The metric describing the miverse as whole is usually written as ds2dt where a(t) 0 characterizes the change to the size of the niverse from expansion in time (i) show that we can write this as where a(r) at() derive an integral expression for r in terms of t. (ii) what is τ in terms of t when a("'? if t € 0.oc), what is the range of r? (ii) in terms of r and ž, what are the trajectories that light follows?