Current and future supernova constraints on decaying $\Lambda$ cosmologies

We investigate observational constraints from present and future supernova data on a large class of decaying vacuum cosmologies. In such scenarios the present value of the vacuum energy density is quantified by a positive $\beta$ parameter smaller than unity. By assuming a Gaussian prior on the matter density parameter ($\Omega_{\rm{m}} = 0.35 \pm 0.07$) we find $\Omega_{\rm{m}} = 0.34^{+0.14}_{-0.12}$ and $\beta = 0.62^{+0.12}_{-0.24}$ (95% c.l.) as the best fit values for the present data. We show that, while the current data cannot provide restrictive constraints on the $\Omega_{\rm{m}} - \beta$ plane, the future SNe data will limit considerably the allowed space of parameter. A brief discussion about the equivalence between dynamical-$\Lambda$ scenarios and scalar field cosmologies is also included.