  High-precision cosmological probes have revealed a small but significant
tension between the parameters measured with different techniques, among which
there is one based on time delays in gravitational lenses. We discuss a new way
of using time delays for cosmology, taking advantage of the extreme precision
expected for lensed fast radio bursts (FRBs), which are short flashes of radio
emission originating at cosmological distances. With coherent methods, the
achievable precision is sufficient for measuring how time delays change over
the months and years, which can also be interpreted as differential redshifts
between the images. It turns out that uncertainties arising from the unknown
mass distribution of gravitational lenses can be eliminated by combining time
delays with their time derivatives. Other effects, most importantly relative
proper motions, can be measured accurately and disentangled from the
cosmological effects. With a mock sample of simulated lenses, we show that it
may be possible to attain strong constraints on cosmological parameters.
Finally, the lensed images can be used as galactic interferometer to resolve
structures and motions of the burst sources with incredibly high resolution and
help reveal their physical nature, which is currently unknown.
