Reconstructing projected matter density power spectrum from cosmic microwave background - art. no. 123507

Gravitational lensing distorts the cosmic microwave background (CMB) anisot ropies and imprints a characteristic pattern onto it. The distortions depen d on the projected matter density between today and the redshift z similar to 1100. In this paper we develop a method for a direct reconstruction of t he projected matter density from the CMB anisotropies. This reconstruction is obtained by averaging over quadratic combinations of the derivatives of the CMB field. We test the method using simulations and show that it can su ccessfully recover a projected density profile of a cluster of galaxies if there are measurable anisotropies on scales smaller than the characteristic cluster size. In the absence of a sufficient small scale power the reconst ructed maps have a low signal to noise ratio on individual structures, but can give a positive detection of the power spectrum or when cross correlate d with other maps of large scale structure. We develop an analytic method t o reconstruct the power spectrum including the effects of noise and beam sm oothing. Tests with Monte Carlo simulations show that we can recover the in put power spectrum both on large and small scales, provided that we use map s with sufficiently low noise and high angular resolution. [S0556-2821(99)0 1212-6].