Publication : t96/122

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 {\it four-point correlation function} of the CMB anisotropies. The magnitude and geometrical dependences of this correlation function are investigated in details. 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 in 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. I stress that, as the amplitude gravitational lens effects has a specific dependence with the cosmological parameters, the detection of the four-point correlation function can provide precious complementary constraints to these brought by the temperature power spectrum.

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