= Scale factor in a conformal-time density parameter
{title2=$\Omega_i=8\pi G a^2\bar\rho_i/(3\mathcal H^2)$}
For physical density $\bar\rho_i$ and <conformal time>, $\mathcal H=a'/a=aH$. Substitution into the definition $\Omega_i=8\pi G\bar\rho_i/(3H^2)$ gives the displayed formula. Omitting $a^2$ gives $\Omega_i/a^2$, which need not equal one even in a spatially flat matter-only universe. In particular, the conformal growth source $\tfrac32\mathcal H^2\Omega_m$ equals $4\pi G a^2\bar\rho_m$ with the physical density parameter.
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