The Integrated Sachs-Wolfe Effect in Time Varying Vacuum Model

Understand

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.