{\rm log} r = -0.2$ [@Davies+93], metallicity only changes by 0.2 dex within this region. This is fairly small and the single-metallicity approximation affects our results well within the 1$\sigma$ value of the error in the recovered metallicity.

An age–redshift relation and $w(z)$
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Figure 4 shows the derived single-burst equivalent ages of the galaxies as a function of redshift. The circles correspond to galaxies in the SDSS LRG sample, triangles to the Treu et al. sample, diamonds are galaxies in MS1054$-$0321, and crosses are 53W091 and 53W069. For clarity, the SDSS LRG points have not been plotted for ages $<7$ Gyr. Typical errors on the ages of LRG galaxies are 10% and are not plotted. An age–redshift relation (i.e., an “edge” or “envelope” of the galaxy distribution in the age–redshift plane) is apparent from $z=0$ to $z=1.5$.

Although an envelope can be identified, it is important to notice that there is a large spread of ages at any given redshift. In particular, the measured age for many galaxies makes them significantly younger than the age–redshift envelope. This is in part due to a real spread in the star formation histories of early-type galaxies, especially in the field, but mostly 