Cosmic curvature tested directly from observations

Abstract

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