reach equilibrium are different. This shows that in the collapsing system, DE does not fully cluster along with DM. Thus, the energy conservation breaks down inside the collapsing system. It would be fair to say that this result was obtained in the linear level. It would be more interesting to examine the result in the non-linear perturbation and obtain clearer dynamics on how DE participates in the structure formation. The simplest analytical tool to study the structure formation is the spherical collapse model. The continuity equation for the background DM and DE energy densities are given by Considering now the spherically symmetric region of radius R and with the energy density ρ cluster λ = ρ$_{λ}$ + σ$_{λ}$ , where “ λ ” denotes DM and DE respectively, it will eventually collapse from its gravitational pull provided that σ$_{λ}$ > 0. The equation of motion for the collapsing model is governed by Raychaudhuri’s equation. where θ = 3 R R and Raychaudhuri’s equation can be rewritten as, where R is the local expansion scale factor which is determined by the total energy density in the spherical model. If the matter distribution is homogenous in the interior of the spherical region, the local expansion scale factor R will have the same value inside the spherical region and from the Birkhoff theorem, the behavior of R is only determined by the interior matter and is not affected by the matter distributed outside the spherical region. In the spherically symmetric region, supposing the DE distribution is homogeneous ( σ$_{d}$ = 0) and its evolution is still described in (22), the evolution of the DM energy density in the spherical region behaves as where h = ˙ R/R . The Raychaudhuri’s equation applied to the spherical region has the form 8 ˙ ρ cluster m + 3 hρ cluster m = 3 H ( ξ$_{1}$ρ cluster m + ξ$_{2}$ρ$_{d}$ ) , (25) ¨ R = − 4 πG [ 1 3 ρ cluster m + ( 1 3 + w ) ρ$_{d}$ ] R . (26) ¨ R R = − 4 πG 3 ∑ λ ( ρ$_{λ}$ + 3 p$_{λ}$ ) (24) ˙ θ = − 1 3 θ 2 − 4 πG ∑ λ ( ρ$_{λ}$ + 3 p$_{λ}$ ) (23) ˙ ρ$_{m}$ + 3 Hρ$_{m}$ = 3 H ( ξ$_{1}$ρ$_{m}$ + ξ$_{2}$ρ$_{d}$ ) , ˙ ρ$_{d}$ + 3 H (1 + w ) ρ$_{d}$ = − 3 H ( ξ$_{1}$ρ$_{m}$ + ξ$_{2}$ρ$_{d}$ ) . (22) IV. SPHERICAL COLLAPSE MODEL AND THE PRESS-SCHECHTER FORMALISM