Lensing of 21-cm Fluctuations by Primordial Gravitational Waves

Weak-gravitational-lensing distortions to the intensity pattern of 21-cm radiation from the dark ages can be decomposed geometrically into curl and curl-free components. Lensing by primordial gravitational waves induces a curl component, while the contribution from lensing by density fluctuations is strongly suppressed. Angular fluctuations in the 21-cm background extend to very small angular scales, and measurements at different frequencies probe different shells in redshift space. There is thus a huge trove of information with which to reconstruct the curl component of the lensing field, allowing tensor-to-scalar ratios conceivably as small as $r\sim {10}^{-9}$—far smaller than those currently accessible—to be probed.

Figure 1

The power spectrum for the deflection-field curl component for the lensing of sources at various redshifts by a scale-invariant spectrum of IGWs of the largest amplitude ($r=0.2$) consistent with current measurements. We also superimpose noise power spectra for lensing reconstruction carried out to various values of $l_{\max }$. Also shown is the noise power spectrum we estimate from coadding the signals from all possible redshifts, assuming $l_{\max }={10}^6$.