Inflationary solution of the flatness problem
= Inflationary solution of the flatness problem
The continuity equation gives
$$
\frac d{dt}(\rho a^2)=-Ha^2(\rho+3P).
$$
During expansion with $\rho+3P<0$, the product $\rho a^2$ grows and $|\Omega^{-1}-1|\propto(\rho a^2)^{-1}$ decreases.