Cosmic age, statefinder, and Om diagnostics in the decaying vacuum cosmology

As an extension of the cosmological constant model (ΛCDM), the decaying vacuum (DV) model describes dark energy as a varying vacuum whose energy density decays linearly with the Hubble parameter at late times, ρ_Λ(t)∝H(t), and produces the matter component. We examine the high-z cosmic age problem in the DV model, and compare it with ΛCDM and the Yang-Mills condensate (YMC) dark energy model. Without employing a dynamical scalar field for dark energy, these three models share a similar behavior of late-time evolution. It is found that the DV model, like the YMC, can accommodate the high-z quasar APM 08279+5255, thus greatly alleviating the high-z cosmic age problem. We also calculate the statefinder (r,s) and the Om diagnostics in the model. It is found that the evolutionary trajectories of r(z) and s(z) in the DV model are similar to those in the kinessence model, but are distinguished from those in ΛCDM and the YMC. The Om(z) in the DV model has a negative slope and its height depends on the matter fraction, while the YMC has a rather flat Om(z), whose magnitude depends sensitively on the coupling.