Einstein-de Sitter round-trip message time ($t_n=t_0[1+n(1-(1+z{)}^{-1/2}){]}^3$)

For two comoving observers in an Einstein-de Sitter universe, light observed at redshift $z$ today fixes their separation through the past null geodesic. A newly sent signal needs the same comoving distance for every one-way leg. Since $a=(t/t_0{)}^{2/3}$, each leg adds a fixed conformal time interval, producing the displayed reception time after $n$ legs when replies are immediate. At $z=1$ the first round-trip wait is $[(3-\sqrt{2}{)}^3-1]t_0$. There is no finite count limit because future conformal time diverges, though infinitely many legs require infinite cosmic time.