Gravitational Magnification of the Cosmic Microwave Background

Abstract

Some aspects of gravitational lensing by large scale structure (LSS) are investigated. We show that lensing causes the damping tail of the cosmic microwave background (CMB) power spectrum to fall less rapidly with decreasing angular scale than previously expected. This is due to a transfer of power from larger to smaller angular scales which produces a fractional change in power spectrum that increases rapidly beyond $\ell \sim 2000$. We also find that lensing produces a nonzero mean magnification of structures on surfaces of constant redshift if weighted by area on the sky. This is a result of the fact that light-rays that are evenly distributed on the sky oversample overdense regions. However this mean magnification has a negligible affect on the CMB power spectrum. A new expression for the lensed power spectrum is derived and it is found that future precision observations the high-$\ell$ tail of the power spectrum will need to take into account lensing when determining cosmological parameters.