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Motivated by the cosmological constant and the coincidence problems, weconsider a cosmological model where the dark sectors are interacting togetherthrough 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 explanationto the coincidence problem) is $n=3/2$. For each value of $Q$, there are twodistinct solutions. One of them involves a spatial curvature approaching zeroat late times ($\rho_k\approx0$) and is stable when the interaction is weakerthan a critical value ${Q_0=-\sqrt{32\pi G/c^2}}$. The other one allows for anon-negligible spatial curvature ($\rho_k\napprox0$) at late times and isstable when the interaction is stronger than $Q_0$. We constrain the modelparameters using various observational data (SNeIa, GRB, CMB, BAO, OHD). Thelimits obtained on the parameters exclude the regions where the cosmologicalconstant problem is significantly ameliorated and do not allow for a completelysatisfying explanation for the coincidence problem.

Can the coincidence problem be solved by a cosmological model of coupled dark energy and dark matter?