Moving gravitational lenses: imprints on the cosmic microwave background

With the new generation of instruments for Cosmic Microwave Background (CMB) observations aiming at an accuracy level of a few percent in the measurement of the angular power spectrum of the anisotropies, the study of the contributions due to secondary effects has gained impetus. Furthermore, a reinvestigation of the main secondary effects is crucial in order to predict and quantify their effects on the CMB and the errors that they induce in the measurements. In this paper, we investigate the contribution, to the CMB, of secondary anisotropies induced by the transverse motions of clusters of galaxies. This effect is similar to the Kaiser-Stebbins effect. In order to address this problem, we model the gravitational potential well of an individual structure using the Navarro, Frenk & White profile. We generalise the effect of one structure to a population of objects predicted using the Press-Schechter formalism. We simulate maps of these secondary fluctuations, compute the angular power spectrum and derive the average contributions for three cosmological models. We then investigate a simple method to separate this new contribution from the primary anisotropies and from the main secondary effect, the Sunyaev-Zel'dovich kinetic effect from the lensing clusters.