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.
