Constraints on Λ(t)-cosmology with power law interacting dark sectors

Motivated by the cosmological constant and the coincidence problems, we consider a cosmological model where the cosmological constant Lambda(0) is replaced by a cosmological term Lambda(t) which is allowed to vary in time. More specifically, we are considering that this dark energy term interacts with dark matter through the phenomenological decay law (rho)over dot(Lambda) = -Q rho(n)(Lambda). We have constrained the model for the range n is an element of [0, 10] using various observational data (SNeIa, GRB, CMB, BAO, OHD), emphasizing the case where n = 3/2. This case is the only one where the late-time value for the ratio of dark energy density and matter energy density rho(Lambda)/rho(m) is constant, which could provide an interesting explanation to the coincidence problem. We obtain strong limits on the model parameters which however exclude the region where the coincidence or the cosmological constant problems are significantly ameliorated.