WEAK LENSING DETECTION IN CMB MAPS

The weak lensing effects are known to change only weakly the shape of the power spectrum of the Cosmic Microwave Background (CMB) temperatur e fluctuations. I show here that they nonetheless induce specific non- Gaussian effects that can be detectable with the four-point correlatio n function of the CMB anisotropies. The magnitude and geometrical depe ndences of this correlation function are investigated in details. It i s thus found to scale as the square of the derivative of the two-point correlation function and as the angular correlation function of the g ravitational displacement field. It also contains specific dependences on the shape of the quadrangle formed by the four directions. When av eraged at a given scale, the four-point function, that identifies with the connected part of the fourth moment of the probability distributi on function of the local filtered temperature, scales as the square of logarithmic slope of its second moment, and as the variance of the gr avitational magnification at the same angular scale. All these effects have been computed for specific cosmological models. It is worth noti ng that, as the amplitude of the gravitational lens effects has a spec ific dependence on the cosmological parameters, the detection of the f our-point correlation function could provide precious complementary co nstraints to those brought by the temperature power spectrum.