Testing flatness of the universe with probes of cosmic distances and growth

Understand

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.