The Integrated Sachs-Wolfe Effect in Time Varying Vacuum Model
  The integrated Sachs-Wolfe (ISW) effect is an important implication for dark
energy. In this paper, we have calculated the power spectrum of the ISW effect
in the time varying vacuum cosmological model, where the model parameter
$\beta=4.407$ is obtained by the observational constraint of the growth rate.
It's found that the source of the ISW effect is not only affected by the
different evolutions of the Hubble function $H(a)$ and the dimensionless matter
density $\Omega_m(a)$, but also by the different growth function $D_+(a)$, all
of which are changed due to the presence of matter production term in the time
varying vacuum model. However, the difference of the ISW effect in
$\Lambda(t)\textmd{CDM}$ model and $\Lambda \textmd{CDM}$ model is lessened to
a certain extent due to the integration from the time of last scattering to the
present. It's implied that the observations of the galaxies with high redshift
are required to distinguish the two models.
