Conformal Riccati equation for matter and a coasting fluid
= Conformal Riccati equation for matter and a coasting fluid
{title2=$2\mathcal H'+\mathcal H^2=H_0^2(1-\Omega_m)$}
The conformal <Friedmann equation> is $\mathcal H^2=H_0^2[\Omega_m/a+1-\Omega_m]$. Differentiating and using $a'=a\mathcal H$ eliminates the matter term and yields a first-order <Riccati equation>. The expanding Big-Bang branch for $0<\Omega_m<1$ has $\mathcal H=\alpha\coth(\alpha\tau/2)$.