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

Abstract

Non-linear 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 using analytical models as well as $N$-body simulations. We show that an analytical model based upon the time derivative of non-linear matter power spectrum agrees with simulations. All-sky cosmic-variance limited CMB and WL surveys allow us to measure the correlation from non-linearity with high significance ($50\sigma$) for $l_{\max }=10^4$, whereas the forthcoming missions such as Planck and LSST are expected to yield only marginal detections. The CMB-WL correlation is sensitive to the time derivative of structure growth. We study how this property may be used to constrain the nature of dark energy. While the expected constraints are not very strong, they may provide a cross check of results from other observations.

4 pages, 3 figures

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• The full squeezed CMB bispectrum from inflation
• Integrated Sachs Wolfe Effect and Rees Sciama Effect
• Towards accurate modelling of the ISW effect, the non-linear contribution
• Seeding supermassive black holes with a non-vortical dark-matter subcomponent
• The cross-correlation between 3d cosmic shear and the integrated Sachs-Wolfe effect
• Cosmic Microwave Background Bispectrum from the Lensing--Rees-Sciama Correlation Reexamined: Effects of Non-linear Matter Clustering
• Parameter estimation biases due to contributions from the Rees-Sciama effect to the integrated Sachs-Wolfe spectrum
• Ray tracing the integrated Sachs-Wolfe effect through the light cones of the Dark Energy Universe Simulation -- Full Universe Runs
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• Probing the Neutrino Mass through the Cross Correlation between the Rees-Sciama Effect and Weak Lensing
• Cross bispectra and trispectra of the non-linear integrated Sachs-Wolfe effect and the tracer galaxy density field