0 1 2 3 4 1.2 1.4 1.6 1.8 2 W=−1.04, $_{1}$=0,Ce$^{2}$=1 CDM $_{2}$=0.01 $_{2}$=0.01 $_{2}$=−0.01 $_{2}$=−0.01 $_{2}$=−0.03 $_{2}$=−0.03 z c 0 1 2 3 4 5 10 15 20 25 30 35 40 W=−1.04, $_{1}$=0,Ce$^{2}$=1 fixed  8 CDM $_{2}$=0.01 $_{2}$=0.01 $_{2}$=−0.01 $_{2}$=−0.01 $_{2}$=−0.03 $_{2}$=−0.03 10$^{13}$<M/(h$^{−1}$M$_{s}$)<10 14 z dN/dz/10 6 (a) (b) 0 1 2 3 4 50 100 150 W=−1.04, $_{1}$=0,Ce$^{2}$=1 fixed  8 CDM $_{2}$=0.01 $_{2}$=0.01 $_{2}$=−0.01 $_{2}$=−0.01 $_{2}$=−0.03 $_{2}$=−0.03 10$^{14}$<M/(h$^{−1}$M$_{s}$)<10 15 z dN/dz/10 4 0 0.5 1 1.5 2 5 10 15 20 25 30 W=−1.04, $_{1}$=0,Ce$^{2}$=1 fixed  8 CDM $_{2}$=0.01 $_{2}$=0.01 $_{2}$=−0.01 $_{2}$=−0.01 $_{2}$=−0.03 $_{2}$=−0.03 10$^{15}$<M/(h$^{−1}$M$_{s}$)<10 16 z dN/dz/10 (c) (d) Figure 2: The numerical results for the coupling proportional to the energy density of DE when the EOS of DE w < − 1 . The solid lines show the results calculated when DE is distributed homogeneously and the dotted lines are for inhomogeneous DE model. B. The interaction proportional to the energy density of DM ( ξ$_{1}$ > 0 , ξ$_{2}$ = 0 ) 15 in the structure formation is consistent with the finding that the DE perturbation is small compared with the DM perturbation in the subhorizon approximation [19]. In this case, the stable curvature perturbation can only hold when DE EOS is smaller than -1[8]. The coupling between DE and DM should be positive to avoid the negative energy density of DE at the early time of the universe[18]