Current and future supernova constraints on decaying<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Λ</mml:mi></mml:math>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 $\ensuremath{\beta}$ parameter smaller than unity. By assuming a Gaussian prior on the matter density parameter $({\ensuremath{\Omega}}_{\mathrm{m}}=0.35\ifmmode\pm\else\textpm\fi{}0.07)$ we find ${\ensuremath{\Omega}}_{\mathrm{m}}{=0.34}_{\ensuremath{-}0.12}^{+0.14}$ and $\ensuremath{\beta}{=0.62}_{\ensuremath{-}0.24}^{+0.12}$ (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 ${\ensuremath{\Omega}}_{\mathrm{m}}\ensuremath{-}\ensuremath{\beta}$ plane, the future SNe data will limit considerably the allowed parameter space. A brief discussion about the equivalence between dynamical $\ensuremath{\Lambda}$ scenarios and scalar field cosmologies is also included.