Cosmic Curvature Tested Directly from Observations
  Cosmic spatial curvature is a fundamental geometric quantity of the Universe.
We investigate a model independent, geometric approach to measure spatial
curvature directly from observations, without any derivatives of data. This
employs strong lensing time delays and supernova distance measurements to
measure the curvature itself, rather than just testing consistency with
flatness. We define two curvature estimators, with differing error propagation
characteristics, that can crosscheck each other, and also show how they can be
used to map the curvature in redshift slices, to test constancy of curvature as
required by the Robertson-Walker metric. Simulating realizations of redshift
distributions and distance measurements of lenses and sources, we estimate
uncertainties on the curvature enabled by next generation measurements. The
results indicate that the model independent methods, using only geometry
without assuming forms for the energy density constituents, can determine the
curvature at the $\sim6\times10^{-3}$ level.
