In this lecture, we considered a simple example of QFT in curved space, by considering a massive scalar field in an expanding Universe. The expansion dynamically creates particles and we were able to calculate the exact Bogoliubov coefficients between the modes appropriate to an observer in the asymptotic future, and the modes appropriate to an observer in the asymptotic past.
Then we introduced Rindler coordinates in Minkowski space. This is an important example since a lot of our intuition about the black hole derives from this setup.