Baryon Euler equation with Thomson drag (${\dot{v}}_b+\mathcal{H}{v}_b+k\psi =(\dot{\tau }/R)(v_b-v_{\gamma })$)

For the velocity convention $v_{\gamma }=-{\Theta }_1$ and $\dot{\tau }<0$, momentum-conserving Thomson scattering gives ${\dot{v}}_b+\mathcal{H}{v}_b+k\psi =(\dot{\tau }/R)(v_b-v_{\gamma })$. Here $R$ is the baryon loading parameter. Its collision force is opposite to the photon force when both are weighted by their enthalpies.