General feedback on milestone II

It was generally better on all aspects than last time which is good. Here is just a few points to keep in mind:

• Some of you write that recombination happens as soon as k_b T = 13.6 eV, but actually it happens when k_b T ~ 0.3 eV or so. Remember that the photons have a Planck distribution so there will be photons with high energy even though the mean temperature is less than 13.6 eV. And since there is almost a billion photons per baryon (n_photon / n_baryon ~10^9) in our Universe there will be enough photons with high energy to delay it significantly.
• When it comes to the approximation sqrt(1+x) = 1 + x/2. Remember that the error is O(x^2) so if you apply this when |x| < eps then the error is ~eps^2. Some used eps = 0.1 which is way too high.
• Remember to always give some physical insight into the quantities you are introducing, if possible, like tau, g, r_s. Most of you do a good job here.
• Regarding last scattering, recombination, etc. The definitions we use for these are somewhat arbitrary. If we look at the visibility functions we notice it¡¯s not just a delta-function, but it has a width so last scattering is not really a sharp point. And X_e = 0.1 is also just an arbitrary number for recombination. Thus the exact values here are not *that* important, it¡¯s more to give you a rough idea of when these things happened. Also remember that ignoring Helium (which is 25% of the baryons) we are making a big approximation so if you don¡¯t get perfect agreement (you will still get a 1% accurate result which is pretty good) of decoupling with, say, Planck then that is ok.
• Most of you just mention Xe(0) without saying anything about why we get a finite value today (and not 0.0 as Saha predicts).