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

TL;DR

This paper investigates the impact of second-order gravitational lensing on the distance to the CMB, clarifying its significance and showing it is already included in standard analyses, with a focus on the area distance.

Contribution

The paper clarifies the role of second-order lensing corrections on the CMB distance and demonstrates they are accounted for in current standard analyses.

Findings

Second-order lensing causes a 1% shift in CMB distance at high redshift.

Standard CMB analyses already incorporate these second-order effects.

The role of area distance in the presence of second-order lensing is clarified.

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.