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Dark energy affects the Hubble expansion rate (namely, the expansion history) $H(z)$ by an integral over $w(z)$.
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M. Li, X. D. Li, S. Wang and Y. Wang, Dark energy. Commun. Theor. Phys. 56
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J. J. Geng, J. F. Zhang and X. Zhang, Parameter estimation with Sandage-Loeb test. JCAP 1412
2014
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F. Melia, The high-z quasar Hubble diagram. JCAP 1401
2014
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