Even if the luminosity distance as a function of redshift is obtained accurately using, for example, Type Ia supernovae, the equation of state of the Universe cannot be determined uniquely, as it depends on one free parameter Οk0=k/(a02H02), where a0 and H0 are the present scalefactor and the Hubble parameter, respectively. This degeneracy might be resolved if, for example, the time variations of the redshift of quasars are measured as proposed recently by Loeb. Therefore, the equation of state of the Universe (or the metric of the Universe) might be determined in future without any theoretical assumption on the matter content of the Universe.
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A 1999 study studied this question.
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