Cross correlation of Cosmic Microwave background and Weak Lensing

TL;DR

This paper investigates the cross-correlation between the CMB and large-scale structure to understand the ISW and RS effects, highlighting how these correlations depend on dark energy models and proposing momentum-density cross-correlation as a potential tool.

Contribution

It analyzes the dependence of the RS effect's flipping scale on dark energy models and suggests using momentum-density cross-correlation to break parameter degeneracies.

Findings

The RS effect causes a transition from anti-correlation to positive correlation in CMB-LSS cross-correlation.

The flipping scale of the cross-correlation depends on dark energy models.

Momentum-density cross-correlation may help distinguish dark energy parameters.

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.