Einstein-de Sitter photon flight time ($\Delta t=\frac{2}{3H_0}[(1+z_2{)}^{-3/2}-(1+z_1{)}^{-3/2}]$)

For an earlier emission epoch $z_1>z_2$, the matter-only flat model gives $R\propto t^{2/3}$ and $t(z)=2(1+z{)}^{-3/2}/(3H_0)$. Subtraction gives the displayed elapsed cosmic time. It is not the comoving travel distance divided by $c$, because expansion changes the spatial scale during flight. An Einstein-de Sitter approximation fixed to the same $H_0$ differs from a matter-era approximation normalized to $H_0\sqrt{{\Omega }_{m0}}$.