  When using distance measurements to probe spatial curvature, the geometric
degeneracy between curvature and dark energy in the distance-redshift relation
typically requires either making strong assumptions about the dark energy
evolution or sacrificing precision in a more model-independent approach.
Measurements of the redshift evolution of the linear growth of perturbations
can break the geometric degeneracy, providing curvature constraints that are
both precise and model-independent. Future supernova, CMB, and cluster data
have the potential to measure the curvature with an accuracy of
sigma(Omega_K)=0.002, without specifying a particular dark energy
phenomenology. In combination with distance measurements, the evolution of the
growth function at low redshifts provides the strongest curvature constraint if
the high-redshift universe is well approximated as being purely matter
dominated. However, in the presence of early dark energy or massive neutrinos,
the precision in curvature is reduced due to additional degeneracies, and
precise normalization of the growth function relative to recombination is
important for obtaining accurate constraints. Curvature limits from distances
and growth compare favorably to other approaches to curvature estimation
proposed in the literature, providing either greater accuracy or greater
freedom from dark energy modeling assumptions, and are complementary due to the
use of independent data sets. Model-independent estimates of curvature are
critical for both testing inflation and obtaining unbiased constraints on dark
energy parameters.
