Past exam of the mathematics course of the University of Cambridge / 2007 / iii / Paper 67 / 2 / iv / Solution

Normalize the Einstein-de Sitter universe by $a(t_0)=1$, giving $a(t)=(t/t_0{)}^{2/3}$. A photon emitted inward today at the current comoving particle horizon starts at ${\chi }_0=3c{t}_0$. By time $t$ it has traversed the comoving distanceAt arrival at Earth this equals ${\chi }_0$, hence $(t/t_0{)}^{1/3}=2$ andThe emitting point is at the horizon location today, not a photon already arriving today from the initial singularity. The calculation of photon arrival from an Einstein-de Sitter particle horizon follows the future inward null geodesic from that event.