The cosmological constant, i.e., the energy density stored in the true vacuum
state of all existing fields in the Universe, is the simplest and the most
natural possibility to describe the current cosmic acceleration. However,
despite its observational successes, such a possibility exacerbates the well
known cosmological constant problem, requiring a natural explanation for its
small, but nonzero, value. In this paper we study cosmological consequences of
a scenario driven by a varying cosmological term, in which the vacuum energy
density decays linearly with the Hubble parameter. We test the viability of
this scenario and study a possible way to distinguish it from the current
standard cosmological model by using recent observations of type Ia supernova
(Supernova Legacy Survey Collaboration), measurements of the baryonic acoustic
oscillation from the Sloan Digital Sky Survey and the position of the first
peak of the cosmic microwave background angular spectrum from the three-year
Wilkinson Microwave Anisotropy Probe.Comment: Some important revisions. To appear in Physical Review