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Non-linear evolution of density fluctuations yields secondary anisotropies inthe cosmic microwave background (CMB), which are correlated with the samedensity fluctuations that can be measured by weak lensing (WL) surveys. Westudy the CMB-WL correlation using analytical models as well as $N$-bodysimulations. We show that an analytical model based upon the time derivative ofnon-linear matter power spectrum agrees with simulations. All-skycosmic-variance limited CMB and WL surveys allow us to measure the correlationfrom non-linearity with high significance ($50\sigma$) for $l_{\rm max}=10^4$,whereas the forthcoming missions such as Planck and LSST are expected to yieldonly marginal detections. The CMB-WL correlation is sensitive to the timederivative of structure growth. We study how this property may be used toconstrain the nature of dark energy. While the expected constraints are notvery strong, they may provide a cross check of results from other observations.

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