Solution
= Solution
The <entropy density> is
$$
s=\frac{\rho+P-\mu n}{T}.
$$
For the homogeneous cosmological plasma, adiabaticity gives the <cosmological entropy conservation> equation
$$
\nabla_\mu(su^\mu)=0,
\qquad
\dot s+3Hs=0,
$$
or equivalently $sa^3=\text{constant}$ in a comoving volume.