If we let t1 be some arbitrary time, and t2 be the reference epoch t0 (for which R = 1), this becomes

= 1 + AtR (t0 ) Combining this with equation (20.29b) gives

Setting t = t0 in equation (20.12) gives us, R(to) = Ho, so z = H0 At (20.31)

If a photon takes At to reach us, it must have been emitted from a distance d = c At. Using this to eliminate At in equation (20.31) gives cz = H0 d

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