Solution
= Solution
The conservation equation with $P=w\rho$ gives $d\rho/\rho=-3(1+w)\,da/a$, hence
$$
\rho=\rho_0a^{-3(1+w)}.
$$
The critical density and density parameter are
$$
\boxed{\rho_{\rm crit}=\frac{3c^2H^2}{8\pi G},\qquad \Omega_i=\frac{\rho_i}{\rho_{\rm crit}}.}
$$