CMB Temperature and Matter Power Spectrum in a Decay Vacuum Dark Energy Model

In this paper, a decay vacuum model $\bar{\rho}_\Lambda=3\sigma M_p^2H_0 H$ is revisited by detailed analysis of background evolution and perturbation equations. We show the imprints on CMB temperature and matter power spectrum from the effective coupling terms between dark sectors by comparing to the standard cosmological constant model and observational data points (WMAP7 and SDSS DR7). We find that the decay vacuum model can describe the expansion rate at late times as well as the standard cosmological constant model but it fails to simultaneously reproduce the observed CMB and matter power spectrum. Its generalization $\bar{\rho}_\Lambda=3M_p^2(\xi_1 H_0 H+\xi_2 H^2)$ is also discussed. Detailed analysis of the background evolution shows that the dimensionless parameter $\xi_{2}$ would be zero to avoid the unnatural 'fine tuning' and to keep the positivity of energy density of dark matter and dark energy in the early epoch.