content_image/305087.jpg content_image/305089.jpg content_image/305088.jpg content_image/305090.jpg content_image/305085.jpg content_image/305086.jpg content_image/305083.jpg
yields: 

<img src='content_image/305087.jpg'>

<img src='content_image/305089.jpg'>

<img src='content_image/305088.jpg'>

<img src='content_image/305090.jpg'>

and the perturbed energy-momentum conservation equation gives: 

<img src='content_image/305085.jpg'>

<img src='content_image/305086.jpg'>

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. 

## B IMSE 

Assuming that the inhomogenity of CMB to be produced by the perturbation of the background inflation field ¯ ϕ , the action functional would be: 

<img src='content_image/305083.jpg'>

where M 2 pl = (8 πG$_{0}$ ) − 1 2 is the reduced Planck mass. 

The dynamics of the model is given by the Friedmann equation for the classical background 

