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, ρ_Λ ∝ 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 ≳ 10¹⁴ M_⊙ h^-1) when compared to the standard Λ 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.