Weak lensing induced by second-order vector mode

TL;DR

This paper investigates how second-order vector modes, generated by scalar perturbations, influence weak lensing signals like curl- and B-modes, and finds their effects are likely undetectable with current or upcoming measurements.

Contribution

It provides a detailed analysis of second-order vector mode effects on weak lensing curl- and B-modes, highlighting their relative magnitude and detectability.

Findings

Second-order vector modes induce curl- and B-modes in weak lensing.

The induced curl-mode is comparable to primordial gravitational wave signals at certain scales.

The B-mode from second-order vector modes dominates on most scales but remains undetectable.

Abstract

The vector mode of cosmological perturbation theory imprints characteristic signals on the weak lensing signals such as curl- and B-modes which are never imprinted by the scalar mode. However, the vector mode is neglected in the standard first-order cosmological perturbation theory since it only has a decaying mode. This situation changes if the cosmological perturbation theory is expanded up to second order. The second-order vector and tensor modes are inevitably induced by the product of the first-order scalar modes. We study the effect of the second-order vector mode on the weak lensing curl- and B-modes. We find that the curl-mode induced by the second-order vector mode is comparable to that induced by the primordial gravitational waves with the tensor-to-scalar ratio $r = 0.1$ at $\ell \approx 200$. In this case, the curl-mode induced by the second-order vector mode dominates at $\ell > 200$. Furthermore, the B-mode cosmic shear induced by the second-order vector mode dominates on almost all scales. However, we find that the observational signatures of the second-order vector and tensor modes cannot exceed the expected noise of ongoing and upcoming weak lensing measurements. We conclude that the curl- and B-modes induced by the second-order vector and tensor modes are unlikely to be detected in future experiments.