Number counts and dynamical vacuum cosmologies

We study non-linear structure formation in an interacting model of the dark sector of the Universe in which the dark energy density decays linearly with the Hubble parameter, rho(Lambda) alpha H, leading to a constant-rate creation of cold dark matter. We derive all relevant expressions to calculate the mass function and the cluster number density using the Sheth-Torman formalism and show that the effect of the interaction process is to increase the number of bound structures of large masses (M greater than or similar to 10(14) M(circle dot)h(-1)) when compared to the standard Lambda cold dark matter model. Since these models are not reducible to each other, this number counts signature can in principle be tested in future surveys.