The clean distance

If one considers the two points in co-ordinates comobiles: $\Delta \chi = \chi_1 - \chi_2$. The clean distance between these two points is defined by:

$$D_{propre}(t) = R(t) \Delta\chi$$ (2.4)

This distance does not correspond to any practical measurement, it would be the distance obtained if one measured the distance with a gigantic cosmic rule. In the case of a closed universe (k=1), $D_{max}^{propre } = \pi R(t)$. In this case, R(t) has really the smell of a `` ray of the universe ' '.