How Sensitive is the CMB to a Single Lens?

TL;DR

This paper investigates how a single lens, such as a void or texture, affects the CMB's statistical isotropy and assesses the detectability of such lenses through weak lensing signals, highlighting the limitations imposed by non-Gaussianities.

Contribution

It provides a detailed calculation of the S/N ratio for detecting a single lens in the CMB, emphasizing the impact of non-Gaussianities and showing the difficulty in testing hypotheses like voids or textures for the WMAP cold spot.

Findings

S/N ratio for detecting a single lens is generally very low.

Non-Gaussianities significantly reduce the detectability of lensing signals.

Weak lensing cannot reliably test the void or texture hypothesis for the WMAP cold spot.

Abstract

We study the imprints of a single lens, that breaks statistical isotropy, on the CMB and calculate the signal to noise ratio (S/N) for its detection. We emphasize the role of non-Gaussianities induced by LCDM weak lensing in this calculation and show that typically the S/N is much smaller than expected. In particular we find that the hypothesis that a void (texture) is responsible for the WMAP cold spot can barely (cannot) be tested via weak lensing of the CMB.