Gravitational lensing of cosmological 21 cm emission

We investigate the feasibility of measuring weak gravitational lensing using 21-cm intensity mapping with special emphasis on the performance of the planned Square Kilometre Array (SKA). We find that the current design for SKA_Mid should be able to measure the evolution of the lensing power spectrum at z ~ 2-3 using this technique. This will be a probe of the expansion history of the Universe and gravity at a unique range in redshift. The signal to noise is found to be highly dependent on evolution of the neutral hydrogen fraction in the Universe with a higher HI density resulting in stronger signal. With realistic models for this, SKA Phase 1 should be capable of measuring the lensing power spectrum and its evolution. The dependence of signal to noise on the area and diameter of the array is quantified. We further demonstrate the applications of this technique by applying it to two specific coupled dark energy models that would be difficult to observationally distinguish without information from this range of redshift. We also investigate measuring the lensing signal with 21 cm emission from the Epoch of Reionization (EoR) using SKA and find that it is unlikely to constrain cosmological parameters because of the small survey size, but could provide a map of the dark matter within a small region of the sky.