  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 the equation of state of the
Universe (or the metric of the universe) might be determined without any
theoretical assumption on the matter content of the Universe in future.
