Time-valued FLRW interval convention ($d{s}^2=d{t}^2-(R^2/c^2)d{\Sigma }_k^2$)

A cosmological metric can measure the interval in units of time rather than length. With dimensionless comoving spatial coordinates, its scale factor $R$ then has units of length and a comoving clock has $ds=dt$. Proper spatial length is $c\sqrt{-d{s}^2}$ at constant cosmic time. This convention is equivalent to the more common length-valued interval $d{\ell }^2=c^{2}d{t}^2-R^{2}d{\Sigma }_k^2$, not a different cosmology.