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Arman Shafieloo, “Model Independent Reconstruction of the Expansion History of the Universe and the Properties of Dark Energy,” Mon. Not. Roy. Astron. Soc. 380
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2018

Cosmic Curvature Tested Directly from Observations

Denissenya, Mikhail, Linder, Eric V., Shafieloo, Arman

Understand

Cosmic spatial curvature is a fundamental geometric quantity of the Universe.

We investigate a model independent, geometric approach to measure spatial curvature directly from observations, without any derivatives of data.
This employs strong lensing time delays and supernova distance measurements to measure the curvature itself, rather than just testing consistency with flatness.
We define two curvature estimators, with differing error propagation characteristics, that can crosscheck each other, and also show how they can be used to map the curvature in redshift slices, to test constancy of curvature as required by the Robertson-Walker metric.