  Since the geodesics of the galaxies are orthogonal to a layer of spacelike hypersrfaces according to Weyl’s Postulate, one can introduce coordinates \((x^{0}, x^{1}, x^{2}, x^{3})\) such that the spacelike hypersurfaces are given by \(x^{0} =\) constant, and the spacelike coordinates \(x^{\alpha}\) \((\alpha = 1, 2, 3)\) are constant along the geodesics of each galaxy. Therefore, the spacelike coordinates \(x^{\alpha}\) are co-moving coordinates along  the geodesics of each galaxy. The  orthogonality condition permits a choice of the time coordinate  \(x^{0}\) such that the metric or line element has the  form 