Strong gravitational lensing with upcoming wide-field radio surveys

The number of strong lensing systems will soon increase by orders of magnitude thanks to sensitive, wide-field optical and infrared imaging surveys such as Euclid, Rubin-LSST, and Roman. A dramatic increase in strong lenses will also occur at radio wavelengths. The 2000-antenna Deep Synoptic Array (DSA-2000) will detect $\sim10^9$ continuum sources in the Northern Hemisphere with a high mean redshift ($\langle z_s \rangle \approx2$), the Square Kilometre Array mid frequency telescope (SKA-Mid) will observe a large sample of extragalactic sources in the South with sub-arcsecond resolution, and the Very Large Array Sky Survey (VLASS) has recently completed. We forecast lensing rates for these telescopes, finding that each of the DSA-2000 and SKA-Mid will conservatively discover $\mathcal{O}(10^4)$ strongly lensed systems, and optimistically as many as $\mathcal{O}(10^5)$, a significant fraction of which will be galaxy group and cluster lenses. We propose strategies for strong lensing discovery in the limit where the Einstein radii are comparable to the PSF angular scale, taking advantage of modern computer vision techniques and multi-survey data. Finally, we describe applications of the expected radio strong lensing systems, including time-delay cosmography with transient and variable sources. We find that $\sim$30-300 time-variable flat-spectrum AGN discovered by the DSA-2000 and SKA-Mid could be used to constrain H_0$ at the percent level with the appropriate follow-up.