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]
