Out of curiosity, what package/command do you use to get the caligraphic S in the lecture notes?
I'm thinking of the one you use to define, e.g. the comoving coordinate (eq. 1.21).
I've searched for it a bit, but can't find the exact S that you use, and I want to use it myself, as I think it's more distinct than other caligraphic versions of S that I've found.