Lensing of the Cosmic Microwave Background

The most distant light source that can be observed is the cosmic microwave background. Its cosmological significance is outlined in Sect. 9.1. As in the case of cosmic shear, the lensed power spectrum is the key quantity of interest. However, shear is ill-defined when the background source is the entire sky. Nevertheless, lensing “rearranges” the distribution of photons in a way that alters the observed pattern of temperature fluctuations that characterize cosmic background radiation. The spherical nature of the sky results in a power spectrum that depends on a discrete index, rather than a continuous wavenumber (Sect. 9.2). On the angular scales affected by lensing, the sky can be treated as “flat” in the vicinity of a given point. We use this approximation to derive expressions for the lensed power spectrum (Sect. 9.3.1) and the lens potential (Sect. 9.3.2). Finally, we mention a few applications in Sect. 9.4.