A constraint on the integrated mass power spectrum out to z = 1100 from lensing of the cosmic microwave background

The temperature fluctuations and polarization of the cosmic microwave background (CMB) are now a well-known probe of the universe at an infant age of 400,000 years. During the transit to us from the surface of last scattering, the CMB photons are expected to undergo modifications induced by the intervening large-scale structure. Among the expected secondary effects is the weak gravitational lensing of the CMB by the foreground dark matter distribution. We derive a quadratic estimator that uses the non-Gaussianities generated by the lensing effect at the four-point function level to extract the power spectrum of lensing potential fluctuations integrated out to z ~ 1100 with peak contributions from potential fluctuations at z of 2-3. Using Wilkinson Microwave Anisotropy Probe seven-year temperature maps, we report the first direct constraints of this lensing potential power spectrum and find that it has an amplitude of A L = 0.96 ± 0.60, 1.06 ± 0.69, and 0.97 ± 0.47 using the W , V , and W + V bands, respectively