Analysis of gravitationally lensed microwave background anisotropies

A thorough analytic investigation of the influence of gravitational lensing on the anisotropy correlation function of the cosmic background radiation is given. Particular attention is paid to the effects of coherent versus incoherent deflections and the resultant enhancement or dilution of the temperature fluctuations. At scales less than the intrinsic anisotropy coherence angle, substantial enhancement can result, leading to the possibility of constraining the (dark) matter distribution if this excess is not detected. At larger angles, mild dilution is found. The methods developed can be applied very generally to problems where the source positions might not coincide with the observed images. Possible consequences for the X-ray background and quasar correlation function are discussed. (author)