Time taken for light to circle the universe.

[Tido611]

Homework Statement

if a(t) = a0(t/t0)^(alpha) how long does it take for a light ray to circle the universe if K = 1

Homework Equations

The LFRW metric

The Attempt at a Solution

it involves that metric and an integral at theta = pi/2 , phi [0,2pi], l [?] and ... and something about proper time.

also we know that for null geodesics Guv*dXu*dXv = 0

very interesting question but i can't seem to start it, any suggestions?

 

[Tido611]

i can't write the metric out but here it is.
http://en.wikipedia.org/wiki/FLRW_metric