.jpg
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: 

<img src='content_image/298198.jpg'>

where 

Putting everything in place, the gauge invariant quantity would be: 

<img src='content_image/298197.jpg'>

<img src='content_image/298195.jpg'>

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. 

## V Improved power spectrum 

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: 

<img src='content_image/298194.jpg'>

Using the results of the previous section we can easily obtain the correlation function for the first case (Λ$_{0}$ = 0) as 

<img src='content_image/298193.jpg'>

