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Cosmological distances as a function of redshift depend on the effectivecurvature density via the effect on the geometrical path of photons from largescale spatial curvature and its effect on the expansion history, H(z).Cosmological time, however, depends on the expansion history only. Therefore,by combining distance and lookback time observations (or other estimates of theexpansion history), it is possible to isolate the geometrical curvaturecontribution and measure the curvature in a model independent way, i.e., freefrom assumptions about the energy content of the universe.  We investigate two different approaches to accomplish this task; thedifferential and the integral approach. The differential approach requires, inaddition to distances, derivatives of distance with respect to redshift as wellas knowledge of the expansion history. The integral approach is based onmeasuring the integral of the inverse of the expansion history via measurementsof cosmic time as derived, e.g., from galaxy ages.  In this paper, we attempt to constrain the large scale curvature of theUniverse using distances obtained from observations of Type Ia supernovaetogether with inferred ages of passively evolving galaxies and Hubble parameterestimates from the large scale clustering of galaxies. Current data areconsistent with zero spatial curvature, although the uncertainty on thecurvature density is of order unity. Future data sets with on the order ofthousands of Type Ia supernovae distances and galaxy ages will allow us toconstrain the curvature density with an uncertainty of less than 0.1 at the 95%confidence level.

A model independent measure of the large scale curvature of the Universe