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, $\rho_{\Lambda} \propto H$, 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 ($M \gtrsim 10^{14}
M_{\odot}h^{-1}$) when compared to the standard $\Lambda$CDM model. Since these
models are not reducible to each other, this number counts signature can in
principle be tested in future surveys.
