Dependence of the cosmic microwave background lensing power spectrum on the matter density

The anisotropies in the cosmic microwave background (CMB) provide our best laboratory for testing models of the formation and evolution of large-scale structure. The rich features in the CMB anisotropy spectrum, in combination with highly precise observations and theoretical predictions, also allow us to simultaneously constrain a number of cosmological parameters. As observations have progressed, measurements at smaller angular scales have provided increasing leverage. These smaller angular scales provide sensitive measures of the matter density through the effect of gravitational lensing. In this work, we provide an analytic explanation of the manner in which the lensing of CMB anisotropies depends on the matter density, finding that the dominant effect comes from the shape of the matter power spectrum set by the decay of small-scale potentials between horizon crossing and matter-radiation equality.