ISW-Galaxy Cross Correlation:A probe of Dark Energy clustering and distribution of Dark Matter tracers

Cross correlation of the Integrated Sachs-Wolfe signal (ISW) with the galaxy distribution in late time is a promising tool for constraining the dark energy properties. Here, we study the effect of dark energy clustering on the ISW-galaxy cross correlation and demonstrate the fact that the bias parameter between the distribution of the galaxies and the underlying dark matter introduces a degeneracy and complications. We argue that as the galaxy's host halo formation time is different from the observation time, we have to consider the evolution of the halo bias parameter. It will be shown that any deviation from $\Lambda$CDM model will change the evolution of the bias as well. Therefore, it is deduced that the halo bias depends strongly on the sub-sample of galaxies which is chosen for cross correlation and that the joint kernel of ISW effect and the galaxy distribution has a dominant effect on the observed signal. In this work, comparison is made specifically between the clustered dark energy models using two samples of galaxies. The first one is a sub-sample of galaxies from Sloan Digital Sky Survey, chosen with the r-band magnitude $18 < r < 21$ and the dark matter halo host of mass $M \sim10^{12}M_{\odot}$ and formation redshift of $z_{f}\sim 2.5$. The second one is the sub-sample of Luminous Red galaxies with the dark matter halo hosts of mass $M \sim 10^{13}M_{\odot}$ and formation redshift of $z_{f}\sim 2.0$. Using the evolved bias we improve the $\chi^2$ for the $\Lambda$CDM which reconciles the $\sim$1$\sigma$-2$\sigma$ tension of the ISW-galaxy signal with $\Lambda$CDM prediction.[abridged]