The integrated Sachs–Wolfe effect in the extended quintessence cosmological models

We investigate the integrated Sachs–Wolfe (ISW) effect and its power spectra in the extended quintessence cosmological models in both the metric and Palatini formalisms. We find that the ISW effect depends on the Hubble function H(a), the growth function $D_{+}\left(a\right)$, the dimensionless matter density ${\Omega }_m\left(a\right)$ and the coupling function F(a). When the coupling constant of the extended quintessence is negative, the differences of the ISW effect and its power spectra between two different formalisms are negligibly small, and the deviation of the extended quintessence models from the ΛCDM is insignificant, which indicates that in this case the cosmological constant can be taken as a good approximation to the extended quintessence. However, a positive non-minimal coupling leads to an appreciable deviation from the ΛCDM, and the difference between two different formalisms is also very obvious. (paper)