Determining the equation of state of the expanding Universe: inverse problem in cosmology

@article{Nakamura1998DeterminingTE,
  title={Determining the equation of state of the expanding Universe: inverse problem in cosmology},
  author={Takashi Nakamura and Takeshi Chiba},
  journal={Monthly Notices of the Royal Astronomical Society},
  year={1998},
  volume={306},
  pages={696-700}
}
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 but depends on one free parameter $\Omega_{k0} ={k}/(a_0^2H_0^2)$, where $a_0$ and $H_0$ are the present scale factor 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… 
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