Test of the FLRW metric and curvature with strong lens time delays
  We present a new model-independent strategy for testing the
Friedmann-Lema\^{\i}tre-Robertson-Walker metric and constraining cosmic
curvature, based on future time delay measurements of strongly lensed
quasar-elliptical galaxy systems from the Large Synoptic Survey Telescope and
supernova observations from the Dark Energy Survey. The test only relies on
geometric optics. It is independent of the energy contents of the universe and
the validity of the Einstein equation on cosmological scales. The study
comprises two levels: testing the FLRW metric through the Distance Sum Rule and
determining/constraining cosmic curvature. We propose an effective and
efficient (redshift) evolution model for performing the former test, which
allows us to concretely specify the violation criterion for the FLRW Distance
Sum Rule. If the FLRW metric is consistent with the observations, then, on the
second level, the cosmic curvature parameter will be constrained to $\sim0.057$
or $\sim0.041$ ($1\sigma$), depending on the availability of high-redshift
supernovae, much more stringent than current model-independent techniques. We
also show that the bias in the time delay method might be well controlled,
leading to robust results. The proposed method is a new independent tool for
both testing the fundamental assumptions of homogeneity and isotropy in
cosmology and for determining cosmic curvature. It is complementary to cosmic
microwave background plus baryon acoustic oscillation analyses, which normally
assume a cosmological model with dark energy domination in the late-time
universe.
