< 0.12$. In the next section we will investigate this phenomenon in more detail and use it to determine $H_0$.

The value of $H_0$
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By concentrating on the age–redshift relation for SDSS LRG galaxies at $z \la 0.2$, we now determine the Hubble constant $H_0$. This procedure relies upon determining the “edge” of the galaxy age distribution in different redshift intervals.

If the ages of the galaxies were known with infinite accuracy, for each galaxy$_i$ at redshift $z_i$, one could associate an age $a_i$. The probability for the age of the oldest stellar population in galaxy$_i$, $P(t|a_i)$, would be given by a step function which jumps from 0 to 1 at $a_i$. An age–redshift relation edge could then be obtained by dividing the galaxy sample into suitably-large redshift bins and multiplying the $P(t|a_i)$ for all the galaxies in each bin.

In practice, the age of each galaxy is measured with some error $\delta a_i$. We thus assume $P(t|a_i)=1$ if $t>a_i+\delta_{a_i}$ and $\ln P(a_i)=-x^2$ where $x=(a_i+\delta_{a_i}-t)/(\sqrt{2}\delta_{a_i})$ otherwise. We have divided the $z < 0.2$ portion of the LRG sample into 51 redshift bins. For each bin, we obtain $P(z,t)$ by multiplying the $P(t|a_i)$ of the galaxies in that bin. We 