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The ultimate application of Einstein's field equations is to empiricallydetermine the geometry of the Universe from its matter content, rather thansimply assuming the Universe can be represented by a homogeneous model on allscales. Choosing an LTB model as the most convenient inhomogeneous model forthe early stages of development, a data reduction procedure was recentlyvalidated using perfect test data. Here we simulate observational uncertaintiesand improve the previous numerical scheme to ensure that it will be usable withreal data as soon as observational surveys are sufficiently deep and complete.Two regions require special treatment--the origin and the maximum in the arealradius. To minimize numerical errors near the origin, we use an LTB seriesexpansion to provide the initial values for integrating the differentialequations. We also use an improved method to match the numerical integration tothe series expansion that bridges the region near the maximum in the arealradius. Because the mass enclosed within the maximum obeys a specificrelationship, we show that it is possible to correct for a fixed systematicerror in either the distance scale or the redshift-space mass density, suchthat the integrated values are consistent with the data at the maximum.

Determining the metric of the Cosmos: stability, accuracy, and consistency