Future detectability of gravitational-wave induced lensing from high-sensitivity CMB experiments

TL;DR

Future high-sensitivity CMB experiments could detect gravitational-wave induced lensing signals through the curl mode, providing an independent method to confirm primordial gravitational waves and constrain late-time gravitational wave backgrounds.

Contribution

This paper demonstrates that the curl mode in CMB lensing can be used to detect gravitational waves, offering a new approach complementary to B-mode polarization measurements.

Findings

Future experiments can detect gravitational-wave induced lensing signals.

Curl mode is sensitive to low-redshift gravitational waves.

Potential to tightly constrain gravitational wave energy density.

Abstract

We discuss the future detectability of gravitational-wave induced lensing from high-sensitivity cosmic microwave background (CMB) experiments. Gravitational waves can induce a rotational component of the weak-lensing deflection angle, usually referred to as the curl mode, which would be imprinted on the CMB maps. Using the technique of reconstructing lensing signals involved in CMB maps, this curl mode can be measured in an unbiased manner, offering an independent confirmation of the gravitational waves complementary to the B-mode polarization experiments. Based on the Fisher matrix analysis, we first show that with the noise levels necessary to confirm the consistency relation for the primordial gravitational waves, the future CMB experiments will be able to detect the gravitational-wave induced lensing signals. For a tensor-to-scalar ratio of $r < 0.1$, even if the consistency relation is difficult to confirm with a high significance, the gravitational-wave induced lensing would be detected at more than $3\,\sigma$ significance level. Further, we point out that high-sensitivity experiments will be also powerful to constrain the gravitational waves generated after the recombination epoch. Compared to the B-mode polarization, the curl mode is particularly sensitive to gravitational waves generated at low redshifts ($z < 10$) with a low frequency ($k < 10^{-3}$ Mpc$^{-1}$), and it could give a much tighter constraint on their energy density $\Omega_{\rm GW}$ by more than three orders of magnitude.