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

TL;DR

This study analyzes the correlation between CMB secondary anisotropies and weak lensing, using analytical models and simulations, to understand non-linearity effects and explore implications for dark energy constraints.

Contribution

It demonstrates that an analytical model based on the non-linear matter power spectrum's time derivative agrees with simulations and assesses the potential of future surveys to measure this correlation.

Findings

High-significance detection possible with all-sky surveys

Forthcoming missions like Planck and LSST will have marginal detections

Correlation sensitive to the time derivative of structure growth

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 $l_{\rm max}=10^4$, 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.