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

Abstract

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 (${\Omega }_{\mathrm{m}}=0.35\pm 0.07$) we find ${\Omega }_{\mathrm{m}}=0.34_{-0.12}^{+0.14}$ and $\beta =0.62_{-0.24}^{+0.12}$ (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 ${\Omega }_{\mathrm{m}}-\beta$ 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.

6 pages, 4 figures, to appear in Phys. Rev. D

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