Spherical spatial slices of a closed FLRW universe
= Spherical spatial slices of a closed FLRW universe
A round <three-sphere> of radius $R$ embedded by $|\mathbf x|^2+u^2=R^2$ has metric $R^2\{dr^2/(1-r^2)+r^2d\Omega^2\}$ for $r=|\mathbf x|/R$. Multiplying by $b(t)^2$ gives a <scale factor> $a=Rb$ and normalized positive <spatial curvature of an FLRW universe> $K=1$. This radial chart covers a hemisphere; $r=\sin\chi$ gives the global polar description.