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Cosmological distances as a function of redshift depend on the effective curvature density via the effect on the geometrical path of photons from large scale spatial curvature and its effect on the expansion history, H(z).
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Z. Huang, B. Wang, and R. Su, Uncertainty on Determining the Dark Energy Equation of State due to the Spatial Curvature
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E. L. Wright, Constraints on Dark Energy from Supernovae, Gamma-Ray Bursts, Acoustic Oscillations, Nucleosynthesis, Large-Scale Structure, and the Hubble Constant
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G. Zhao, J. Xia, H. Li, C. Tao, J. Virey, Z. Zhu, and X. Zhang, Probing for dynamics of dark energy and curvature of universe with latest cosmological observations
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