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Cosmic Microwave Background and Shape of the Universe

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A future experiment finds that the angular diameter distance to the CMB is .1% larger than it would be in a flat universe. Assume a Universe with only matter (and curvature) with a redshift to the CMB of z=1000.
a. Is the Universe positively or negatively curved?
b. What is 1 - omega(0)

See attached file for additional information.

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Solution Summary

This solution contains step by step calculations to determine the energy density as compared to critical using the Taylor expansion and the assumption that the distance is small as compared to the curvature radius.

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