Solution
= Solution
With $P=-2\rho/3$, the continuity equation becomes
$$
\dot\rho=-\frac{\dot a}{a}\rho,
$$
hence $\rho a$ is constant. Since $a(t_0)=1$, one has $\rho=\rho_0/a$. The Friedmann equation is therefore
$$
\left(\frac{\dot a}{a}\right)^2=\frac\gamma a+\frac\beta{a^2},
$$
where
$$
\gamma=\frac{8\pi G\rho_0}{3c^2},\qquad \beta=-kc^2>0.
$$