= Time-valued FLRW interval convention
{title2=$ds^2=dt^2-(R^2/c^2)d\Sigma_k^2$}
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 $c\sqrt{-ds^2}$ at constant <cosmic time>. This convention is equivalent to the more common length-valued interval $d\ell^2=c^2dt^2-R^2d\Sigma_k^2$, not a different cosmology.
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