= Einstein-de Sitter luminosity-distance relation
{c}
{title2=$d_L=2(c/H_0)[1+z-\sqrt{1+z}]$}
In an <Einstein-de Sitter universe> normalized by $a_0=1$, the <Friedmann equation> gives $H(z)=H_0(1+z)^{3/2}$. Integrating the radial <null geodesic> gives $r(z)=c\int_0^z dz'/H(z')=2(c/H_0)[1-(1+z)^{-1/2}]$. The <luminosity distance> is $(1+z)r(z)$, yielding the displayed expression. Near the observer it is $(c/H_0)[z+z^2/4+O(z^3)]$; the limiting radial <comoving distance> is finite even though the <luminosity distance> diverges.
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