I have been thinking about this and I came to the conclusion that the fact that this coincidence arises in the Milne universe (linearly expanding universe) is natural (actually it is not a coincidence in that model). In that model t = 1/H, for every t, since [itex]\dot a = k[/itex] (the first time derivative of the scale factor is a constant; note that [itex]H = \dot a / a[/itex]). I wonder now whether there is an explanation for the the similarity between the Milne universe and the concordance model today at H_{0} = 71 Km/s Mpc.
