Cosmic Microwave Background-Weak Lensing Correlation: Analytical and Numerical Study of Nonlinearity and Implications for Dark Energy

Abstract

Evolution of density fluctuations yields secondary anisotropies in the cosmic microwave background (CMB), which are correlated with the same density fluctuations that can be measured by weak lensing (WL) surveys. We study the CMB-WL correlation induced by the integrated Sachs-Wolfe (ISW) effect and its nonlinear extension, the Rees-Sciama (RS) effect, using analytical models as well as N-body simulations. We show that an analytical model based on the time derivative of matter power spectrum agrees with simulations. All-sky cosmic-variance-limited CMB and WL surveys allow us to measure the correlation from the nonlinear RS effect with high significance (50 σ) for lmax=104, whereas forthcoming missions such as Planck and LSST are expected to yield 1.5 σ detections, on the assumption of that the point-source contributions are negligible. We find that the CMB-WL correlation has a characteristic scale which is sensitive to the nature of dark energy.