Gravitational lensing effect on the two-point correlation of hot spots in the cosmic microwave background

We investigate the weak gravitational lensing effect that is due to the lar ge-scale structure of the universe on two-point correlations of local maxim a (hot spots) in the two-dimensional sky map of the cosmic microwave backgr ound (CMB) anisotropy. According to the Gaussian random statistics, as most inflationary scenarios predict, the hot spots are discretely distributed, with some characteristic angular separations on the last scattering surface that are due to oscillations of the CMB angular power spectrum. The weak l ensing then causes pairs of hot spots, which are separated with the charact eristic scale, to be observed with various separations. We found that the l ensing fairly smooths out the oscillatory features of the two-point correla tion function of hot spots. This indicates that the hot spot correlations c an be a new statistical tool for measuring the shape and normalization of t he power spectrum of matter fluctuations from the lensing signatures.