Spatially flat FLRW metric

In Cartesian comoving coordinates and signature $(-,+,+,+)$, a spatially flat FLRW universe has

For coordinates $(t,x,y,z)$ and line element $d{s}^2=c^{2}d{t}^2-a^2(t)d{\mathbf{x}}^2$, these are the nonzero Christoffel symbols. The prime means differentiation with respect to $t$, and coordinate zero is $t$, not $ct$. They follow either from the metric-derivative formula or the Euler-Lagrange equations for the affine geodesic Lagrangian. Both mixed lower-index orders must be counted to obtain the factor of two in the spatial geodesic equation.