Time taken for light to circle the universe.

Tido611
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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?
 
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