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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]. 

## B. The interaction proportional to the energy density of DM ( ξ$_{1}$ > 0 , ξ$_{2}$ = 0 ) 

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] 

