Cosmic age, Statefinder and $Om$ diagnostics in the decaying vacuum cosmology

Abstract

As an extension of $\Lambda$CDM, the decaying vacuum model (DV) describes the dark energy as a varying vacuum whose energy density decays linearly with the Hubble parameter in the late-times, ${\rho }_{\Lambda }(t)\propto H(t)$, and produces the matter component. We examine the high-$z$ cosmic age problem in the DV model, and compare it with $\Lambda$CDM 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 YMC, can accommodate the high-$z$ quasar APM 08279+5255, thus greatly alleviates the high-$z$ cosmic age problem. We also calculate the Statefinder $(r,s)$ and the {\it 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 $\Lambda$CDM and YMC. The $Om(z)$ in DV has a negative slope and its height depends on the matter fraction, while YMC has a rather flat $Om(z)$, whose magnitude depends sensitively on the coupling.

12 pages, 4 figures, with some corrections

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