 Mass-equivalent cosmological critical density

The mass-density convention for the cosmological critical density. If $u$ denotes energy per unit volume, $\rho =u/c^2$ and $u_{\mathrm{crit}}=3c^2{H}^2/(8\pi G)$. Both conventions give the same dimensionless density parameter when numerator and denominator use consistent units. This distinction avoids inserting an extra $c^2$ into a Friedmann equation written in terms of mass-equivalent density.