Do we care about the distance to the CMB? Clarifying the impact of second-order lensing

Abstract

It has recently been shown that second-order corrections to the background distance-redshift relation can build up significantly at large redshifts, due to an aggregation of gravitational lensing events. This shifts the expectation value of the distance to the CMB by 1%. In this paper we show that this shift is already properly accounted for in standard CMB analyses. We clarify the role that the area distance to the CMB plays in the presence of second-order lensing corrections.

15 pages, no figure; v2: some typos and an error in eq. (20) (v1) corrected. Conclusion unchanged; v3: reference added, minor changes to the text, matches published version