Strongly lensed repeating Fast Radio Bursts as precision probes of the
  universe
  Fast Radio bursts (FRBs), bright transients with millisecond durations at
$\sim$ GHz and typical redshifts probably $>0.8$, are likely to be
gravitationally lensed by intervening galaxies. Since the time delay between
images of strongly lensed FRB can be measured to extremely high precision
because of the large ratio $\sim10^9$ between the typical galaxy-lensing delay
time $\sim\mathcal{O}$(10 days) and the width of bursts $\sim\mathcal{O}$(ms),
we propose strongly lensed FRBs as precision probes of the universe. We show
that, within the flat $\Lambda$CDM model, the Hubble constant $H_0$ can be
constrained with a $\sim0.91\%$ uncertainty from 10 such systems probably
observed with the Square Kilometer Array (SKA) in $<$ 30 years. More
importantly, the cosmic curvature can be model-independently constrained to a
precision of $\sim0.076$. This constraint can directly test the validity of the
cosmological principle and break the intractable degeneracy between the cosmic
curvature and dark energy.
