of DM and DE in the spherical region described by 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 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] 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 11 ϑ ′ + R ′ R (1 − 3 w ) ϑ = 3 a ( ξ$_{1}$ Γ + ξ$_{2}$ ) ϑ, ζ ′ m = 3 a { 1 − ξ$_{2}$/r } ζ$_{m}$ − 3 R ′ R ζ$_{m}$ + 3 a ξ$_{2}$ζ$_{d}$/r, ζ ′ d = 3 a (1 + w + ξ$_{1}$r ) ζ$_{d}$ − 3(1 + w ) R ′ R ζ$_{d}$ − 3 a ξ$_{1}$ζ$_{m}$r − ϑ (1 + w ) ζ$_{d}$. (37) 2 a $^{2}$(1 + 1 r ) R ′′ − R ′ [1 + (3 w + 1) /r ] a = − R [(3 w + 1) ζ$_{d}$/r + ζ$_{m}$ ] . (38) d $^{2}$lnδ$_{m}$ dlna 2 = − ( dlnδ$_{m}$ dlna ) 2 − [ 1 2 − 3 2 w (1 − Ω$_{m}$) ] dlnδ$_{m}$ dlna − (3 ξ$_{1}$ + 6 ξ$_{2}$ r ) dlnδ$_{m}$ dlna + 3 ξ$_{2}$ r dlnδ$_{d}$ dlna exp ( ln δ$_{d}$ δ$_{m}$ ) + 3[ exp ( ln δ d δ $_{m}$) − 1] r { ξ$_{2}$ + 3 ξ$_{1}$ξ$_{2}$ + 3 ξ 2 $_{2}$/r + ξ$_{2}$ ( dlnH dlna + 1) − ξ$_{2}$ dlnr dlna } + 3 2 [ Ω$_{m}$ + (1 − Ω$_{m}$) exp ( ln δ$_{d}$ δ$_{m}$ ) ] , (39) d $^{2}$lnδ$_{d}$ dlna 2 = − ( dlnδ$_{d}$ dlna ) 2 − [ 1 2 − 3 2 w (1 − Ω$_{m}$) ] dlnδ$_{d}$ dlna + (1 + w ) 3 2 [ Ω$_{m}$ exp ( ln δ$_{m}$ δ$_{d}$ ) + (1 − Ω$_{m}$) ] − k $^{2}$C2 e a $^{2}$H2 + [ 3 ξ$_{2}$ + 6 ξ$_{1}$r + 6 w − 3 C 2 a + 3( C 2 e − C 2 $_{a}$) ξ$_{1}$r + ξ$_{2}$ 1 + w + C 2 e 1 + w dlnρ$_{d}$ dlna ] dlnδ$_{d}$ dlna − 3 rξ$_{1}$exp ( ln δ$_{m}$ δ$_{d}$ ) dlnδ$_{m}$ dlna + 3( dlnH dlna + 1)( w − C 2 $_{e}$) + 3 ξ$_{1}$ ( dlnH dlna r + r + dr dlna ) − 3 ξ$_{1}$ [ ( dlnH dlna + 1) r + dr dlna ] exp ( ln δ$_{m}$ δ$_{d}$ ) + 3 [ w − C 2 e + ξ$_{1}$r (1 − exp ( ln δ$_{m}$ δ$_{d}$ )) ] [ (1 − 3 w ) − 3 C 2 e − C 2 a 1 + w (1 + w + ξ$_{1}$r + ξ$_{2}$ ) − 3( ξ$_{1}$r + ξ$_{2}$ ) − C 2 e 1 + w dlnρ$_{d}$ dlna ] . (40)