Motivated by the cosmological constant and the coincidence problems , we consider a cosmological model where the dark sectors are interacting together through a phenomenological decay law \dot { \rho } _ { \Lambda } = Q \rho _ { \Lambda } ^ { n } in a FRW spacetime with spatial curvature .
We show that the only value of n for which the late-time matter energy density to dark energy density ratio ( r { { } _ { m } } = \rho _ { m } / \rho _ { \Lambda } ) is constant ( which could provide an explanation to the coincidence problem ) is n = 3 / 2 .
For each value of Q , there are two distinct solutions .
One of them involves a spatial curvature approaching zero at late times ( \rho _ { k } \approx 0 ) and is stable when the interaction is weaker than a critical value { Q _ { 0 } = - \sqrt { 32 \pi G / c ^ { 2 } } } .
The other one allows for a non-negligible spatial curvature ( \rho _ { k } \napprox 0 ) at late times and is stable when the interaction is stronger than Q _ { 0 } .
We constrain the model parameters using various observational data ( SNeIa , GRB , CMB , BAO , OHD ) .
The limits obtained on the parameters exclude the regions where the cosmological constant problem is significantly ameliorated and do not allow for a completely satisfying explanation for the coincidence problem .