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of DM and DE in the spherical region described by 

<img src='content_image/325063.jpg'>

When DE fully traces along DM, ϑ = 0, only the last two equations above are needed to discuss the structure formation. The Raychaudhuri’s equation now becomes 

<img src='content_image/325064.jpg'>

Taking the same initial conditions as above for the spherical region of radius R and in addition adopting the adiabatic initial conditions, δ$_{di}$ = (1 + w ) δ$_{mi}$ , and ζ$_{mi}$ = δ$_{mi}$ + 1 , ζ$_{di}$ = δ$_{di}$ + 1 which lead to ζ$_{di}$ = (1 + w ) ζ$_{mi}$ − w , we can study the spherical collapse of DM and DE . However, it is important to note that due to the coupling, ζ$_{d}$ may get negative at sometime during the collapse. To avoid this unphysical point, we make a cut-off of the coupling when ζ$_{d}$ becomes negative to guarantee ζ$_{d}$ > = 0 in our analysis. For linear perturbation, we adopt the equations in the subhorizon approximation through [19] 

<img src='content_image/325065.jpg'>

<img src='content_image/325066.jpg'>

We see that the DE and DM perturbations are entangled. In the subhorizon approximation, it was observed that the influence of the DE perturbation is small if compared with that DM [19]. Using ( 39, 40) together with ( 37, 38), we can obtain in the spherical model with inhomogeneous DE distribution the linearly extrapolated density threshold, δ$_{c}$ ( z ) = δ$_{m}$ ( z = z$_{coll}$ ), above which structure collapse. 

The spherical collapse model was used by Press and Schechter[39] in providing a formalism to predict the number density of collapsed objects. Although this formalism is crude as found in [40] etc., it predicts the evolution of the 

