Weak Lensing Detection in CMB Maps

TL;DR

This paper demonstrates that weak gravitational lensing in CMB maps induces detectable non-Gaussian signals in the four-point correlation function, offering a new way to constrain cosmological parameters beyond the power spectrum.

Contribution

It provides a detailed analysis of the non-Gaussian effects caused by weak lensing in CMB maps and explores their potential for cosmological parameter estimation.

Findings

Four-point correlation function scales with the square of the derivative of the two-point function.

The four-point function depends on the shape of the quadrangle formed by four directions.

Detection of this non-Gaussian signal can complement traditional power spectrum analyses.

Abstract

The weak lensing effects are known to change only weakly the shape of the power spectrum of the Cosmic Microwave Background (CMB) temperature fluctuations. I show here that they nonetheless induce specific non-Gaussian effects that can be detectable with the four-point correlation function of the CMB anisotropies. The magnitude and geometrical dependences of this correlation function are investigated in detail. It is thus found to scale as the square of the derivative of the two-point correlation function and as the angular correlation function of the gravitational displacement field. It also contains specific dependences on the shape of the quadrangle formed by the four directions. When averaged at a given scale, the four-point function, that identifies with the connected part of the fourth moment of the probability distribution function of the local filtered temperature, scales as the square of logarithmic slope of its second moment, and as the variance of the gravitational magnification at the same angular scale. All these effects have been computed for specific cosmological models. It is worth noting that, as the amplitude of the gravitational lens effects has a specific dependence on the cosmological parameters, the detection of the four-point correlation function could provide precious complementary constraints to those brought by the temperature power spectrum.