 Photon arrival from an Einstein-de Sitter particle horizon

For an Einstein-de Sitter universe normalized by $a(t_0)=1$, $a=(t/t_0{)}^{2/3}$. Its current comoving particle horizon is $3c{t}_0$. A photon emitted inward at that location at $t_0$ covers $3c{t}_0[(t/t_0{)}^{1/3}-1]$ in comoving distance by time $t$. Equating these distances gives arrival at $8t_0$, a travel time of $7t_0$.