Can't quite get the algebra out...

1. The maximum proper distance a photon can travel in the interval (0, t) is given by the horizon size dt o R(t')' where we work in units in which c- 1. Show that, for a matter dominated universe, for ? 1 -2H 10+2)-3/2 for 9-1 for ? 1. (3) Show also that dH 3cHG1%, 1/20+ z)-3/2 for (1 + z> ?-1 1. The maximum proper distance a photon can travel in the interval (0, t) is given by the horizon size dt o R(t')' where we work in units in which c- 1. Show that, for a matter dominated universe, for ? 1 -2H 10+2)-3/2 for 9-1 for ? 1. (3) Show also that dH 3cHG1%, 1/20+ z)-3/2 for (1 + z> ?-1