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 \sim 10 ^ { 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 .
Finally , we study the parameter estimation of a dark energy model with free parameters w _ { 0 } and w _ { a } in the equation of state w _ { de } = w _ { 0 } + w _ { a } z / ( 1 + z ) with the constant bias parameter and also with an evolved bias model with free parameters of galaxy ’ s host halo mass and the halo formation redshift .