Solution
= Solution
Differentiate the <Friedmann equation> $H^2=8\pi G\rho/3$ and use the <continuity equation> $\dot\rho=-3H(\rho+P)$:
$$
2H\dot H=\frac{8\pi G}{3}\dot\rho
=-8\pi GH(\rho+P),
$$
so $\dot H=-4\pi G(\rho+P)$. Since $H=\dot a/a$,
$$
\frac{\ddot a}{a}=\dot H+H^2
=-4\pi G(\rho+P)+\frac{8\pi G}{3}\rho.
$$
Hence the <Raychaudhuri equation> is
$$
\boxed{\frac{\ddot a}{a}=-\frac{4\pi G}{3}(\rho+3P).}
$$