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On Precision Measurement of the Mean Curvature

Lloyd Knox
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Abstract

Very small mean curvature is a robust prediction of inflation worth rigorous checking. Since current constraints are derived from determinations of the angular-diameter distance to the CMB last-scattering surface, which is also affected by dark energy, they are limited by our understanding of the dark energy. Measurements of luminosity or angular-diameter distances to redshifts in the matter-dominated era can greatly reduce this uncertainty. With a one percent measurement of the distance to z=3, combined with the CMB data expected from Planck, one can achieve sigma(Ω_k h^2) \sim 10^{-3}. A non-zero detection at this level would be evidence against inflation or for unusually large curvature fluctuations on super-Hubble scales.

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Lloyd Knox. 2006-01-10. On Precision Measurement of the Mean Curvature. https://doi.org/10.1103/physrevd.73.023503

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