Cross correlation of Cosmic Microwave background and Weak Lensing

Abstract: The integrated Sachs-Wolfe (ISW) effect and its non-linear extension Rees-Sciama (RS) effect provide us the information of the time evolution of gravitational potential. The cross-correlation between the cosmic microwave background (CMB) and the large scale structure (LSS) is known as a promising way to extract the ISW (RS) effect. It is known that the RS effect shows the unique behavior by changing the anti-correlated cross correlation between the CMB and the mass tracer into the positively correlated cross correlation compared to the linear ISW effect. We show that the dependence of this flipping scale of the cross-correlation between RS and weak lensing on dark energy models. However, there exists the degeneracy between DE and $\Omega_{\rm{m}0}$ which might be broken by redshift dependent observables. The cross-correlation between the momentum field and the density field might be served as the better observable to be used for this purpose.