How to handle electron-electron or proton-proton repulsion in Cosmology? In Scott Dodleson's book, he considers that baryons are all tightly coupled. I know this can be proved by calculating the interaction time scales and comparing with Hubble's Expansion time scale. 
However I don't understand how we can neglect repulsive interaction like e-e or p-p. Shouldn't they destablise the baryon fluid because e-e interaction will perhaps be the strongest and make electrons fly away.
Can someone explain?
 A: In the integrated Boltzmann equation for electrons, the corresponding collision term for electron-electron repulsion $e(\vec{p})+e(\vec{q})\leftrightarrow e(\vec{p}^\prime)+e(\vec{q}^\prime)$ would be, following the notation given in section 4.6 in Scott Dodelson's book, $$\langle c_{ee}\rangle_{pqp^\prime q^\prime}=\int\frac{d^3p}{(2\pi)^3}\int\frac{d^3q}{(2\pi)^3}\int\frac{d^3p^\prime}{(2\pi)^3}\int\frac{d^3q^\prime}{(2\pi)^3}\delta^{(4)}(p+q-p^\prime-q^\prime)|\mathcal M|^2\\\frac{1}{8E(p)E(q)E(p^\prime)E(q^\prime)} \left[f(p^\prime)f(q^\prime)-f(p)f(q)\right].$$ Notice that all the distribution functions ($f$) and the energy functions are exactly same as we are considering scattering within the same species. Now it is important to understand that the variables $\vec{p},\vec{q},\vec{p}^\prime$, and $\vec{p}^\prime$ are dummy variables and can be interchanged, as follows, in principle without any resulting change in the integral value, $p\leftrightarrow p^\prime,q\leftrightarrow q^\prime$. This alteration keeps the integration measure unchanged but the integrand, being antisymmetric in the exchange, gains a negative sign. Thus, the integral value is its own negative, i.e., the integral vanishes. It makes sense as a scattering process which which keeps the number of particles conserved shouldn't change the nuber density of the particles, i.e., $\frac{dn_e}{dt}$ should have no contribution from such a collision process.
Similarly, the argument also works for proton-proton scattering. And that's why one can be excused from not mentioning this detail.
Caveat: However, this is only the zeroth moment of the Boltzmann equation. There is no guarantee that the higher order moments of the equation will also vanish because in higher moments this nice antisymmetric property of the integrand may disappear. This should not be a huge problem in the approximations considered here: in this particular situation, the contribution from Compton scattering predominates over that from Coulomb's scattering. And also the velocity of Baryons is pretty small.
