used to determine $H(z)= - \frac{1}{1+z}
\frac{dz}{dt}$ and therefore to measure $w(z)$ and $H_0$. The Hubble parameter is given by $H^2(z) = H^2_0 [\rho_{\rm tot}(z) / \rho_{\rm tot}(0)]$, where $\rho_{\rm tot}$ is the total density of the universe. For a flat universe composed of matter and dark energy, $H(z)$ is related to the equation of state by $$H_0^{-1}{dz\over dt} = - (1+z) {H(z)\over H_0}= -(1+z)^{5/2}
\left [\Omega_m +\Omega_{\Lambda} \exp \left \{3 \int_{0}^{z}
\frac{w(z^\prime)}{(1+z^\prime)} dz^\prime  \right \} \right ]^{1/2} ,
\label{eq0}$$ where we have used the conservation equation for dark energy density, $\dot{\rho_\Lambda} = -3 H(z) [1 + w(z)] \rho_\Lambda$. Thus a measurement of $dz/dt$ is also a measurement of $w(z)$; for further details, see @JL02.

To obtain $dz/dt$, @JL02 proposed to use the old envelope of the age–redshift relation of E/S0 galaxies. We assume that E/S0 at different redshifts are drawn from the same parent population with the bulk of their stellar populations formed at relatively high redshift [e.g., @Bower+92; @Stanford+98]. Then, at relatively low redshift, they are evolving passively and may be used as “cosmic chronometers”.

In the rest of this section we will apply this method to a sample of spectra (described in §3.2) to identify the age–redshift 